diff --git a/Optimal_bounding_box/benchmarks/Optimal_bounding_box/CMakeLists.txt b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/CMakeLists.txt
new file mode 100644
index 00000000000..b66879123fe
--- /dev/null
+++ b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/CMakeLists.txt
@@ -0,0 +1,29 @@
+# Created by the script cgal_create_CMakeLists
+# This is the CMake script for compiling a set of CGAL applications.
+
+cmake_minimum_required(VERSION 3.1...3.15)
+project( Optimal_bounding_box_Benchmark )
+
+# CGAL and its components
+find_package( CGAL QUIET )
+
+if ( NOT CGAL_FOUND )
+  message(STATUS "This project requires the CGAL library, and will not be compiled.")
+  return()
+endif()
+
+# include helper file
+include( ${CGAL_USE_FILE} )
+
+find_package(Eigen3 3.1.0 REQUIRED) #(3.1.0 or greater)
+if (NOT EIGEN3_FOUND)
+  message(STATUS "This project requires the Eigen library, and will not be compiled.")
+  return()
+else()
+  include(${EIGEN3_USE_FILE})
+endif()
+
+create_single_source_cgal_program("bench_obb.cpp")
+create_single_source_cgal_program("bench_perfomance.cpp")
+create_single_source_cgal_program("bench_custom.cpp")
+create_single_source_cgal_program("bench_fitness_function.cpp")
diff --git a/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_custom.cpp b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_custom.cpp
new file mode 100644
index 00000000000..220aabab3b5
--- /dev/null
+++ b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_custom.cpp
@@ -0,0 +1,64 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/Surface_mesh.h>
+
+#include <CGAL/Eigen_linear_algebra_traits.h>
+#include <CGAL/Optimal_bounding_box/optimal_bounding_box.h>
+#include <CGAL/subdivision_method_3.h>
+#include <CGAL/Timer.h>
+
+#include <iostream>
+#include <fstream>
+#include <vector>
+
+//#define CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_BENCHMARK
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
+
+void bench(const char* fname)
+{
+  std::vector<K::Point_3> sm_points, obb_points;
+  std::ifstream in(fname);
+
+  K::Point_3 p;
+  int i = 0;
+  while(in >> p)
+  {
+    if(i % 2 == 0) // avoid normals
+      sm_points.push_back(p);
+
+    ++i;
+  }
+
+  std::cout << "input data (points + normals)= " << i << std::endl;
+  std::cout << "number of points= " << sm_points.size() << std::endl;
+
+  CGAL::Eigen_linear_algebra_traits la_traits;
+
+  // use convex hull - > true
+  // no convex hull - > false
+  CGAL::Optimal_bounding_box::compute_optimal_bounding_box(sm_points, obb_points, la_traits, false);
+
+  std::cout << "done" << '\n';
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_BENCHMARK
+  std::cout.precision(17);
+  for(int i =0; i < obb_points.size(); i++)
+    std::cout << obb_points[i] << std::endl;
+
+  CGAL::Surface_mesh<K::Point_3> mesh;
+  CGAL::make_hexahedron(obb_points[0], obb_points[1], obb_points[2], obb_points[3],
+                        obb_points[4], obb_points[5], obb_points[6], obb_points[7], mesh);
+
+  std::ofstream out("/tmp/result_obb.off");
+  out << mesh;
+  out.close();
+#endif
+}
+
+int main(int argc, char* argv[])
+{
+  bench(argv[1]);
+
+  return 0;
+}
diff --git a/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_fitness_function.cpp b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_fitness_function.cpp
new file mode 100644
index 00000000000..15414eaee48
--- /dev/null
+++ b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_fitness_function.cpp
@@ -0,0 +1,64 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/Surface_mesh.h>
+
+#include <CGAL/Eigen_linear_algebra_traits.h>
+#include <CGAL/Optimal_bounding_box/fitness_function.h>
+#include <CGAL/Optimal_bounding_box/helper.h>
+#include <CGAL/Optimal_bounding_box/population.h>
+
+#include <CGAL/subdivision_method_3.h>
+#include <CGAL/Timer.h>
+
+#include <fstream>
+#include <iostream>
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
+
+int main()
+{
+  const char* fname = "data/elephant.off";
+
+  // 1) import a lot a mesh and subdivide it to create a big mesh
+  std::ifstream input(fname);
+  
+  CGAL::Surface_mesh<K::Point_3> mesh;
+  if (!input || !(input >> mesh) || mesh.is_empty())
+  {
+    std::cerr << fname << " is not a valid off file.\n";
+    std::exit(1);
+  }
+
+  CGAL::Subdivision_method_3::CatmullClark_subdivision(mesh,
+                              CGAL::parameters::number_of_iterations(6));
+
+  int nb_points = static_cast<int>(vertices(mesh).size());
+  std::cout << "number of points= " << nb_points << std::endl;
+
+
+  // 2) fill a Matrix with them
+  typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits;
+  typedef Linear_algebra_traits::MatrixX3d MatrixX3d;
+  typedef Linear_algebra_traits::Matrix3d Matrix3d;
+
+  MatrixX3d points_mat(nb_points, 3);
+  CGAL::Optimal_bounding_box::sm_to_matrix(mesh, points_mat);
+
+  // 3) create a population of simplices
+  CGAL::Optimal_bounding_box::Population<Linear_algebra_traits> pop(50);
+
+  CGAL::Timer timer;
+  timer.start();
+
+  // 4) compute fitness of population via the Fitness map
+  CGAL::Optimal_bounding_box::Fitness_map<Linear_algebra_traits,
+                                          Matrix3d, MatrixX3d> fit_map(pop, points_mat);
+  double result = fit_map.get_best_fitness_value();
+
+  timer.stop();
+
+  std::cout << "took " << timer.time() << " to compute the fitness of all vertices.\n";
+  std::cout << "value of fittest vertex= " << result << std::endl;
+
+  return 0;
+}
diff --git a/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_obb.cpp b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_obb.cpp
new file mode 100644
index 00000000000..44e85c184bf
--- /dev/null
+++ b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_obb.cpp
@@ -0,0 +1,115 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/Surface_mesh.h>
+#include <CGAL/Polyhedron_3.h>
+
+#include <CGAL/Eigen_linear_algebra_traits.h>
+#include <CGAL/Optimal_bounding_box/population.h>
+#include <CGAL/Optimal_bounding_box/optimal_bounding_box.h>
+
+#include <CGAL/convex_hull_3.h>
+#include <CGAL/Timer.h>
+
+#include <iostream>
+#include <fstream>
+
+//#define CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_BENCHMARK
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
+
+bool assert_doubles(double d1, double d2, double epsilon)
+{
+  return (d1 < d2 + epsilon && d1 > d2 - epsilon) ? true : false;
+}
+
+template <typename SurfaceMesh, typename Point>
+void gather_mesh_points(SurfaceMesh& mesh, std::vector<Point>& points)
+{
+  typedef typename boost::graph_traits<SurfaceMesh>::vertex_descriptor vertex_descriptor;
+  typedef typename boost::property_map<SurfaceMesh, CGAL::vertex_point_t>::type PointPMap;
+  PointPMap pmap = get(boost::vertex_point, mesh);
+  BOOST_FOREACH(vertex_descriptor v, vertices(mesh))
+    points.push_back(get(pmap, v));
+}
+
+template <typename Point>
+double calculate_volume(std::vector<Point> points)
+{
+  CGAL::Bbox_3 bbox;
+  bbox = bbox_3(points.begin(), points.end());
+  K::Iso_cuboid_3 ic(bbox);
+  return ic.volume();
+}
+
+void bench_finding_obb(std::string fname)
+{
+  std::ifstream input(fname);
+
+  CGAL::Eigen_linear_algebra_traits la_traits;
+  std::vector<K::Point_3> sm_points;
+
+  // import a mesh
+  CGAL::Surface_mesh<K::Point_3> mesh;
+  if (!input || !(input >> mesh) || mesh.is_empty())
+  {
+    std::cerr << fname << " is not a valid off file.\n";
+    std::exit(1);
+  }
+
+  // get mesh points
+  gather_mesh_points(mesh, sm_points);
+
+  CGAL::Timer timer;
+
+  // 1) measure convex hull calculation
+  timer.start();
+  CGAL::Polyhedron_3<K> poly;
+  convex_hull_3(sm_points.begin(), sm_points.end(), poly);
+  std::vector<K::Point_3> ch_points(poly.points_begin(), poly.points_end());
+  timer.stop();
+  std::cout << "takes : " << timer.time() << " seconds to find the convex hull\n";
+
+  // 2) using convex hull
+  timer.reset();
+  timer.start();
+  std::vector<K::Point_3> obb_points1;
+  CGAL::Optimal_bounding_box::compute_optimal_bounding_box(sm_points, obb_points1, la_traits, true);
+  timer.stop();
+  std::cout << "found obb using convex hull: " << timer.time() << " seconds\n";
+
+  // 3) without convex hull
+  timer.reset();
+  timer.start();
+  std::vector<K::Point_3> obb_points2;
+  CGAL::Optimal_bounding_box::compute_optimal_bounding_box(sm_points, obb_points2, la_traits, false);
+  timer.stop();
+  std::cout << "found obb without convex hull: " <<  timer.time() << " seconds\n";
+  timer.reset();
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_BENCHMARK
+  CGAL::Surface_mesh<K::Point_3> result_mesh1;
+  CGAL::make_hexahedron(obb_points1[0], obb_points1[1], obb_points1[2], obb_points1[3],
+                        obb_points1[4], obb_points1[5], obb_points1[6], obb_points1[7],
+                        result_mesh1);
+
+  CGAL::Surface_mesh<K::Point_3> result_mesh2;
+  CGAL::make_hexahedron(obb_points2[0], obb_points2[1], obb_points2[2], obb_points2[3],
+                        obb_points2[4], obb_points2[5], obb_points2[6], obb_points2[7],
+                        result_mesh2);
+
+  std::ofstream out1("data/obb_result1.off");
+  out1 << result_mesh1;
+  out1.close();
+
+  std::ofstream out2("data/obb_result2.off");
+  out2 << result_mesh2;
+  out2.close();
+#endif
+}
+
+int main()
+{
+  bench_finding_obb("data/elephant.off");
+
+  return 0;
+}
diff --git a/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_perfomance.cpp b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_perfomance.cpp
new file mode 100644
index 00000000000..2cab424a549
--- /dev/null
+++ b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/bench_perfomance.cpp
@@ -0,0 +1,85 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/Surface_mesh.h>
+
+#include <CGAL/Eigen_linear_algebra_traits.h>
+#include <CGAL/Optimal_bounding_box/optimal_bounding_box.h>
+
+#include <CGAL/subdivision_method_3.h>
+#include <CGAL/Timer.h>
+
+#include <fstream>
+#include <iostream>
+
+//#define CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_BENCHMARK
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
+
+void bench_finding_obb(std::string fname)
+{
+  std::ifstream input(fname);
+
+  // import a mesh
+  CGAL::Surface_mesh<K::Point_3> mesh;
+  if (!input || !(input >> mesh) || mesh.is_empty())
+  {
+    std::cerr << fname << " is not a valid off file.\n";
+    std::exit(1);
+  }
+
+  // export some times
+  std::ofstream outt("data/times.txt");
+  outt << "nb_vertices "<<  "with_ch " << "without_ch" << std::endl;
+
+  CGAL::Timer timer;
+  std::size_t measurements = 4;
+  CGAL::Eigen_linear_algebra_traits la_traits;
+
+  for (std::size_t t = 0; t < measurements; ++t)
+  {
+    std::cout << "#vertices= " << vertices(mesh).size() << " |";
+
+    // 1) using convex hull
+    timer.start();
+    CGAL::Surface_mesh<K::Point_3> obb_mesh1;
+    CGAL::Optimal_bounding_box::compute_optimal_bounding_box(mesh, obb_mesh1, la_traits, true);
+    timer.stop();
+    double t_ch = timer.time();
+    std::cout << " with ch: " << timer.time() << " s |";
+
+    // 2) without convex hull
+    timer.reset();
+    timer.start();
+    CGAL::Surface_mesh<K::Point_3> obb_mesh2;
+    CGAL::Optimal_bounding_box::compute_optimal_bounding_box(mesh, obb_mesh2, la_traits, false);
+    timer.stop();
+    double t_no_ch = timer.time();
+    std::cout << " without ch: " <<  timer.time() << " s\n";
+    timer.reset();
+
+    outt << vertices(mesh).size() << " " << t_ch << " " << t_no_ch << std::endl;
+
+    // 3) subdivision
+    CGAL::Subdivision_method_3::CatmullClark_subdivision(mesh,
+                                      CGAL::parameters::number_of_iterations(1));
+  }
+
+  outt.close();
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_BENCHMARK
+  std::ofstream out1("data/obb_result1.off");
+  out1 << obb_points1;
+  out1.close();
+
+  std::ofstream out2("data/obb_result2.off");
+  out2 << obb_points2;
+  out2.close();
+#endif
+}
+
+int main()
+{
+  bench_finding_obb("data/elephant.off");
+
+  return 0;
+}
diff --git a/Optimal_bounding_box/benchmarks/Optimal_bounding_box/data/elephant.off b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/data/elephant.off
new file mode 100644
index 00000000000..cf7cc2b68ca
--- /dev/null
+++ b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/data/elephant.off
@@ -0,0 +1,8337 @@
+OFF
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diff --git a/Optimal_bounding_box/benchmarks/Optimal_bounding_box/data/times.txt b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/data/times.txt
new file mode 100644
index 00000000000..2ef3396b31b
--- /dev/null
+++ b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/data/times.txt
@@ -0,0 +1,5 @@
+nb_vertices with_ch without_ch
+2775 0.037331 0.327787
+16670 0.118251 1.96901
+66692 0.362664 7.75459
+266780 1.20984 32.166
diff --git a/Optimal_bounding_box/benchmarks/Optimal_bounding_box/draw_benchmark_graph.py b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/draw_benchmark_graph.py
new file mode 100644
index 00000000000..8fc416ac260
--- /dev/null
+++ b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/draw_benchmark_graph.py
@@ -0,0 +1,19 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+#path-to-benchmarks
+benchmarkfile='data/times.txt'
+
+data = np.loadtxt(benchmarkfile, skiprows = 1)
+
+x = data[:, 0]
+y1 = data[:, 1]
+y2 = data[:, 2]
+
+plt.plot(x, y1, 'go--', label='with convex hull')
+plt.plot(x, y2, 'ro--', label='without convex hull')
+legend = plt.legend(loc='best')
+plt.xlabel('#vertices')
+plt.ylabel('seconds')
+
+plt.show()
diff --git a/Optimal_bounding_box/benchmarks/Optimal_bounding_box/readme.txt b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/readme.txt
new file mode 100644
index 00000000000..ac22f73a877
--- /dev/null
+++ b/Optimal_bounding_box/benchmarks/Optimal_bounding_box/readme.txt
@@ -0,0 +1 @@
+To draw a graph with the benchmark times set the path-to-the-measurments in draw_benchmark_times.py if necessary, and run the script with python 3.
diff --git a/Optimal_bounding_box/doc/Optimal_bounding_box/Doxyfile.in b/Optimal_bounding_box/doc/Optimal_bounding_box/Doxyfile.in
new file mode 100644
index 00000000000..c01165a4dee
--- /dev/null
+++ b/Optimal_bounding_box/doc/Optimal_bounding_box/Doxyfile.in
@@ -0,0 +1,6 @@
+@INCLUDE = ${CGAL_DOC_PACKAGE_DEFAULTS}
+
+PROJECT_NAME = "CGAL ${CGAL_DOC_VERSION} - Optimal Bounding Box"
+EXTRACT_ALL                =  false
+HIDE_UNDOC_CLASSES         =  true
+WARN_IF_UNDOCUMENTED       =  false
diff --git a/Optimal_bounding_box/doc/Optimal_bounding_box/NamedParameters.txt b/Optimal_bounding_box/doc/Optimal_bounding_box/NamedParameters.txt
new file mode 100644
index 00000000000..d9b8e95c9ac
--- /dev/null
+++ b/Optimal_bounding_box/doc/Optimal_bounding_box/NamedParameters.txt
@@ -0,0 +1,315 @@
+/*!
+\defgroup pmp_namedparameters Named Parameters for Polygon Mesh Processing
+\ingroup PkgPolygonMeshProcessing
+
+In this package, all functions optional parameters are implemented as BGL optional
+named parameters (see \ref BGLNamedParameters for more information on how to use them).
+Since the parameters of the various polygon mesh processing functions defined
+in this package are redundant, their long descriptions are centralized below.
+The sequence of named parameters should start with `CGAL::parameters::`.
+`CGAL::parameters::all_default()` can be used to indicate
+that default values of optional named parameters must be used.
+
+In the following, we assume that the following types are provided as template parameters
+of polygon mesh processing functions and classes. Note that, for some of these functions,
+the type is more specific:
+<ul>
+<li>`PolygonMesh` is a model of the concept `FaceGraph`</li>.
+<li>`GeomTraits` a geometric traits class in which constructions are performed and
+     predicates evaluated. Everywhere in this package, a \cgal `Kernel` fulfills the requirements.</li>
+</ul>
+
+The following named parameters, offered by the package \ref PkgBGLSummary
+(see \ref bgl_namedparameters), are used in this package:
+
+\cgalNPTableBegin
+\cgalNPBegin{vertex_point_map} \anchor PMP_vertex_point_map
+is the property map with the points associated to the vertices of the polygon mesh `pmesh`.\n
+<b>Type:</b> a class model of `ReadablePropertyMap` with
+`boost::graph_traits<PolygonMesh>::%vertex_descriptor` as key type and
+`GeomTraits::Point_3` as value type. \n
+<b>Default:</b> \code boost::get(CGAL::vertex_point, pmesh) \endcode
+\cgalNPEnd
+
+\cgalNPBegin{vertex_index_map} \anchor PMP_vertex_index_map
+is the property map containing the index of each vertex of the input polygon mesh.\n
+<b>Type:</b> a class model of `ReadablePropertyMap` with
+`boost::graph_traits<PolygonMesh>::%vertex_descriptor` as key type and the value type
+\code typename boost::property_traits<typename boost::property_map<PolygonMesh, CGAL::vertex_index_t>::type>::value_type \endcode
+<b>Default:</b> \code boost::get(CGAL::vertex_index, pmesh)\endcode
+\cgalNPEnd
+
+\cgalNPBegin{face_index_map} \anchor PMP_face_index_map
+is the property map containing the index of each face of the input polygon mesh.\n
+<b>Type:</b> a class model of `ReadablePropertyMap` with
+`boost::graph_traits<PolygonMesh>::%face_descriptor` as key type and the value type:
+\code typename boost::property_traits<typename boost::property_map<PolygonMesh, CGAL::face_index_t>::type>::value_type \endcode
+<b>Default:</b> \code boost::get(CGAL::face_index, pmesh)\endcode
+If this internal property map exists, its values should be initialized.
+\cgalNPEnd
+
+\cgalNPBegin{edge_is_constrained_map} \anchor PMP_edge_is_constrained_map
+is the property map containing information about edges of the input polygon mesh
+being marked or not. In `isotropic_remeshing()` and `connected_components()`,
+the marked edges are constrained.\n
+<b>Type:</b> a class model of `ReadWritePropertyMap` with
+`boost::graph_traits<PolygonMesh>::%edge_descriptor` as key type and
+`bool` as value type. It should be default constructible.\n
+<b>Default:</b> a default property map where no edge is constrained
+\cgalNPEnd
+\cgalNPTableEnd
+
+In addition to these named parameters, this package offers the following named parameters:
+
+\cgalNPTableBegin
+\cgalNPBegin{geom_traits} \anchor PMP_geom_traits
+is the geometric traits instance in which the mesh processing operation should be performed.\n
+<b>Type:</b> a Geometric traits class.\n
+<b>Default</b>:
+\code typename CGAL::Kernel_traits<
+        typename boost::property_traits<
+          typename boost::property_map<PolygonMesh, CGAL::vertex_point_t>::type>::value_type>::Kernel \endcode
+\cgalNPEnd
+
+\cgalNPBegin{vertex_incident_patches_map} \anchor PMP_vertex_incident_patches_map
+is the property map containing the surface patches incident to each vertex of the input polygon mesh.\n
+<b>Type:</b> a class model of `LvaluePropertyMap` with
+`boost::graph_traits<PolygonMesh>::%vertex_descriptor` as key type. Its value type
+must be a container of `boost::property_traits<PatchIdMap>::%value_type` and have a function `insert()`.
+A `std::set` or a `boost::unordered_set` are recommended, as a patch index may be
+inserted several times.\n
+<b>Default:</b> \code boost::get(CGAL::vertex_incident_patches_t, pmesh)\endcode
+\cgalNPEnd
+
+\cgalNPBegin{vertex_feature_degree_map} \anchor PMP_vertex_feature_degree_map
+is the property map containing the number of feature edges being incident to the vertices of the polygon mesh `pmesh`.\n
+<b>Type:</b> a class model of `ReadWritePropertyMap` with
+`boost::graph_traits<PolygonMesh>::%vertex_descriptor` as key type and
+`int` as value type. It should be default constructible.\n
+<b>Default:</b> \code boost::get(CGAL::vertex_feature_degree_t(), pmesh) \endcode
+\cgalNPEnd
+
+\cgalNPBegin{vertex_is_constrained_map} \anchor PMP_vertex_is_constrained_map
+is the property map containing information about vertices of the input polygon mesh being constrained or not.
+Constrained vertices may be replaced by new vertices, but the number and location
+of vertices remain unchanged.\n
+<b>Type:</b> a class model of `ReadWritePropertyMap` with
+`boost::graph_traits<PolygonMesh>::%vertex_descriptor` as key type and
+`bool` as value type. It should be default constructible.\n
+<b>Default:</b> a default property map where no vertex is constrained is provided.
+\cgalNPEnd
+
+\cgalNPBegin{face_patch_map} \anchor PMP_face_patch_map
+is a property map containing information about faces.
+It is particularly well-suited for preserving surface patch IDs,
+or face colors.
+The edges at the interface between surface patches are treated similarly
+to the ones of `edge_is_constrained_map`.\n
+<b>Type:</b> a class model of `ReadWritePropertyMap` with
+`boost::graph_traits<PolygonMesh>::%face_descriptor` as key type and
+the desired property, model of `CopyConstructible` as value type.\n
+<b>Default:</b> a default property map where each face is associated with the ID of
+the connected component it belongs to. Connected components are
+computed with respect to the constrained edges listed in the property map
+`edge_is_constrained_map`
+\cgalNPEnd
+
+\cgalNPBegin{first_index} \anchor PMP_first_index
+is the index of the first surface patch.\n
+<b>Type:</b> `std::size_t`\n
+<b>Default:</b> 1
+\cgalNPEnd
+
+\cgalNPBegin{density_control_factor} \anchor PMP_density_control_factor
+controls the density of the mesh generated by refinement, with larger values causing denser refinements.
+The density of vertices in the refined region is this factor times higher than before refinement.\n
+<b>Type:</b> floating scalar value\n
+<b>Default:</b> `CGAL::sqrt(2)`
+\cgalNPEnd
+
+\cgalNPBegin{fairing_continuity} \anchor PMP_fairing_continuity
+controls the tangential continuity of the output surface in `fair()`.
+The possible values are 0, 1 and 2, refering to the  C<sup>0</sup>, C<sup>1</sup>
+and C<sup>2</sup> continuity.\n
+<b>Type:</b> \c unsigned \c int between 0 and 2\n
+<b>Default:</b> `1`
+\cgalNPEnd
+
+\cgalNPBegin{sparse_linear_solver} \anchor PMP_sparse_linear_solver
+is the solver used in `fair()`.\n
+<b>Type:</b> a class model of `SparseLinearAlgebraWithFactorTraits_d`.\n
+<b>Default:</b> if \ref thirdpartyEigen "Eigen" 3.2 (or greater) is available and
+`CGAL_EIGEN3_ENABLED` is defined, then the following overload of `Eigen_solver_traits`
+is provided as default value:\n
+\code CGAL::Eigen_solver_traits<Eigen::SparseLU<CGAL::Eigen_sparse_matrix<double>::EigenType, Eigen::COLAMDOrdering<int> > > \endcode
+\cgalNPEnd
+
+\cgalNPBegin{number_of_iterations} \anchor PMP_number_of_iterations
+is the number of iterations of the sequence of iterations performed in `isotropic_remeshing()`.\n
+<b>Type:</b> \c unsigned \c int \n
+<b>Default:</b> `1`
+\cgalNPEnd
+
+\cgalNPBegin{protect_constraints} \anchor PMP_protect_constraints
+enables the protection of constraints listed by \ref PMP_edge_is_constrained_map
+"edge_is_constrained_map" and boundary edges
+in `isotropic_remeshing()`. If `true`, constraint edges cannot be modified at all
+during the remeshing process.\n
+<b>Type:</b> `bool` \n
+<b>Default:</b> `false`
+\cgalNPEnd
+
+\cgalNPBegin{relax_constraints} \anchor PMP_relax_constraints
+enables the tangential relaxation step in `isotropic_remeshing()`
+to be performed on vertices that are endpoints of constraints listed
+by \ref PMP_edge_is_constrained_map "edge_is_constrained_map", and boundary edges.
+The vertices move along the constrained polylines they belong to.
+Corners (i.e. vertices incident to more than 2 constraints, and vertices listed in
+\ref PMP_vertex_is_constrained_map "vertex_is_constrained_map") are not allowed
+to move at all.
+If \ref PMP_protect_constraints "protect_constraints" is
+set to `true`, this parameter is ignored.\n
+<b>Type:</b> `bool` \n
+<b>Default:</b> `true`
+\cgalNPEnd
+
+\cgalNPBegin{number_of_relaxation_steps} \anchor PMP_number_of_relaxation_steps
+is the number of iterations of tangential relaxation that are performed at each iteration
+of `isotropic_remeshing()`. A larger number of relaxation steps lead to
+a more isotropic mesh.\n
+<b>Type:</b> \c unsigned \c int \n
+<b>Default:</b> `1`
+\cgalNPEnd
+
+\cgalNPBegin{use_delaunay_triangulation} \anchor PMP_use_delaunay_triangulation
+enables the use of the Delaunay triangulation facet search space for hole filling functions.\n
+<b>Type:</b> `bool` \n
+<b>Default:</b> `true`
+\cgalNPEnd
+
+\cgalNPBegin{use_random_uniform_sampling} \anchor PMP_use_random_uniform_sampling
+is a parameter used in `sample_triangle_mesh()` to indicate if points should be picked
+in a random uniform way.\n
+<b>Type:</b> `bool` \n
+<b>Default:</b> `true`
+\cgalNPEnd
+
+\cgalNPBegin{use_grid_sampling} \anchor PMP_use_grid_sampling
+is a parameter used in `sample_triangle_mesh()` to indicate if points should be picked
+in on a grid in each face.\n
+<b>Type:</b> `bool` \n
+<b>Default:</b> `false`
+\cgalNPEnd
+
+\cgalNPBegin{use_monte_carlo_sampling} \anchor PMP_use_monte_carlo_sampling
+is a parameter used in `sample_triangle_mesh()` to indicate if points should be picked
+using a Monte-Carlo approach.\n
+<b>Type:</b> `bool` \n
+<b>Default:</b> `false`
+\cgalNPEnd
+
+\cgalNPBegin{sample_edges} \anchor PMP_sample_edges
+is a parameter used in `sample_triangle_mesh()` to indicate if a dedicated sampling
+of edges should be done.\n
+<b>Type:</b> `bool` \n
+<b>Default:</b> `true`
+\cgalNPEnd
+
+\cgalNPBegin{sample_vertices} \anchor PMP_sample_vertices
+is a parameter used in `sample_triangle_mesh()` to indicate if triangle vertices should
+be copied in the output iterator.\n
+<b>Type:</b> `bool` \n
+<b>Default:</b> `true`
+\cgalNPEnd
+
+\cgalNPBegin{sample_faces} \anchor PMP_sample_faces
+is a parameter used in `sample_triangle_mesh()` to indicate if the interior of faces
+should be considered for the sampling.\n
+<b>Type:</b> `bool` \n
+<b>Default:</b> `true`
+\cgalNPEnd
+
+\cgalNPBegin{number_of_points_on_faces} \anchor PMP_number_of_points_on_faces
+is a parameter used in `sample_triangle_mesh()` to set the number of points picked
+using the random uniform method on faces.\n
+<b>Type:</b> `std::size_t` \n
+<b>Default:</b> `0`
+\cgalNPEnd
+
+\cgalNPBegin{number_of_points_on_edges} \anchor PMP_number_of_points_on_edges
+is a parameter used in `sample_triangle_mesh()` to set the number of points picked
+using the random uniform method on edges.\n
+<b>Type:</b> `std::size_t` \n
+<b>Default:</b> `0`
+\cgalNPEnd
+
+\cgalNPBegin{number_of_points_per_face} \anchor PMP_number_of_points_per_face
+is a parameter used in `sample_triangle_mesh()` to set the number of points picked
+per face using the Monte-Carlo method.\n
+<b>Type:</b> `std::size_t` \n
+<b>Default:</b> `0`
+\cgalNPEnd
+
+\cgalNPBegin{number_of_points_per_edge} \anchor PMP_number_of_points_per_edge
+is a parameter used in `sample_triangle_mesh()` to set the number of points picked
+per edge using the Monte-Carlo method.\n
+<b>Type:</b> `std::size_t` \n
+<b>Default:</b> `0`
+\cgalNPEnd
+
+\cgalNPBegin{grid_spacing} \anchor PMP_grid_spacing
+is a parameter used in `sample_triangle_mesh()` to set the grid spacing when using
+the grid sampling method.\n
+<b>Type:</b> `double` \n
+<b>Default:</b> `0`
+\cgalNPEnd
+
+\cgalNPBegin{number_of_points_per_area_unit} \anchor PMP_number_of_points_per_area_unit
+is a parameter used in `sample_triangle_mesh()` to set the number of points per
+area unit to be picked up in faces for the random uniform sampling and
+Monte-Carlo methods.\n
+<b>Type:</b> `double` \n
+<b>Default:</b> `0`
+\cgalNPEnd
+
+\cgalNPBegin{number_of_points_per_distance_unit} \anchor PMP_number_of_points_per_distance_unit
+is a parameter used in `sample_triangle_mesh()` to set the number of points per
+distance unit to be picked up on edges for the random uniform sampling and
+Monte-Carlo methods.\n
+<b>Type:</b> `double` \n
+<b>Default:</b> `0`
+\cgalNPEnd
+
+\cgalNPBegin{do_project} \anchor PMP_do_project
+is a parameter used in `random_perturbation()` to set whether vertices should be re-projected
+to the input surface after their geometric perturbation.\n
+<b>Type:</b> `bool` \n
+<b>Default:</b> `true`
+\cgalNPEnd
+
+\cgalNPBegin{random_seed} \anchor PMP_random_seed
+is a parameter used in `random_perturbation()` to choose a seed to initialize
+the random number generator `CGAL::Random()`.
+If this parameter is not provided, the perturbation is not deterministic
+(i.e. not reproducible from one run to the other).\n
+<b>Type:</b> `unsigned int` \n
+<b>Default:</b> the random number generator is initialized with `CGAL::Random()`
+\cgalNPEnd
+
+\cgalNPBegin{outward_orientation} \anchor PMP_outward_orientation
+Parameter used in orientation functions to choose between an outward or inward orientation.
+\n
+\b Type : `bool` \n
+\b Default value is `true`
+
+\cgalNPBegin{do_overlap_test_of_bounded_sides} \anchor PMP_do_overlap_test_of_bounded_sides
+Parameter used in intersection test functions to indicate whether overlapping tests of bounded sides
+of close meshes should be done in addition to surface intersection tests.
+\n
+\b Type : `bool` \n
+\b Default value is `false`
+\cgalNPEnd
+
+\cgalNPTableEnd
+
+*/
diff --git a/Optimal_bounding_box/doc/Optimal_bounding_box/Optimal_bounding_box.txt b/Optimal_bounding_box/doc/Optimal_bounding_box/Optimal_bounding_box.txt
new file mode 100644
index 00000000000..d84814bee40
--- /dev/null
+++ b/Optimal_bounding_box/doc/Optimal_bounding_box/Optimal_bounding_box.txt
@@ -0,0 +1,9 @@
+namespace CGAL {
+/*!
+\mainpage User Manual
+\anchor Chapter_OptimalBoundingBox
+
+\cgalAutoToc
+\authors
+
+} /* namespace CGAL */
diff --git a/Optimal_bounding_box/doc/Optimal_bounding_box/PackageDescription.txt b/Optimal_bounding_box/doc/Optimal_bounding_box/PackageDescription.txt
new file mode 100644
index 00000000000..496066da185
--- /dev/null
+++ b/Optimal_bounding_box/doc/Optimal_bounding_box/PackageDescription.txt
@@ -0,0 +1,30 @@
+/// \defgroup PkgOptimalBoundingBox Optimal Bounding Box Reference
+/// \defgroup PkgOptimalBoundingBoxConcepts Concepts
+/// \ingroup PkgOptimalBoundingBox
+
+\cgalPkgDescriptionBegin{Optimal Bounding Box, PkgOptimalBoundingBoxSummary}
+\cgalPkgPicture{}
+
+\cgalPkgSummaryBegin
+\cgalPkgAuthor{}
+\cgalPkgDesc{This package provides stuff.}
+\cgalPkgManuals{Chapter_OptimalBoundingBox,PkgOptimalBoundingBox}
+\cgalPkgSummaryEnd
+
+\cgalPkgShortInfoBegin
+\cgalPkgSince{5.2}
+\cgalPkgDependsOn{documented for each function;}
+\cgalPkgBib{cgal:lty-pmp}
+\cgalPkgLicense{\ref licensesGPL "GPL"}
+\cgalPkgDemo{Polyhedron demo,polyhedron_3.zip}
+\cgalPkgShortInfoEnd
+
+\cgalPkgDescriptionEnd
+
+\cgalClassifedRefPages
+
+## Parameters ##
+
+## Functions ##
+
+*/
diff --git a/Optimal_bounding_box/doc/Optimal_bounding_box/dependencies b/Optimal_bounding_box/doc/Optimal_bounding_box/dependencies
new file mode 100644
index 00000000000..52428e7009d
--- /dev/null
+++ b/Optimal_bounding_box/doc/Optimal_bounding_box/dependencies
@@ -0,0 +1,14 @@
+Manual
+Kernel_23
+STL_Extension
+Algebraic_foundations
+Circulator
+Stream_support
+Polyhedron
+BGL
+Solver_interface
+Surface_mesh
+Surface_mesh_deformation
+AABB_tree
+Triangulation_2
+Spatial_sorting
diff --git a/Optimal_bounding_box/doc/Optimal_bounding_box/examples.txt b/Optimal_bounding_box/doc/Optimal_bounding_box/examples.txt
new file mode 100644
index 00000000000..76aff917caf
--- /dev/null
+++ b/Optimal_bounding_box/doc/Optimal_bounding_box/examples.txt
@@ -0,0 +1,4 @@
+/*!
+
+\example Optimal_bounding_box/example_todo.cpp
+*/
diff --git a/Optimal_bounding_box/examples/Polygon_mesh_processing/CMakeLists.txt b/Optimal_bounding_box/examples/Polygon_mesh_processing/CMakeLists.txt
new file mode 100644
index 00000000000..0faa74ffe4e
--- /dev/null
+++ b/Optimal_bounding_box/examples/Polygon_mesh_processing/CMakeLists.txt
@@ -0,0 +1,24 @@
+# Created by the script cgal_create_cmake_script
+# This is the CMake script for compiling a CGAL application.
+
+cmake_minimum_required(VERSION 3.1...3.15)
+project( Optimal_bounding_box_Examples )
+
+find_package(CGAL QUIET)
+
+if (NOT CGAL_FOUND)
+  message(STATUS "This project requires the CGAL library, and will not be compiled.")
+  return()
+endif()
+
+include( ${CGAL_USE_FILE} )
+
+find_package(Eigen3 3.1.0 REQUIRED) #(3.1.0 or greater)
+if (NOT EIGEN3_FOUND)
+  message(STATUS "This project requires the Eigen library, and will not be compiled.")
+  return()
+else()
+  include(${EIGEN3_USE_FILE})
+endif()
+
+create_single_source_cgal_program("example.cpp")
diff --git a/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/evolution.h b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/evolution.h
new file mode 100644
index 00000000000..2089beb9a8c
--- /dev/null
+++ b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/evolution.h
@@ -0,0 +1,252 @@
+// Copyright (c) 2018 GeometryFactory (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+// You can redistribute it and/or modify it under the terms of the GNU
+// General Public License as published by the Free Software Foundation,
+// either version 3 of the License, or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0+
+//
+// Author(s)     : Konstantinos Katrioplas
+
+#ifndef CGAL_OPTIMAL_BOUNDING_BOX_EVOLUTION_H
+#define CGAL_OPTIMAL_BOUNDING_BOX_EVOLUTION_H
+
+#include <CGAL/Optimal_bounding_box/population.h>
+#include <CGAL/Optimal_bounding_box/nelder_mead_functions.h>
+#include <CGAL/Optimal_bounding_box/fitness_function.h>
+
+#include <CGAL/Random.h>
+#include <CGAL/number_utils.h>
+
+#include <algorithm>
+#include <iostream>
+#include <vector>
+
+namespace CGAL {
+
+namespace Optimal_bounding_box {
+
+template <typename Linear_algebra_traits>
+class Evolution
+{
+  typedef typename Linear_algebra_traits::MatrixXd MatrixXd;
+  typedef typename Linear_algebra_traits::Matrix3d Matrix3d;
+  typedef typename Linear_algebra_traits::Vector3d Vector3d;
+
+public:
+  Evolution(Population<Linear_algebra_traits>& pop, MatrixXd& points)
+    : population(pop), point_data(points)
+  {}
+
+  void genetic_algorithm()
+  {
+    // random permutations
+    std::size_t m = population.size();
+
+    //groups 1,2 : size m/2  groups 3,4 : size (m - m/2).   m/2 is floored
+    std::size_t size_first_group = m/2;
+    std::size_t size_second_group = m - m/2;
+
+    std::vector<std::size_t> ids1(m/2), ids2(m/2);
+    std::vector<std::size_t> ids3(m - m/2), ids4(m - m/2);
+
+    CGAL::Random rng;
+    int im = static_cast<int>(m);
+    std::generate(ids1.begin(), ids1.end(),
+                  [&rng, &im] () { return rng.get_int(0, im); });
+    std::generate(ids2.begin(), ids2.end(),
+                  [&rng, &im] () { return rng.get_int(0, im); });
+    std::generate(ids3.begin(), ids3.end(),
+                  [&rng, &im] () { return rng.get_int(0, im); });
+    std::generate(ids4.begin(), ids4.end(),
+                  [&rng, &im] () { return rng.get_int(0, im); });
+
+    Population<Linear_algebra_traits> group1(m/2), group2(m/2);
+    Population<Linear_algebra_traits> group3(m - m/2), group4(m - m/2);
+
+    for(std::size_t i = 0; i < ids1.size(); ++i)
+      group1[i] = population[ids1[i]];
+
+    for(std::size_t i = 0; i < ids2.size(); ++i)
+      group2[i] = population[ids2[i]];
+
+    for(std::size_t i = 0; i < ids3.size(); ++i)
+      group3[i] = population[ids3[i]];
+
+    for(std::size_t i = 0; i < ids4.size(); ++i)
+      group4[i] = population[ids4[i]];
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG
+    check_det(group1);
+    check_det(group2);
+    check_det(group3);
+    check_det(group4);
+#endif
+
+    // crossover I
+    Population<Linear_algebra_traits> offspringsA(size_first_group);
+    double bias = 0.1;
+
+    for(std::size_t i = 0; i < size_first_group; ++i)
+    {
+      std::vector<Matrix3d> offspring(4);
+      for(int j = 0; j < 4; ++j)
+      {
+        double r = rng.get_double();
+        double fitnessA = compute_fitness<Linear_algebra_traits>(group1[i][j], point_data);
+        double fitnessB = compute_fitness<Linear_algebra_traits>(group2[i][j], point_data);
+        double threshold;
+
+        if(fitnessA < fitnessB)
+          threshold = 0.5 + bias;
+        else
+          threshold = 0.5 - bias;
+
+        if(r < threshold) // choose A
+          offspring[j] = group1[i][j];
+        else // choose B
+          offspring[j] = group2[i][j];
+      }
+      offspringsA[i] = offspring;
+    }
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG
+    std::cout << "offspringsA: \n" ;
+    check_det(offspringsA);
+#endif
+
+    // crossover II
+    Population<Linear_algebra_traits> offspringsB(size_second_group);
+    bias = 0.1;
+
+    for(std::size_t i = 0; i < size_second_group; ++i)
+    {
+      std::vector<Matrix3d> offspring(4);
+      for(int j = 0; j < 4; ++j)
+      {
+        double fitnessA = compute_fitness<Linear_algebra_traits>(group3[i][j], point_data);
+        double fitnessB = compute_fitness<Linear_algebra_traits>(group4[i][j], point_data);
+        double lambda;
+        if(fitnessA < fitnessB)
+          lambda = 0.5 + bias;
+        else
+          lambda = 0.5 - bias;
+        // combine information from A and B
+        offspring[j] = lambda * group3[i][j] + lambda * group4[i][j];
+      }
+
+      // qr factorization of the offspring
+      Linear_algebra_traits::qr_factorization(offspring);
+      offspringsB[i] = offspring;
+    }
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG
+    std::cout << "offspringsB: \n" ;
+    check_det(offspringsB);
+#endif
+
+    CGAL_assertion(offspringsA.size() == size_first_group);
+    CGAL_assertion(offspringsB.size() == size_second_group);
+    CGAL_assertion(offspringsA.size() + offspringsB.size() == population.size());
+
+    // next generatrion
+    for(std::size_t i = 0; i < size_first_group; ++i)
+      population[i] = offspringsA[i];
+
+    for(std::size_t i = 0; i < size_second_group; ++i)
+      population[size_first_group + i] = offspringsB[i];
+  }
+
+  void evolve(std::size_t generations)
+  {
+    // hardcoded nelder_mead_iterations
+    std::size_t nelder_mead_iterations = 20;
+
+    // stopping criteria prameters
+    double prev_fit_value = 0;
+    double new_fit_value = 0;
+    double tolerance = 1e-2;
+    int stale = 0;
+
+    for(std::size_t t = 0; t < generations; ++t)
+    {
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG
+      std::cout << "generation= " << t << "\n";
+#endif
+
+      genetic_algorithm();
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG
+      //std::cout << "pop after genetic" << std::endl;
+      //pop.show_population();
+      //std::cout << std::endl;
+#endif
+
+      for(std::size_t s = 0; s < population.size(); ++s)
+        nelder_mead<Linear_algebra_traits>(population[s], point_data, nelder_mead_iterations);
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG
+      //std::cout << "pop after nelder mead: " << std::endl;
+      //pop.show_population();
+      //std::cout << std::endl;
+      Fitness_map<Linear_algebra_traits, Matrix3d, MatrixXd> fitness_map_debug(population, point_data);
+      Matrix3d R_now = fitness_map_debug.get_best();
+      std::cout << "det= " << Linear_algebra_traits::determinant(R_now) << std::endl;
+#endif
+
+      // stopping criteria
+      Fitness_map<Linear_algebra_traits, Matrix3d, MatrixXd> fitness_map(population, point_data);
+      new_fit_value = fitness_map.get_best_fitness_value();
+      double difference = new_fit_value - prev_fit_value;
+
+      if(CGAL::abs(difference) < tolerance * new_fit_value)
+        stale++;
+
+      if(stale == 5)
+        break;
+
+      prev_fit_value = new_fit_value;
+    }
+  }
+
+  const Matrix3d get_best()
+  {
+    Fitness_map<Linear_algebra_traits, Matrix3d, MatrixXd> fitness_map(population, point_data);
+    return fitness_map.get_best();
+  }
+
+private:
+  // data
+  Population<Linear_algebra_traits> population;
+  MatrixXd point_data;
+};
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG
+template <typename Simplex>
+void check_det(Population<Simplex>& pop)
+{
+  for(std::size_t i = 0; i < pop.size(); ++i)
+  {
+    for(std::size_t j = 0; j < 4; ++j)
+    {
+      auto A = pop[i][j]; // Simplex
+      std::cout << Linear_algebra_traits::determinant(A) << std::endl;
+    }
+  }
+}
+#endif
+
+} // end namespace Optimal_bounding_box
+} // end namespace CGAL
+
+#endif // CGAL_OPTIMAL_BOUNDING_BOX_EVOLUTION_H
diff --git a/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/fitness_function.h b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/fitness_function.h
new file mode 100644
index 00000000000..649dacb40d5
--- /dev/null
+++ b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/fitness_function.h
@@ -0,0 +1,117 @@
+// Copyright (c) 2018 GeometryFactory (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+// You can redistribute it and/or modify it under the terms of the GNU
+// General Public License as published by the Free Software Foundation,
+// either version 3 of the License, or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0+
+//
+// Author(s)     : Konstantinos Katrioplas
+
+#ifndef CGAL_OPTIMAL_BOUNDING_FITNESS_FUNCTION_H
+#define CGAL_OPTIMAL_BOUNDING_FITNESS_FUNCTION_H
+
+#include <CGAL/Optimal_bounding_box/population.h>
+
+#include <CGAL/assertions.h>
+
+#include <limits>
+
+namespace CGAL {
+
+namespace Optimal_bounding_box {
+
+template <typename Linear_algebra_traits, typename Vertex, typename Matrix>
+double compute_fitness(const Vertex& R, const Matrix& data)
+{
+  // R: rotation matrix
+  CGAL_assertion(R.cols() == 3);
+  CGAL_assertion(R.rows() == 3);
+  // data: points
+  CGAL_assertion(data.cols() == 3);
+  CGAL_assertion(data.rows() >= 3);
+
+  typedef typename Linear_algebra_traits::Vector3d Vector3d;
+  typedef typename Linear_algebra_traits::Index Index;
+
+  double xmin, xmax, ymin, ymax, zmin, zmax;
+  for(Index i = 0; i < static_cast<Index>(data.rows()); ++i){
+
+    Vector3d vec = Linear_algebra_traits::row3(data, i);
+    vec = R * vec;
+
+    if(i == 0){
+      xmin = xmax = vec.coeff(0);
+      ymin = ymax = vec.coeff(1);
+      zmin = zmax = vec.coeff(2);
+    }else {
+      if(vec.coeff(0) < xmin) xmin = vec.coeff(0);
+      if(vec.coeff(1) < ymin) ymin = vec.coeff(1);
+      if(vec.coeff(2) < zmin) zmin = vec.coeff(2);
+      if(vec.coeff(0) > xmax) xmax = vec.coeff(0);
+      if(vec.coeff(1) > ymax) ymax = vec.coeff(1);
+      if(vec.coeff(2) > zmax) zmax = vec.coeff(2);
+    }
+  }
+
+  CGAL_assertion(xmax > xmin);
+  CGAL_assertion(ymax > ymin);
+  CGAL_assertion(zmax > zmin);
+
+  // volume
+  return ((xmax - xmin) * (ymax - ymin) * (zmax - zmin));
+}
+
+template <typename Linear_algebra_traits, typename Vertex, typename Matrix>
+struct Fitness_map
+{
+  Fitness_map(Population<Linear_algebra_traits>& p, Matrix& points)
+    : pop(p), points(points)
+  {}
+
+  const Vertex get_best()
+  {
+    std::size_t simplex_id, vertex_id;
+    double best_fitness = std::numeric_limits<int>::max();
+    for(std::size_t i = 0; i < pop.size(); ++i)
+    {
+      for(std::size_t j =0; j < 4; ++j)
+      {
+        const Vertex vertex = pop[i][j];
+        const double fitness = compute_fitness<Linear_algebra_traits>(vertex, points);
+        if (fitness < best_fitness)
+        {
+          simplex_id = i;
+          vertex_id = j;
+          best_fitness = fitness;
+        }
+      }
+    }
+
+    return pop[simplex_id][vertex_id];
+  }
+
+  double get_best_fitness_value()
+  {
+    const Vertex best_mat = get_best();
+    return compute_fitness<Linear_algebra_traits>(best_mat, points);
+  }
+
+  Population<Linear_algebra_traits>& pop;
+  const Matrix& points;
+};
+
+} // end namespace Optimal_bounding_box
+} // end namespace CGAL
+
+#endif // CGAL_OPTIMAL_BOUNDING_FITNESS_FUNCTION_H
diff --git a/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/helper.h b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/helper.h
new file mode 100644
index 00000000000..d207feb93ea
--- /dev/null
+++ b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/helper.h
@@ -0,0 +1,113 @@
+// Copyright (c) 2018 GeometryFactory (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+// You can redistribute it and/or modify it under the terms of the GNU
+// General Public License as published by the Free Software Foundation,
+// either version 3 of the License, or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0+
+//
+//
+// Author(s)     : Konstantinos Katrioplas
+
+#ifndef CGAL_OPTIMAL_BOUNDING_BOX_HELPER_H
+#define CGAL_OPTIMAL_BOUNDING_BOX_HELPER_H
+
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/Bbox_3.h>
+#include <CGAL/boost/graph/helpers.h>
+#include <CGAL/number_utils.h>
+#include <CGAL/Simple_cartesian.h>
+#include <CGAL/Surface_mesh.h>
+
+#include <fstream>
+#include <string>
+#include <vector>
+
+namespace CGAL {
+
+namespace Optimal_bounding_box {
+
+template <typename Matrix, typename Point>
+void fill_matrix(const std::vector<Point>& v_points, Matrix& points_mat)
+{
+  points_mat.resize(v_points.size(), 3);
+  for(std::size_t i = 0; i < v_points.size(); ++i)
+  {
+    Point p = v_points[i];
+    points_mat.set_coef(i, 0, CGAL::to_double(p.x()));
+    points_mat.set_coef(i, 1, CGAL::to_double(p.y()));
+    points_mat.set_coef(i, 2, CGAL::to_double(p.z()));
+  }
+}
+
+template <typename SurfaceMesh, typename Matrix>
+void sm_to_matrix(SurfaceMesh& sm, Matrix& mat)
+{
+  typedef typename boost::property_map<SurfaceMesh, boost::vertex_point_t>::const_type Vpm;
+  typedef typename boost::property_traits<Vpm>::reference Point_ref;
+  typedef typename boost::graph_traits<SurfaceMesh>::vertex_descriptor vertex_descriptor;
+  Vpm vpm = get(boost::vertex_point, sm);
+
+  mat.resize(vertices(sm).size(), 3);
+  std::size_t i = 0;
+  for(vertex_descriptor v : vertices(sm))
+  {
+    Point_ref p = get(vpm, v);
+    mat.set_coef(i, 0, CGAL::to_double(p.x()));
+    mat.set_coef(i, 1, CGAL::to_double(p.y()));
+    mat.set_coef(i, 2, CGAL::to_double(p.z()));
+    ++i;
+  }
+}
+
+template <typename Point>
+double calculate_volume(const std::vector<Point>& points)
+{
+  typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
+
+  CGAL::Bbox_3 bbox = bbox_3(points.begin(), points.end());
+  K::Iso_cuboid_3 ic(bbox);
+  return ic.volume();
+}
+
+// it is called after post processing in debug only
+template <typename Matrix>
+void matrix_to_mesh_and_draw(Matrix& data_points, std::string filename)
+{
+  typedef CGAL::Simple_cartesian<double> K;
+  typedef K::Point_3 Point;
+  typedef CGAL::Surface_mesh<Point> Mesh;
+
+  // Simplex -> std::vector
+  std::vector<Point> points;
+
+  for(int i = 0; i < data_points.rows(); ++i)
+  {
+    Point p(data_points(i, 0), data_points(i, 1), data_points(i, 2));
+    points.push_back(p);
+  }
+
+  Mesh mesh;
+  CGAL::make_hexahedron(points[0], points[1], points[2], points[3],
+                        points[4], points[5], points[6], points[7], mesh);
+
+  std::ofstream out(filename);
+  out << mesh;
+  out.close();
+}
+
+} // end namespace Optimal_bounding_box
+} // end namespace CGAL
+
+#endif // CGAL_OPTIMAL_BOUNDING_BOX_HELPER_H
diff --git a/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/nelder_mead_functions.h b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/nelder_mead_functions.h
new file mode 100644
index 00000000000..3d7de8c8db3
--- /dev/null
+++ b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/nelder_mead_functions.h
@@ -0,0 +1,184 @@
+// Copyright (c) 2018 GeometryFactory (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+// You can redistribute it and/or modify it under the terms of the GNU
+// General Public License as published by the Free Software Foundation,
+// either version 3 of the License, or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0+
+//
+// Author(s)     : Konstantinos Katrioplas
+
+#ifndef CGAL_OPTIMAL_BOUNDING_BOX_NEALDER_MEAD_FUNCTIONS_H
+#define CGAL_OPTIMAL_BOUNDING_BOX_NEALDER_MEAD_FUNCTIONS_H
+
+#include <CGAL/assertions.h>
+#include <boost/iterator/counting_iterator.hpp>
+#include <CGAL/Optimal_bounding_box/fitness_function.h>
+#include <vector>
+
+namespace CGAL {
+
+namespace Optimal_bounding_box {
+
+template <typename Linear_algebra_traits, typename Matrix>
+const Matrix reflection(const Matrix& S_centroid, const Matrix& S_worst)
+{
+  CGAL_assertion(S_centroid.rows() == 3);
+  CGAL_assertion(S_centroid.rows() == 3);
+  CGAL_assertion(S_worst.cols() == 3);
+  CGAL_assertion(S_worst.cols() == 3);
+
+  return S_centroid * Linear_algebra_traits::transpose(S_worst) * S_centroid;
+}
+
+template <typename Linear_algebra_traits, typename Matrix>
+const Matrix expansion(const Matrix& S_centroid, const Matrix& S_worst, const Matrix& S_reflection)
+{
+  CGAL_assertion(S_centroid.rows() == 3);
+  CGAL_assertion(S_centroid.rows() == 3);
+  CGAL_assertion(S_worst.cols() == 3);
+  CGAL_assertion(S_worst.cols() == 3);
+  CGAL_assertion(S_reflection.cols() == 3);
+  CGAL_assertion(S_reflection.cols() == 3);
+
+  return S_centroid * Linear_algebra_traits::transpose(S_worst) * S_reflection;
+}
+
+template <typename Linear_algebra_traits, typename Matrix>
+Matrix mean(const Matrix& m1, const Matrix& m2)
+{
+  // same API for reduction
+  CGAL_assertion(m1.rows() == 3);
+  CGAL_assertion(m1.rows() == 3);
+  CGAL_assertion(m2.cols() == 3);
+  CGAL_assertion(m2.cols() == 3);
+
+  Matrix reduction = 0.5 * m1 + 0.5 * m2;
+  Matrix Q = Linear_algebra_traits::qr_factorization(reduction);
+  double det = Linear_algebra_traits::determinant(Q);
+  return Q / det;
+}
+
+template <typename Linear_algebra_traits, typename Matrix>
+const Matrix nm_centroid(const Matrix& S1, const Matrix& S2, const Matrix& S3)
+{
+  Matrix mean = (S1 + S2 + S3) / 3.0;
+  Matrix Q = Linear_algebra_traits::qr_factorization(mean);
+  double det = Linear_algebra_traits::determinant(Q);
+  return Q / det;
+}
+
+// needed in nelder mead algorithm
+struct Comparator
+{
+  Comparator(const std::vector<double>& in) : fitness(in) {}
+
+  inline bool operator() (std::size_t& i, std::size_t& j) {
+    return fitness[i] < fitness[j];
+  }
+
+  const std::vector<double>& fitness;
+};
+
+// simplex: 4 rotation matrices are its vertices
+template <typename Linear_algebra_traits>
+void nelder_mead(std::vector<typename Linear_algebra_traits::Matrix3d>& simplex,
+                 const typename Linear_algebra_traits::MatrixXd& point_data,
+                 std::size_t nelder_mead_iterations)
+{
+  CGAL_assertion(simplex.size() == 4); // tetrahedron
+
+
+  typedef typename Linear_algebra_traits::Matrix3d Matrix3d;
+
+  std::vector<double> fitness(4);
+  std::vector<std::size_t> indices(boost::counting_iterator<std::size_t>(0),
+                                   boost::counting_iterator<std::size_t>(simplex.size()));
+
+  for(std::size_t t = 0; t < nelder_mead_iterations; ++t)
+  {
+    for(std::size_t i = 0; i < 4; ++i)
+    {
+      fitness[i] = compute_fitness<Linear_algebra_traits>(simplex[i], point_data);
+    }
+
+    CGAL_assertion(fitness.size() == 4);
+    CGAL_assertion(indices.size() == 4);
+
+    // get indices of sorted sequence
+    Comparator compare_indices(fitness);
+    std::sort(indices.begin(), indices.end(), compare_indices);
+
+    // new sorted simplex & fitness
+    std::vector<Matrix3d> s_simplex(4);
+    std::vector<double> s_fitness(4);
+    for(int i = 0; i < 4; ++i)
+    {
+      s_simplex[i] = simplex[indices[i]];
+      s_fitness[i] = fitness[indices[i]];
+    }
+
+    simplex = s_simplex;
+    fitness = s_fitness;
+
+    // centroid
+    const Matrix3d v_centroid = nm_centroid<Linear_algebra_traits>(simplex[0], simplex[1], simplex[2]);
+
+    // find worst's vertex reflection
+    const Matrix3d v_worst = simplex[3];
+    const Matrix3d v_refl = reflection<Linear_algebra_traits>(v_centroid, v_worst);
+    const double f_refl = compute_fitness<Linear_algebra_traits>(v_refl, point_data);
+
+    if(f_refl < fitness[2])
+    {
+      if(f_refl >= fitness[0]) // if reflected point is not better than the best
+      {
+        // do reflection
+        simplex[3] = v_refl;
+      }
+      else
+      {
+        // expansion
+        const Matrix3d v_expand = expansion<Linear_algebra_traits>(v_centroid, v_worst, v_refl);
+        const double f_expand = compute_fitness<Linear_algebra_traits>(v_expand, point_data);
+        if(f_expand < f_refl)
+          simplex[3] = v_expand;
+        else
+          simplex[3] = v_refl;
+      }
+    }
+    else // if reflected vertex is not better
+    {
+      const Matrix3d v_mean = mean<Linear_algebra_traits>(v_centroid, v_worst);
+      const double f_mean = compute_fitness<Linear_algebra_traits>(v_mean, point_data);
+      if(f_mean <= fitness[3])
+        // contraction of worst
+        simplex[3] = v_mean;
+      else
+      {
+        // reduction: move all vertices towards the best
+        for(std::size_t i=1; i < 4; ++i)
+        {
+          simplex[i] = mean<Linear_algebra_traits>(simplex[i], simplex[0]);
+        }
+      }
+    }
+
+    CGAL_assertion(simplex.size() == 4); // tetrahedron
+  } // iterations
+}
+
+} // end namespace Optimal_bounding_box
+} // end namespace CGAL
+
+#endif
diff --git a/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/optimal_bounding_box.h b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/optimal_bounding_box.h
new file mode 100644
index 00000000000..3cb4fc338a1
--- /dev/null
+++ b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/optimal_bounding_box.h
@@ -0,0 +1,273 @@
+// Copyright (c) 2018 GeometryFactory (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+// You can redistribute it and/or modify it under the terms of the GNU
+// General Public License as published by the Free Software Foundation,
+// either version 3 of the License, or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0+
+//
+//
+// Author(s)     : Konstantinos Katrioplas
+
+#ifndef CGAL_OPTIMAL_BOUNDING_BOX_OBB_H
+#define CGAL_OPTIMAL_BOUNDING_BOX_OBB_H
+
+#include <CGAL/Optimal_bounding_box/population.h>
+#include <CGAL/Optimal_bounding_box/evolution.h>
+#include <CGAL/Optimal_bounding_box/helper.h>
+
+#include <CGAL/assertions.h>
+#include <CGAL/Bbox_3.h>
+#include <CGAL/boost/graph/helpers.h>
+#include <CGAL/convex_hull_3.h>
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Iso_cuboid_3.h>
+#include <CGAL/Simple_cartesian.h>
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_BENCHMARKS
+  #include <CGAL/Timer.h>
+#endif
+
+#if defined(CGAL_EIGEN3_ENABLED)
+#include <CGAL/Eigen_linear_algebra_traits.h>
+#endif
+
+#include <iostream>
+#include <iterator>
+#include <vector>
+
+namespace CGAL {
+
+namespace Optimal_bounding_box {
+
+// works on matrices only
+/// \cond SKIP_IN_MANUAL
+template <typename Linear_algebra_traits, typename Vertex, typename Matrix>
+void post_processing(const Matrix& points, Vertex& R, Matrix& obb)
+{
+  CGAL_assertion(points.cols() == 3);
+  CGAL_assertion(R.rows() == 3);
+  CGAL_assertion(R.cols() == 3);
+  CGAL_assertion(obb.rows() == 8);
+  CGAL_assertion(obb.cols() == 3);
+
+  // 1) rotate points with R
+  Matrix rotated_points(points.rows(), points.cols());
+  rotated_points = points * Linear_algebra_traits::transpose(R);
+
+  // 2) get AABB from rotated points
+  typedef CGAL::Simple_cartesian<double> K;
+  typedef K::Point_3 Point;
+  typedef typename Linear_algebra_traits::Index index;
+
+  // Simplex -> std::vector
+  std::vector<Point> v_points;
+  for(index i = 0; i < static_cast<index>(rotated_points.rows()); ++i)
+  {
+    Point p(rotated_points(i, 0), rotated_points(i, 1), rotated_points(i, 2));
+    v_points.push_back(p);
+  }
+  CGAL::Bbox_3 bbox;
+  bbox = bbox_3(v_points.begin(), v_points.end());
+  K::Iso_cuboid_3 ic(bbox);
+
+  Matrix aabb(8, 3);
+  for(std::size_t i = 0; i < 8; ++i)
+  {
+    aabb.set_coef(i, 0, ic[i].x());
+    aabb.set_coef(i, 1, ic[i].y());
+    aabb.set_coef(i, 2, ic[i].z());
+  }
+
+  // 3) apply inverse rotation to rotated AABB
+  obb = aabb * R;
+}
+/// \endcond
+
+/// \ingroup OBB_grp
+/// calculates the optimal bounding box.
+///
+/// @tparam Point the point type
+/// @tparam LinearAlgebraTraits a model of `LinearAlgebraTraits`. If no instance of `LinearAlgebraTraits`
+/// is provided, then `CGAL::Eigen_linear_algebra_traits` is used.
+///
+/// @param points the input points that are included in the optimal bounding box.
+/// @param obb_points the eight points of the optimal bounding box to be calculated.
+/// @param use_ch a bool flag to indicating whether to use the convex hull of the input points
+/// as an optimization step.
+template <typename Point, typename LinearAlgebraTraits>
+void compute_optimal_bounding_box(const std::vector<Point>& points,
+                                  std::vector<Point>& obb_points,
+                                  LinearAlgebraTraits&,
+                                  bool use_ch)
+{
+  CGAL_assertion(points.size() >= 3);
+
+  if(obb_points.size() != 8)
+    obb_points.resize(8);
+  CGAL_assertion(obb_points.size() == 8);
+
+  // eigen linear algebra traits
+  typedef typename LinearAlgebraTraits::MatrixXd MatrixXd;
+  typedef typename LinearAlgebraTraits::Matrix3d Matrix3d;
+  MatrixXd points_mat;
+
+  if(use_ch) // get the ch3
+  {
+    std::vector<Point> ch_points;
+    CGAL::extreme_points_3(points, std::back_inserter(ch_points));
+    CGAL::Optimal_bounding_box::fill_matrix(ch_points, points_mat);
+  }
+  else
+  {
+    CGAL::Optimal_bounding_box::fill_matrix(points, points_mat);
+  }
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_BENCHMARKS
+  CGAL::Timer timer;
+#endif
+
+  std::size_t max_generations = 100;
+  Population<LinearAlgebraTraits> pop(50);
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_BENCHMARKS
+  timer.start();
+#endif
+
+  CGAL::Optimal_bounding_box::Evolution<LinearAlgebraTraits> search_solution(pop, points_mat);
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_BENCHMARKS
+  timer.stop();
+  std::cout << "constructor: " << timer.time() << std::endl;
+  timer.reset();
+  timer.start();
+#endif
+
+  search_solution.evolve(max_generations);
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_BENCHMARKS
+  timer.stop();
+  std::cout << "evolve: " << timer.time() << std::endl;
+  timer.reset();
+  timer.start();
+#endif
+
+  Matrix3d rotation = search_solution.get_best();
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_BENCHMARKS
+  timer.stop();
+  std::cout << "get best: " << timer.time() << std::endl;
+#endif
+
+  MatrixXd obb; // may be preallocated at compile time
+  obb.resize(8, 3);
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_BENCHMARKS
+  timer.reset();
+  timer.start();
+#endif
+
+  post_processing<LinearAlgebraTraits>(points_mat, rotation, obb);
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_BENCHMARKS
+  timer.stop();
+  std::cout << "post porcessing: " << timer.time() << std::endl;
+#endif
+
+  // matrix -> vector
+  for(std::size_t i = 0; i < 8; ++i)
+  {
+    Point p(obb(i, 0), obb(i, 1), obb(i, 2));
+    obb_points[i] = p;
+  }
+}
+
+template <typename Point>
+void compute_optimal_bounding_box(const std::vector<Point>& points,
+                                  std::vector<Point>& obb_points,
+                                  bool use_ch)
+{
+#if defined(CGAL_EIGEN3_ENABLED)
+  typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits;
+#else
+  #pragma message("Error: You must either provide linear traits or link CGAL with the Eigen library")
+  Linear_algebra_traits; // no parameter provided, and Eigen is not enabled --> don't compile!
+#endif
+
+  Linear_algebra_traits la_traits;
+  compute_optimal_bounding_box(points, obb_points, la_traits, use_ch);
+}
+
+/// \ingroup OBB_grp
+/// calculates the optimal bounding box.
+///
+/// @tparam PolygonMesh a model of `FaceListGraph` 
+/// @tparam LinearAlgebraTraits a model of `LinearAlgebraTraits`. If no instance of `LinearAlgebraTraits`
+/// is provided, then `CGAL::Eigen_linear_algebra_traits` is used.
+///
+/// @param pmesh the input mesh.
+/// @param obbmesh the hexaedron mesh to be built out of the optimal bounding box.
+/// @param la_traits an instance of the linear algebra traits.
+/// @param use_ch a bool flag to indicating whether to use the convex hull of the input points
+/// as an optimization step.
+template <typename PolygonMesh, typename LinearAlgebraTraits>
+void compute_optimal_bounding_box(const PolygonMesh& pmesh,
+                                  PolygonMesh& obbmesh,
+                                  LinearAlgebraTraits& la_traits,
+                                  bool use_ch)
+{
+  CGAL_assertion(vertices(pmesh).size() >= 3);
+
+  if(vertices(pmesh).size() <= 3)
+  {
+    std::cerr << "Not enough points in the mesh!\n";
+    return;
+  }
+
+  typedef typename boost::graph_traits<PolygonMesh>::vertex_descriptor vertex_descriptor;
+  typedef typename boost::property_map<PolygonMesh, CGAL::vertex_point_t>::type Vpm;
+  typedef typename boost::property_traits<Vpm>::value_type Point;
+
+  std::vector<Point> points;
+  Vpm pmap = get(boost::vertex_point, pmesh);
+  BOOST_FOREACH(vertex_descriptor v, vertices(pmesh))
+    points.push_back(get(pmap, v));
+
+
+  std::vector<Point> obb_points;
+  compute_optimal_bounding_box(points, obb_points, la_traits, use_ch);
+
+  CGAL::make_hexahedron(obb_points[0], obb_points[1], obb_points[2], obb_points[3],
+                        obb_points[4], obb_points[5], obb_points[6], obb_points[7], obbmesh);
+}
+
+template <typename PolygonMesh>
+void compute_optimal_bounding_box(const PolygonMesh& pmesh,
+                                  PolygonMesh& obbmesh,
+                                  bool use_ch)
+{
+#if defined(CGAL_EIGEN3_ENABLED)
+  typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits;
+#else
+  #pragma message("Error: You must either provide linear traits or link CGAL with the Eigen library")
+  Linear_algebra_traits; // no parameter provided, and Eigen is not enabled --> don't compile!
+#endif
+
+  Linear_algebra_traits la_traits;
+  compute_optimal_bounding_box(pmesh, obbmesh, la_traits, use_ch);
+}
+
+} // end namespace Optimal_bounding_box
+} // end namespace CGAL
+
+#endif // CGAL_OPTIMAL_BOUNDING_BOX_OBB_H
diff --git a/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/population.h b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/population.h
new file mode 100644
index 00000000000..4404acdcd3a
--- /dev/null
+++ b/Optimal_bounding_box/include/CGAL/Optimal_bounding_box/population.h
@@ -0,0 +1,136 @@
+// Copyright (c) 2018 GeometryFactory (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+// You can redistribute it and/or modify it under the terms of the GNU
+// General Public License as published by the Free Software Foundation,
+// either version 3 of the License, or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0+
+//
+//
+// Author(s)     : Konstantinos Katrioplas
+
+#ifndef CGAL_OPTIMAL_BOUNDING_BOX_POPULATION_H
+#define CGAL_OPTIMAL_BOUNDING_BOX_POPULATION_H
+
+#include <CGAL/assertions.h>
+#include <CGAL/Random.h>
+
+#include <vector>
+
+namespace CGAL {
+
+namespace Optimal_bounding_box {
+
+template<typename Linear_algebra_traits>
+class Population
+{
+  typedef typename Linear_algebra_traits::Matrix3d Matrix;
+  typedef std::vector<Matrix> Simplex;
+
+public:
+  Population(std::size_t size)
+    : n(size), random_generator(CGAL::Random())
+  {
+    // reserve pop space
+    pop.reserve(n);
+
+    // create simplices
+    for(std::size_t i = 0 ; i < n; ++i)
+    {
+      Simplex simplex(4);
+      create_simplex(simplex);
+      CGAL_assertion(simplex.size() == 4);
+      pop.push_back(simplex);
+    }
+  }
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG
+  void show_population();
+#endif
+
+  std::size_t size(){return n;}
+
+  // access simplex
+  Simplex& operator[](std::size_t i)
+  {
+    CGAL_assertion(i < n);
+    return pop[i];
+  }
+
+  const Simplex& operator[](std::size_t i) const
+  {
+    CGAL_assertion(i < n);
+    return pop[i];
+  }
+
+private:
+  // create random population
+  void create_simplex(Simplex& simplex)
+  {
+    CGAL_assertion(simplex.size() == 4);
+    for(std::size_t i = 0; i < 4; ++i)
+    {
+      Matrix R;
+      if(R.cols() == 0 || R.rows() == 0)
+        R.resize(3, 3);
+
+      create_vertex(R);
+      Matrix Q = Linear_algebra_traits::qr_factorization(R);
+
+      simplex[i] = Q;
+    }
+    CGAL_assertion(simplex.size() == 4);
+  }
+
+  void create_vertex(Matrix& R)
+  {
+    CGAL_assertion(R.rows() == 3);
+    CGAL_assertion(R.cols() == 3);
+
+    for(std::size_t i = 0; i < 3; ++i)
+    {
+      for(std::size_t j = 0; j < 3; ++j)
+      {
+        R.set_coef(i, j, random_generator.get_double());
+      }
+    }
+  }
+
+  std::size_t n;
+  CGAL::Random random_generator;
+  std::vector<Simplex> pop;
+};
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG
+template <typename Matrix>
+void Population<Matrix>::show_population()
+{
+  std::size_t id = 0;
+  for(const Simplex i : pop)
+  {
+    CGAL_assertion(i.size() == 4);
+    std:: cout << "Simplex: "<< id++ << std::endl;
+    for(const Matrix R : i)
+    {
+      std::cout << R; // eigen out
+      std::cout << "\n\n";
+    }
+    std:: cout << std:: endl;
+  }
+}
+#endif
+
+} // end namespace Optimal_bounding_box
+} // end namespace CGAL
+
+#endif // CGAL_OPTIMAL_BOUNDING_BOX_POPULATION_H
diff --git a/Optimal_bounding_box/package_info/Optimal_bounding_box/copyright b/Optimal_bounding_box/package_info/Optimal_bounding_box/copyright
new file mode 100644
index 00000000000..d76cdbe60d6
--- /dev/null
+++ b/Optimal_bounding_box/package_info/Optimal_bounding_box/copyright
@@ -0,0 +1 @@
+GeometryFactory (France)
\ No newline at end of file
diff --git a/Optimal_bounding_box/package_info/Optimal_bounding_box/dependencies b/Optimal_bounding_box/package_info/Optimal_bounding_box/dependencies
new file mode 100644
index 00000000000..e69de29bb2d
diff --git a/Optimal_bounding_box/package_info/Optimal_bounding_box/license.txt b/Optimal_bounding_box/package_info/Optimal_bounding_box/license.txt
new file mode 100644
index 00000000000..8bb8efcb72b
--- /dev/null
+++ b/Optimal_bounding_box/package_info/Optimal_bounding_box/license.txt
@@ -0,0 +1 @@
+GPL (v3 or later)
diff --git a/Optimal_bounding_box/package_info/Optimal_bounding_box/maintainer b/Optimal_bounding_box/package_info/Optimal_bounding_box/maintainer
new file mode 100644
index 00000000000..2427333ef57
--- /dev/null
+++ b/Optimal_bounding_box/package_info/Optimal_bounding_box/maintainer
@@ -0,0 +1 @@
+GeometryFactory
diff --git a/Optimal_bounding_box/test/Optimal_bounding_box/CMakeLists.txt b/Optimal_bounding_box/test/Optimal_bounding_box/CMakeLists.txt
new file mode 100644
index 00000000000..dc0d5800453
--- /dev/null
+++ b/Optimal_bounding_box/test/Optimal_bounding_box/CMakeLists.txt
@@ -0,0 +1,26 @@
+# Created by the script cgal_create_CMakeLists
+# This is the CMake script for compiling a set of CGAL applications.
+
+cmake_minimum_required(VERSION 3.1...3.15)
+project( Optimal_bounding_box_Tests )
+
+find_package(CGAL QUIET)
+
+if (NOT CGAL_FOUND)
+  message(STATUS "This project requires the CGAL library, and will not be compiled.")
+  return()
+endif()
+
+include( ${CGAL_USE_FILE} )
+
+find_package(Eigen3 3.1.0 REQUIRED) #(3.1.0 or greater)
+if (NOT EIGEN3_FOUND)
+  message(STATUS "This project requires the Eigen library, and will not be compiled.")
+  return()
+else()
+  include(${EIGEN3_USE_FILE})
+endif()
+
+create_single_source_cgal_program("test_linear_algebra_functions.cpp")
+create_single_source_cgal_program("test_optimization_algorithms.cpp")
+
diff --git a/Optimal_bounding_box/test/Optimal_bounding_box/data/elephant.off b/Optimal_bounding_box/test/Optimal_bounding_box/data/elephant.off
new file mode 100644
index 00000000000..cf7cc2b68ca
--- /dev/null
+++ b/Optimal_bounding_box/test/Optimal_bounding_box/data/elephant.off
@@ -0,0 +1,8337 @@
+OFF
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diff --git a/Optimal_bounding_box/test/Optimal_bounding_box/data/long_tetrahedron.off b/Optimal_bounding_box/test/Optimal_bounding_box/data/long_tetrahedron.off
new file mode 100644
index 00000000000..ad966ac795e
--- /dev/null
+++ b/Optimal_bounding_box/test/Optimal_bounding_box/data/long_tetrahedron.off
@@ -0,0 +1,11 @@
+OFF
+4 4 0
+
+-1 -0.1 0
+-1 0.1 0
+1 0 -0.1
+1 0 0.1
+3  0 1 2
+3  2 3 0
+3  1 3 2
+3  0 3 1
\ No newline at end of file
diff --git a/Optimal_bounding_box/test/Optimal_bounding_box/data/random_unit_tetra.off b/Optimal_bounding_box/test/Optimal_bounding_box/data/random_unit_tetra.off
new file mode 100644
index 00000000000..270289e2c6e
--- /dev/null
+++ b/Optimal_bounding_box/test/Optimal_bounding_box/data/random_unit_tetra.off
@@ -0,0 +1,11 @@
+OFF
+4 4 0
+
+0.866802 0.740808 0.895304
+0.912651 0.761565 0.160330
+0.093661 0.892578 0.737412
+0.166461 0.149912 0.364944
+3  0 1 2
+3  2 3 0
+3  1 3 2
+3  0 3 1
\ No newline at end of file
diff --git a/Optimal_bounding_box/test/Optimal_bounding_box/data/reference_tetrahedron.off b/Optimal_bounding_box/test/Optimal_bounding_box/data/reference_tetrahedron.off
new file mode 100644
index 00000000000..d83aa004308
--- /dev/null
+++ b/Optimal_bounding_box/test/Optimal_bounding_box/data/reference_tetrahedron.off
@@ -0,0 +1,12 @@
+OFF
+4 4 0
+
+0 1 0
+1 0 0
+0 0 0
+0 0 1
+3  0 1 2
+3  2 3 0
+3  1 3 2
+3  0 3 1
+
diff --git a/Optimal_bounding_box/test/Optimal_bounding_box/test_linear_algebra_functions.cpp b/Optimal_bounding_box/test/Optimal_bounding_box/test_linear_algebra_functions.cpp
new file mode 100644
index 00000000000..5ae7753271f
--- /dev/null
+++ b/Optimal_bounding_box/test/Optimal_bounding_box/test_linear_algebra_functions.cpp
@@ -0,0 +1,301 @@
+#include <CGAL/Eigen_linear_algebra_traits.h>
+#include <CGAL/Optimal_bounding_box/nelder_mead_functions.h>
+#include <CGAL/Optimal_bounding_box/fitness_function.h>
+
+#include <CGAL/assertions.h>
+
+bool assert_doubles(double d1, double d2, double epsilon)
+{
+  return (d1 < d2 + epsilon && d1 > d2 - epsilon) ? true : false;
+}
+
+void test_qr_factorization()
+{
+  typedef CGAL::Eigen_dense_matrix<double, 3, 3> Mat;
+  Mat A(3, 3);
+  A.set_coef(0, 0, 0.3011944);
+  A.set_coef(0, 1, 0.9932761);
+  A.set_coef(0, 2, 0.5483701);
+  A.set_coef(1, 0, 0.5149142);
+  A.set_coef(1, 1, 0.5973263);
+  A.set_coef(1, 2, 0.5162336);
+  A.set_coef(2, 0, 0.0039213);
+  A.set_coef(2, 1, 0.0202949);
+  A.set_coef(2, 2, 0.9240308);
+
+  CGAL_assertion_code(Mat Q = CGAL::Eigen_linear_algebra_traits::qr_factorization(A));
+  CGAL_assertion_code(double epsilon = 1e-6);
+  CGAL_assertion(assert_doubles(Q(0,0), -0.504895, epsilon));
+  CGAL_assertion(assert_doubles(Q(0,1), 0.862834, epsilon));
+  CGAL_assertion(assert_doubles(Q(0,2), -0.024447, epsilon));
+  CGAL_assertion(assert_doubles(Q(1,0), -0.863156, epsilon));
+  CGAL_assertion(assert_doubles(Q(1,1), -0.504894, epsilon));
+  CGAL_assertion(assert_doubles(Q(1,2), 0.006687, epsilon));
+  CGAL_assertion(assert_doubles(Q(2,0), -0.006573, epsilon));
+  CGAL_assertion(assert_doubles(Q(2,1), 0.024478, epsilon));
+  CGAL_assertion(assert_doubles(Q(2,2), 0.999679, epsilon));
+}
+
+void test_fitness_function()
+{
+  typedef typename CGAL::Eigen_linear_algebra_traits::MatrixXd MatrixXd;
+  MatrixXd data_points(4, 3);
+
+  data_points.set_coef(0, 0, 0.866802);
+  data_points.set_coef(0, 1, 0.740808);
+  data_points.set_coef(0, 2, 0.895304);
+
+  data_points.set_coef(1, 0, 0.912651);
+  data_points.set_coef(1, 1, 0.761565);
+  data_points.set_coef(1, 2, 0.160330);
+
+  data_points.set_coef(2, 0, 0.093661);
+  data_points.set_coef(2, 1, 0.892578);
+  data_points.set_coef(2, 2, 0.737412);
+
+  data_points.set_coef(3, 0, 0.166461);
+  data_points.set_coef(3, 1, 0.149912);
+  data_points.set_coef(3, 2, 0.364944);
+
+  typedef typename CGAL::Eigen_linear_algebra_traits::Matrix3d Matrix3d;
+  Matrix3d rotation;
+  rotation.set_coef(0, 0, -0.809204);
+  rotation.set_coef(0, 1, 0.124296);
+  rotation.set_coef(0, 2, 0.574230);
+  rotation.set_coef(1, 0, -0.574694);
+  rotation.set_coef(1, 1, 0.035719);
+  rotation.set_coef(1, 2, -0.817589);
+  rotation.set_coef(2, 0, -0.122134);
+  rotation.set_coef(2, 1, -0.991602);
+  rotation.set_coef(2, 2, 0.042528);
+
+  CGAL_assertion_code(typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits);
+  CGAL_assertion_code(double fitness = CGAL::Optimal_bounding_box::
+      compute_fitness<Linear_algebra_traits> (rotation, data_points));
+  CGAL_assertion(assert_doubles(fitness, 0.58606, 1e-5));
+}
+
+void test_simplex_operations()
+{
+  CGAL_assertion_code(typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits);
+  typedef CGAL::Eigen_dense_matrix<double, 3, 3> Matrix;
+
+  Matrix Sc(3, 3);
+  Sc.set_coef(0, 0, -0.809204);
+  Sc.set_coef(0, 1, 0.124296);
+  Sc.set_coef(0, 2, 0.574230);
+  Sc.set_coef(1, 0, -0.574694);
+  Sc.set_coef(1, 1, 0.035719);
+  Sc.set_coef(1, 2, -0.817589);
+  Sc.set_coef(2, 0, -0.122134);
+  Sc.set_coef(2, 1, -0.991602);
+  Sc.set_coef(2, 2, 0.042528);
+
+  Matrix S_worst(3, 3);
+  S_worst.set_coef(0, 0, -0.45070);
+  S_worst.set_coef(0, 1, -0.32769);
+  S_worst.set_coef(0, 2, -0.83035);
+  S_worst.set_coef(1, 0, -0.13619);
+  S_worst.set_coef(1, 1, -0.89406);
+  S_worst.set_coef(1, 2, 0.42675);
+  S_worst.set_coef(2, 0, -0.88222);
+  S_worst.set_coef(2, 1, 0.30543);
+  S_worst.set_coef(2, 2, 0.35833);
+
+  CGAL_assertion_code(Matrix Sr = CGAL::Optimal_bounding_box::reflection<Linear_algebra_traits>(Sc, S_worst));
+  CGAL_assertion_code(double epsilon = 1e-5);
+  CGAL_assertion(assert_doubles(Sr(0,0), -0.13359, epsilon));
+  CGAL_assertion(assert_doubles(Sr(0,1), -0.95986, epsilon));
+  CGAL_assertion(assert_doubles(Sr(0,2), -0.24664, epsilon));
+  CGAL_assertion(assert_doubles(Sr(1,0), -0.60307, epsilon));
+  CGAL_assertion(assert_doubles(Sr(1,1), -0.11875, epsilon));
+  CGAL_assertion(assert_doubles(Sr(1,2), 0.78880, epsilon));
+  CGAL_assertion(assert_doubles(Sr(2,0), -0.78642, epsilon));
+  CGAL_assertion(assert_doubles(Sr(2,1), 0.25411, epsilon));
+  CGAL_assertion(assert_doubles(Sr(2,2), -0.56300, epsilon));
+
+  CGAL_assertion_code(Matrix Se =
+      CGAL::Optimal_bounding_box::expansion<Linear_algebra_traits>(Sc, S_worst, Sr));
+  CGAL_assertion(assert_doubles(Se(0,0), -0.87991, epsilon));
+  CGAL_assertion(assert_doubles(Se(0,1), 0.36105, epsilon));
+  CGAL_assertion(assert_doubles(Se(0,2), -0.30888, epsilon));
+  CGAL_assertion(assert_doubles(Se(1,0), -0.11816, epsilon));
+  CGAL_assertion(assert_doubles(Se(1,1), -0.79593, epsilon));
+  CGAL_assertion(assert_doubles(Se(1,2), -0.59375, epsilon));
+  CGAL_assertion(assert_doubles(Se(2,0), -0.460215, epsilon));
+  CGAL_assertion(assert_doubles(Se(2,1), -0.48595, epsilon));
+  CGAL_assertion(assert_doubles(Se(2,2), 0.74300, epsilon));
+
+  Matrix S_a(3, 3);
+  S_a.set_coef(0, 0, -0.277970);
+  S_a.set_coef(0, 1, 0.953559);
+  S_a.set_coef(0, 2, 0.116010);
+  S_a.set_coef(1, 0, -0.567497);
+  S_a.set_coef(1, 1, -0.065576);
+  S_a.set_coef(1, 2, -0.820760);
+  S_a.set_coef(2, 0, -0.775035);
+  S_a.set_coef(2, 1, -0.293982);
+  S_a.set_coef(2, 2, 0.559370);
+
+  Matrix S_b(3, 3);
+  S_b.set_coef(0, 0, -0.419979);
+  S_b.set_coef(0, 1, 0.301765);
+  S_b.set_coef(0, 2, -0.8558940);
+  S_b.set_coef(1, 0, -0.653011);
+  S_b.set_coef(1, 1, -0.755415);
+  S_b.set_coef(1, 2, 0.054087);
+  S_b.set_coef(2, 0, -0.630234);
+  S_b.set_coef(2, 1, 0.581624);
+  S_b.set_coef(2, 2, 0.514314);
+
+  CGAL_assertion_code(Matrix S_c =
+      CGAL::Optimal_bounding_box::mean<Linear_algebra_traits>(S_a, S_b));
+  CGAL_assertion(assert_doubles(S_c(0,0), -0.35111, epsilon));
+  CGAL_assertion(assert_doubles(S_c(0,1), 0.79308, epsilon));
+  CGAL_assertion(assert_doubles(S_c(0,2), -0.49774, epsilon));
+  CGAL_assertion(assert_doubles(S_c(1,0), -0.61398, epsilon));
+  CGAL_assertion(assert_doubles(S_c(1,1), -0.59635, epsilon));
+  CGAL_assertion(assert_doubles(S_c(1,2), -0.51710, epsilon));
+  CGAL_assertion(assert_doubles(S_c(2,0), -0.70693, epsilon));
+  CGAL_assertion(assert_doubles(S_c(2,1), 0.12405, epsilon));
+  CGAL_assertion(assert_doubles(S_c(2,2), 0.69632, epsilon));
+}
+
+void test_centroid()
+{
+  CGAL_assertion_code(typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits);
+  typedef CGAL::Eigen_dense_matrix<double, 3, 3> Matrix;
+
+  Matrix S_a;
+  S_a.set_coef(0, 0, -0.588443);
+  S_a.set_coef(0, 1, 0.807140);
+  S_a.set_coef(0, 2, -0.047542);
+  S_a.set_coef(1, 0, -0.786228);
+  S_a.set_coef(1, 1, -0.584933);
+  S_a.set_coef(1, 2, -0.199246);
+  S_a.set_coef(2, 0, -0.188629);
+  S_a.set_coef(2, 1, -0.079867);
+  S_a.set_coef(2, 2, 0.978795);
+
+  Matrix S_b(3, 3);
+  S_b.set_coef(0, 0, -0.2192721);
+  S_b.set_coef(0, 1, 0.2792986);
+  S_b.set_coef(0, 2, -0.9348326);
+  S_b.set_coef(1, 0, -0.7772152);
+  S_b.set_coef(1, 1, -0.6292092);
+  S_b.set_coef(1, 2, -0.005686);
+  S_b.set_coef(2, 0, -0.5897934);
+  S_b.set_coef(2, 1, 0.7253193);
+  S_b.set_coef(2, 2, 0.3550431);
+
+  Matrix S_c(3, 3);
+  S_c.set_coef(0, 0, -0.32657);
+  S_c.set_coef(0, 1, -0.60013);
+  S_c.set_coef(0, 2, -0.730206);
+  S_c.set_coef(1, 0, -0.20022);
+  S_c.set_coef(1, 1, -0.71110);
+  S_c.set_coef(1, 2, 0.67398);
+  S_c.set_coef(2, 0, -0.92372);
+  S_c.set_coef(2, 1, 0.36630);
+  S_c.set_coef(2, 2, 0.11207);
+
+  CGAL_assertion_code(Matrix S_centroid =
+      CGAL::Optimal_bounding_box::nm_centroid<Linear_algebra_traits>(S_a, S_b, S_c));
+  CGAL_assertion_code(double epsilon = 1e-5);
+  CGAL_assertion(assert_doubles(S_centroid(0,0), -0.419979, epsilon));
+  CGAL_assertion(assert_doubles(S_centroid(0,1), 0.301765, epsilon));
+  CGAL_assertion(assert_doubles(S_centroid(0,2), -0.855894, epsilon));
+  CGAL_assertion(assert_doubles(S_centroid(1,0), -0.653011, epsilon));
+  CGAL_assertion(assert_doubles(S_centroid(1,1), -0.755415, epsilon));
+  CGAL_assertion(assert_doubles(S_centroid(1,2), 0.054087, epsilon));
+  CGAL_assertion(assert_doubles(S_centroid(2,0), -0.630234, epsilon));
+  CGAL_assertion(assert_doubles(S_centroid(2,1), 0.581624, epsilon));
+  CGAL_assertion(assert_doubles(S_centroid(2,2), 0.514314, epsilon));
+}
+
+void test_eigen_matrix_interface()
+{
+  CGAL_assertion_code(typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits);
+  typedef CGAL::Eigen_dense_matrix<double, 3, 3> Matrix;
+
+  Matrix A(3, 3);
+  A.set_coef(0, 0, 0.1);
+  A.set_coef(0, 1, 0.2);
+  A.set_coef(0, 2, 0.3);
+  A.set_coef(1, 0, 0.4);
+  A.set_coef(1, 1, 0.5);
+  A.set_coef(1, 2, 0.6);
+  A.set_coef(2, 0, 0.7);
+  A.set_coef(2, 1, 0.8);
+  A.set_coef(2, 2, 0.9);
+  CGAL_assertion_code(Matrix B);
+  CGAL_assertion_code(B = CGAL::Eigen_linear_algebra_traits::transpose(A));
+  CGAL_assertion_code(Matrix S);
+  CGAL_assertion_code(S = 0.5 * A);
+  Matrix C(3,3);
+  C.set_coef(0, 0, 0.3011944);
+  C.set_coef(0, 1, 0.9932761);
+  C.set_coef(0, 2, 0.5483701);
+  C.set_coef(1, 0, 0.5149142);
+  C.set_coef(1, 1, 0.5973263);
+  C.set_coef(1, 2, 0.5162336);
+  C.set_coef(2, 0, 0.0039213);
+  C.set_coef(2, 1, 0.0202949);
+  C.set_coef(2, 2, 0.9240308);
+
+  CGAL_assertion_code(Matrix Q = CGAL::Eigen_linear_algebra_traits::qr_factorization(C));
+  CGAL_assertion_code(double epsilon = 1e-5);
+  CGAL_assertion(assert_doubles(Q(0,0), -0.504895, epsilon));
+  CGAL_assertion(assert_doubles(Q(0,1), 0.862834, epsilon));
+  CGAL_assertion(assert_doubles(Q(0,2), -0.024447, epsilon));
+  CGAL_assertion(assert_doubles(Q(1,0), -0.863156, epsilon));
+  CGAL_assertion(assert_doubles(Q(1,1), -0.504894, epsilon));
+  CGAL_assertion(assert_doubles(Q(1,2), 0.006687, epsilon));
+  CGAL_assertion(assert_doubles(Q(2,0), -0.006573, epsilon));
+  CGAL_assertion(assert_doubles(Q(2,1), 0.024478, epsilon));
+  CGAL_assertion(assert_doubles(Q(2,2), 0.999679, epsilon));
+
+  Matrix D(3,3);
+  D.set_coef(0, 0, -0.809204);
+  D.set_coef(0, 1, 0.124296);
+  D.set_coef(0, 2, 0.574230);
+  D.set_coef(1, 0, -0.574694);
+  D.set_coef(1, 1, 0.035719);
+  D.set_coef(1, 2, -0.817589);
+  D.set_coef(2, 0, -0.122134);
+  D.set_coef(2, 1, -0.991602);
+  D.set_coef(2, 2, 0.042528);
+
+  Matrix E(3,3);
+  E.set_coef(0, 0, -0.45070);
+  E.set_coef(0, 1, -0.32769);
+  E.set_coef(0, 2, -0.83035);
+  E.set_coef(1, 0, -0.13619);
+  E.set_coef(1, 1, -0.89406);
+  E.set_coef(1, 2, 0.42675);
+  E.set_coef(2, 0, -0.88222);
+  E.set_coef(2, 1, 0.30543);
+  E.set_coef(2, 2, 0.35833);
+
+  CGAL_assertion_code(Matrix Sr = CGAL::Optimal_bounding_box::reflection<Linear_algebra_traits>(D, E));
+  CGAL_assertion(assert_doubles(Sr(0,0), -0.13359, epsilon));
+  CGAL_assertion(assert_doubles(Sr(0,1), -0.95986, epsilon));
+  CGAL_assertion(assert_doubles(Sr(0,2), -0.24664, epsilon));
+  CGAL_assertion(assert_doubles(Sr(1,0), -0.60307, epsilon));
+  CGAL_assertion(assert_doubles(Sr(1,1), -0.11875, epsilon));
+  CGAL_assertion(assert_doubles(Sr(1,2), 0.78880, epsilon));
+  CGAL_assertion(assert_doubles(Sr(2,0), -0.78642, epsilon));
+  CGAL_assertion(assert_doubles(Sr(2,1), 0.25411, epsilon));
+  CGAL_assertion(assert_doubles(Sr(2,2), -0.56300, epsilon));
+}
+
+int main()
+{
+  test_qr_factorization();
+  test_fitness_function();
+  test_simplex_operations();
+  test_centroid();
+  test_eigen_matrix_interface();
+
+  return 0;
+}
diff --git a/Optimal_bounding_box/test/Optimal_bounding_box/test_optimization_algorithms.cpp b/Optimal_bounding_box/test/Optimal_bounding_box/test_optimization_algorithms.cpp
new file mode 100644
index 00000000000..4f03054dcbd
--- /dev/null
+++ b/Optimal_bounding_box/test/Optimal_bounding_box/test_optimization_algorithms.cpp
@@ -0,0 +1,423 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/Surface_mesh.h>
+
+#include <CGAL/Eigen_linear_algebra_traits.h>
+#include <CGAL/Optimal_bounding_box/population.h>
+#include <CGAL/Optimal_bounding_box/optimal_bounding_box.h>
+#include <CGAL/Optimal_bounding_box/helper.h>
+#include <CGAL/Optimal_bounding_box/nelder_mead_functions.h>
+
+#include <iostream>
+#include <fstream>
+
+typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
+
+bool assert_doubles(double d1, double d2, double epsilon)
+{
+  return (d1 < d2 + epsilon && d1 > d2 - epsilon) ? true : false;
+}
+
+void test_nelder_mead()
+{
+  typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits;
+  typedef Linear_algebra_traits::Matrix3d Matrix3d;
+  typedef Linear_algebra_traits::MatrixXd MatrixXd;
+
+  MatrixXd data_points(4,3);
+  data_points(0,0) = 0.866802;
+  data_points(0,1) = 0.740808,
+  data_points(0,2) = 0.895304,
+  data_points(1,0) = 0.912651;
+  data_points(1,1) = 0.761565;
+  data_points(1,2) = 0.160330;
+  data_points(2,0) = 0.093661;
+  data_points(2,1) = 0.892578;
+  data_points(2,2) = 0.737412;
+  data_points(3,0) = 0.166461;
+  data_points(3,1) = 0.149912,
+  data_points(3,2) = 0.364944;
+
+  // one simplex
+  std::vector<Matrix3d> simplex(4);
+  Matrix3d v0(3,3);
+  Matrix3d v1(3,3);
+  Matrix3d v2(3,3);
+  Matrix3d v3(3,3);
+
+  v0(0,0) = -0.2192721;
+  v0(0,1) = 0.2792986,
+  v0(0,2) = -0.9348326,
+  v0(1,0) = -0.7772152;
+  v0(1,1) = -0.6292092;
+  v0(1,2) = -0.0056861;
+  v0(2,0) = -0.5897934;
+  v0(2,1) = 0.7253193;
+  v0(2,2) = 0.3550431;
+
+  v1(0,0) = -0.588443;
+  v1(0,1) = 0.807140;
+  v1(0,2) = -0.047542;
+  v1(1,0) = -0.786228;
+  v1(1,1) = -0.584933;
+  v1(1,2) = -0.199246;
+  v1(2,0) = -0.188629;
+  v1(2,1) = -0.079867;
+  v1(2,2) = 0.978795;
+
+  v2(0,0) = -0.277970;
+  v2(0,1) = 0.953559;
+  v2(0,2) = 0.116010;
+  v2(1,0) = -0.567497;
+  v2(1,1) = -0.065576;
+  v2(1,2) = -0.820760;
+  v2(2,0) = -0.775035;
+  v2(2,1) = -0.293982;
+  v2(2,2) = 0.559370;
+
+  v3(0,0) = -0.32657;
+  v3(0,1) = -0.60013;
+  v3(0,2) = -0.73020;
+  v3(1,0) = -0.20022;
+  v3(1,1) = -0.71110;
+  v3(1,2) = 0.67398;
+  v3(2,0) = -0.92372;
+  v3(2,1) = 0.36630;
+  v3(2,2) = 0.11207;
+
+  simplex[0] = v0;
+  simplex[1] = v1;
+  simplex[2] = v2;
+  simplex[3] = v3;
+
+  std::size_t nm_iterations = 19;
+  CGAL::Optimal_bounding_box::nelder_mead<Linear_algebra_traits>(simplex, data_points, nm_iterations);
+
+  CGAL_assertion_code(double epsilon = 1e-5);
+  CGAL_assertion_code(Matrix3d v0_new = simplex[0]);
+  CGAL_assertion(assert_doubles(v0_new(0,0), -0.288975, epsilon));
+  CGAL_assertion(assert_doubles(v0_new(0,1), 0.7897657, epsilon));
+  CGAL_assertion(assert_doubles(v0_new(0,2), -0.541076, epsilon));
+  CGAL_assertion(assert_doubles(v0_new(1,0), -0.9407046, epsilon));
+  CGAL_assertion(assert_doubles(v0_new(1,1), -0.3391466, epsilon));
+  CGAL_assertion(assert_doubles(v0_new(1,2), 0.0073817, epsilon));
+  CGAL_assertion(assert_doubles(v0_new(2,0), -0.1776743, epsilon));
+  CGAL_assertion(assert_doubles(v0_new(2,1), 0.5111260, epsilon));
+  CGAL_assertion(assert_doubles(v0_new(2,2), 0.84094, epsilon));
+
+  CGAL_assertion_code(Matrix3d v1_new = simplex[1]);
+  CGAL_assertion(assert_doubles(v1_new(0,0), -0.458749, epsilon));
+  CGAL_assertion(assert_doubles(v1_new(0,1), 0.823283, epsilon));
+  CGAL_assertion(assert_doubles(v1_new(0,2), -0.334296, epsilon));
+  CGAL_assertion(assert_doubles(v1_new(1,0), -0.885235, epsilon));
+  CGAL_assertion(assert_doubles(v1_new(1,1), -0.455997, epsilon));
+  CGAL_assertion(assert_doubles(v1_new(1,2), 0.091794, epsilon));
+  CGAL_assertion(assert_doubles(v1_new(2,0), -0.076866, epsilon));
+  CGAL_assertion(assert_doubles(v1_new(2,1), 0.338040, epsilon));
+  CGAL_assertion(assert_doubles(v1_new(2,2), 0.937987, epsilon));
+
+  CGAL_assertion_code(Matrix3d v2_new = simplex[2]);
+  CGAL_assertion(assert_doubles(v2_new(0,0), -0.346582, epsilon));
+  CGAL_assertion(assert_doubles(v2_new(0,1), 0.878534, epsilon));
+  CGAL_assertion(assert_doubles(v2_new(0,2), -0.328724, epsilon));
+  CGAL_assertion(assert_doubles(v2_new(1,0), -0.936885, epsilon));
+  CGAL_assertion(assert_doubles(v2_new(1,1), -0.341445, epsilon));
+  CGAL_assertion(assert_doubles(v2_new(1,2), 0.075251, epsilon));
+  CGAL_assertion(assert_doubles(v2_new(2,0), -0.046131, epsilon));
+  CGAL_assertion(assert_doubles(v2_new(2,1), 0.334057, epsilon));
+  CGAL_assertion(assert_doubles(v2_new(2,2), 0.941423, epsilon));
+
+  CGAL_assertion_code(Matrix3d v3_new = simplex[3]);
+  CGAL_assertion(assert_doubles(v3_new(0,0), -0.394713, epsilon));
+  CGAL_assertion(assert_doubles(v3_new(0,1), 0.791782, epsilon));
+  CGAL_assertion(assert_doubles(v3_new(0,2), -0.466136, epsilon));
+  CGAL_assertion(assert_doubles(v3_new(1,0), -0.912112, epsilon));
+  CGAL_assertion(assert_doubles(v3_new(1,1), -0.398788, epsilon));
+  CGAL_assertion(assert_doubles(v3_new(1,2), 0.094972, epsilon));
+  CGAL_assertion(assert_doubles(v3_new(2,0), -0.110692, epsilon));
+  CGAL_assertion(assert_doubles(v3_new(2,1), 0.462655, epsilon));
+  CGAL_assertion(assert_doubles(v3_new(2,2), 0.879601, epsilon));
+}
+
+void test_genetic_algorithm()
+{
+  CGAL::Eigen_dense_matrix<double, -1, -1> data_points(4, 3); // -1 = dynamic size at run time
+  data_points(0,0) = 0.866802;
+  data_points(0,1) = 0.740808,
+  data_points(0,2) = 0.895304,
+  data_points(1,0) = 0.912651;
+  data_points(1,1) = 0.761565;
+  data_points(1,2) = 0.160330;
+  data_points(2,0) = 0.093661;
+  data_points(2,1) = 0.892578;
+  data_points(2,2) = 0.737412;
+  data_points(3,0) = 0.166461;
+  data_points(3,1) = 0.149912,
+  data_points(3,2) = 0.364944;
+
+  typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits;
+  CGAL::Optimal_bounding_box::Population<Linear_algebra_traits> pop(5);
+  CGAL::Optimal_bounding_box::Evolution<Linear_algebra_traits> evolution(pop, data_points);
+  evolution.genetic_algorithm();
+  CGAL_assertion(pop.size() == 5);
+}
+
+void test_random_unit_tetra()
+{
+  // this is dynamic at run times
+  CGAL::Eigen_dense_matrix<double, -1, -1> data_points(4, 3);
+
+  // points are on their convex hull
+  data_points(0,0) = 0.866802;
+  data_points(0,1) = 0.740808,
+  data_points(0,2) = 0.895304,
+  data_points(1,0) = 0.912651;
+  data_points(1,1) = 0.761565;
+  data_points(1,2) = 0.160330;
+  data_points(2,0) = 0.093661;
+  data_points(2,1) = 0.892578;
+  data_points(2,2) = 0.737412;
+  data_points(3,0) = 0.166461;
+  data_points(3,1) = 0.149912,
+  data_points(3,2) = 0.364944;
+
+  typedef CGAL::Simple_cartesian<double> K;
+  typedef K::Point_3 Point;
+  typedef CGAL::Surface_mesh<Point> Mesh;
+
+  // make a mesh and export it
+  Mesh mesh;
+  Point p1(0.866802, 0.740808, 0.895304);
+  Point p2(0.912651, 0.761565, 0.160330);
+  Point p3(0.093661, 0.892578, 0.737412);
+  Point p4(0.166461, 0.149912, 0.364944);
+  CGAL::make_tetrahedron(p1, p2, p3, p4, mesh);
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_TEST
+  std::ofstream out("data/random_unit_tetra.off");
+  out << mesh;
+  out.close();
+#endif
+
+  typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits;
+  CGAL_assertion_code(typedef Linear_algebra_traits::Matrix3d Matrix3d);
+  std::size_t generations = 10;
+  CGAL::Optimal_bounding_box::Population<Linear_algebra_traits> pop(50);
+  CGAL::Optimal_bounding_box::Evolution<Linear_algebra_traits> evolution(pop, data_points);
+  evolution.evolve(generations);
+
+  CGAL_assertion_code(Matrix3d R = evolution.get_best());
+  CGAL_assertion_code(double epsilon = 1e-3);
+  CGAL_assertion(assert_doubles(Linear_algebra_traits::determinant(R), 1, epsilon));
+  CGAL_assertion(assert_doubles(R(0,0), -0.25791, epsilon));
+  CGAL_assertion(assert_doubles(R(0,1), 0.796512, epsilon));
+  CGAL_assertion(assert_doubles(R(0,2), -0.546855, epsilon));
+  CGAL_assertion(assert_doubles(R(1,0), -0.947128, epsilon));
+  CGAL_assertion(assert_doubles(R(1,1), -0.320242, epsilon));
+  CGAL_assertion(assert_doubles(R(1,2), -0.0197553, epsilon));
+  CGAL_assertion(assert_doubles(R(2,0), -0.190861, epsilon));
+  CGAL_assertion(assert_doubles(R(2,1), 0.512847, epsilon));
+  CGAL_assertion(assert_doubles(R(2,2), 0.836992, epsilon));
+
+#ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_TEST
+  // postprocessing
+  CGAL::Eigen_dense_matrix<double> obb(8, 3);
+  CGAL::Optimal_bounding_box::post_processing(data_points, R, obb);
+  CGAL::Optimal_bounding_box::matrix_to_mesh_and_draw(obb, "data/random_unit_tetra_result.off");
+#endif
+}
+
+void test_reference_tetrahedron(const char* fname)
+{
+  std::ifstream input(fname);
+  CGAL::Surface_mesh<K::Point_3> mesh;
+  if (!input || !(input >> mesh) || mesh.is_empty()) {
+    std::cerr << fname << " is not a valid off file.\n";
+    std::exit(1);
+  }
+
+  typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits;
+  typedef Linear_algebra_traits::MatrixXd MatrixXd;
+  CGAL_assertion_code(typedef Linear_algebra_traits::Matrix3d Matrix3d);
+
+  // points in a matrix
+  MatrixXd points;
+  CGAL::Optimal_bounding_box::sm_to_matrix(mesh, points);
+
+  std::size_t generations = 10;
+  CGAL::Optimal_bounding_box::Population<Linear_algebra_traits> pop(50);
+  CGAL::Optimal_bounding_box::Evolution<Linear_algebra_traits> experiment(pop, points);
+  experiment.evolve(generations);
+
+  CGAL_assertion_code(Matrix3d R = experiment.get_best());
+  CGAL_assertion_code(double epsilon = 1e-5);
+  CGAL_assertion(assert_doubles(Linear_algebra_traits::determinant(R), 1, epsilon));
+
+  #ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_TEST
+  // postprocessing
+  MatrixXd obb(8, 3);
+  CGAL::Optimal_bounding_box::post_processing(points, R, obb);
+  CGAL::Optimal_bounding_box::matrix_to_mesh_and_draw(obb, "data/OBB.off");
+  #endif
+}
+
+void test_long_tetrahedron(std::string fname)
+{
+  std::ifstream input(fname);
+  CGAL::Surface_mesh<K::Point_3> mesh;
+  if (!input || !(input >> mesh) || mesh.is_empty()) {
+    std::cerr << fname << " is not a valid off file.\n";
+    std::exit(1);
+  }
+
+  typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits;
+  typedef Linear_algebra_traits::MatrixXd MatrixXd;
+  CGAL_assertion_code(typedef Linear_algebra_traits::Matrix3d Matrix3d);
+
+  // points in a matrix
+  MatrixXd points;
+  CGAL::Optimal_bounding_box::sm_to_matrix(mesh, points);
+
+  std::size_t max_generations = 10;
+  CGAL::Optimal_bounding_box::Population<Linear_algebra_traits> pop(50);
+  CGAL::Optimal_bounding_box::Evolution<Linear_algebra_traits> experiment(pop, points);
+  experiment.evolve(max_generations);
+
+  CGAL_assertion_code(Matrix3d R = experiment.get_best());
+  CGAL_assertion_code(double epsilon = 1e-3);
+  CGAL_assertion(assert_doubles(Linear_algebra_traits::determinant(R), 1, epsilon));
+  CGAL_assertion(assert_doubles(R(0,0), -1, epsilon));
+  CGAL_assertion(assert_doubles(R(0,1), 0, epsilon));
+  CGAL_assertion(assert_doubles(R(0,2), 0, epsilon));
+  CGAL_assertion(assert_doubles(R(1,0), 0, epsilon));
+  CGAL_assertion(assert_doubles(R(1,1), -0.707107, epsilon));
+  CGAL_assertion(assert_doubles(R(1,2), 0.707106, epsilon) ||
+                 assert_doubles(R(1,2), -0.707106, epsilon));
+  CGAL_assertion(assert_doubles(R(2,0), 0, epsilon));
+  CGAL_assertion(assert_doubles(R(2,1), 0.707106, epsilon) ||
+                 assert_doubles(R(1,2), -0.707106, epsilon));
+  CGAL_assertion(assert_doubles(R(2,2), 0.707107, epsilon));
+
+  #ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_TEST
+  // postprocessing
+  MatrixXd obb(8, 3);
+  CGAL::Optimal_bounding_box::post_processing(points, R, obb);
+  CGAL::Optimal_bounding_box::matrix_to_mesh_and_draw(obb, fname + "result.off");
+  #endif
+}
+
+void test_compute_obb_evolution(std::string fname)
+{
+  std::ifstream input(fname);
+  typedef CGAL::Surface_mesh<K::Point_3> SMesh;
+  SMesh mesh;
+  if (!input || !(input >> mesh) || mesh.is_empty()) {
+    std::cerr << fname << " is not a valid off file.\n";
+    std::exit(1);
+  }
+  // get mesh points
+  std::vector<K::Point_3> sm_points;
+  typedef typename boost::graph_traits<SMesh>::vertex_descriptor vertex_descriptor;
+  typedef typename boost::property_map<SMesh, boost::vertex_point_t>::const_type PointPMap;
+  PointPMap pmap = get(boost::vertex_point, mesh);
+  BOOST_FOREACH(vertex_descriptor v, vertices(mesh))
+    sm_points.push_back(get(pmap, v));
+
+
+  CGAL::Eigen_linear_algebra_traits la_traits;
+  std::vector<K::Point_3> obb_points;
+  CGAL::Optimal_bounding_box::compute_optimal_bounding_box(sm_points, obb_points, la_traits, true);
+
+  CGAL_assertion_code(double epsilon = 1e-3);
+  CGAL_assertion_code(double vol = CGAL::Optimal_bounding_box::calculate_volume(obb_points));
+  CGAL_assertion(assert_doubles(vol, 0.883371, epsilon));
+
+  #ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_TEST
+  /*
+  for(int i = 0; i < 8; ++i)
+    std::cout << obb_points[i].x() << " " << obb_points[i].y() << " " << obb_points[i].z() << "\n" ;
+  */
+  CGAL::Surface_mesh<K::Point_3> result_mesh;
+  CGAL::make_hexahedron(obb_points[0], obb_points[1], obb_points[2], obb_points[3],
+                        obb_points[4], obb_points[5], obb_points[6], obb_points[7], result_mesh);
+
+  std::ofstream out("data/obb_result.off");
+  out << result_mesh;
+  out.close();
+  #endif
+}
+
+void test_compute_obb_mesh(std::string fname)
+{
+  std::ifstream input(fname);
+  CGAL::Surface_mesh<K::Point_3> mesh;
+  if (!input || !(input >> mesh) || mesh.is_empty())
+  {
+    std::cerr << fname << " is not a valid off file.\n";
+    std::exit(1);
+  }
+
+  CGAL::Eigen_linear_algebra_traits la_traits;
+  CGAL::Surface_mesh< K::Point_3> obbmesh;
+  CGAL::Optimal_bounding_box::compute_optimal_bounding_box(mesh, obbmesh, la_traits, true);
+
+  #ifdef CGAL_OPTIMAL_BOUNDING_BOX_DEBUG_TEST
+  std::ofstream out("/tmp/result_elephant.off");
+  out << obbmesh;
+  out.close();
+  #endif
+}
+
+void test_function_defaults_traits(std::string fname1, std::string fname2)
+{
+  std::ifstream input1(fname1);
+  CGAL::Surface_mesh<K::Point_3> mesh1;
+  if (!input1 || !(input1 >> mesh1) || mesh1.is_empty())
+  {
+    std::cerr << fname1 << " is not a valid off file.\n";
+    std::exit(1);
+  }
+
+  std::ifstream input2(fname2);
+  CGAL::Surface_mesh<K::Point_3> mesh2;
+  if (!input2 || !(input2 >> mesh2) || mesh2.is_empty())
+  {
+    std::cerr << fname2 << " is not a valid off file.\n";
+    std::exit(1);
+  }
+
+  // test one
+  std::vector<K::Point_3> sm_points;
+  typedef CGAL::Surface_mesh<K::Point_3> SMesh;
+  typedef typename boost::graph_traits<SMesh>::vertex_descriptor vertex_descriptor;
+  typedef typename boost::property_map<SMesh, boost::vertex_point_t>::const_type PointPMap;
+  PointPMap pmap = get(boost::vertex_point, mesh1);
+
+  BOOST_FOREACH(vertex_descriptor v, vertices(mesh1))
+    sm_points.push_back(get(pmap, v));
+
+  std::vector<K::Point_3> obb_points;
+  CGAL::Optimal_bounding_box::compute_optimal_bounding_box(sm_points, obb_points, true);
+
+  CGAL_assertion_code(double epsilon = 1e-3);
+  CGAL_assertion_code(double vol = CGAL::Optimal_bounding_box::calculate_volume(obb_points));
+  CGAL_assertion(assert_doubles(vol, 0.883371, epsilon));
+
+  // test two
+  CGAL::Surface_mesh< K::Point_3> obbmesh;
+  CGAL::Optimal_bounding_box::compute_optimal_bounding_box(mesh2, obbmesh, true);
+}
+
+int main()
+{
+  test_nelder_mead();
+  test_genetic_algorithm();
+  test_random_unit_tetra();
+  test_reference_tetrahedron("data/reference_tetrahedron.off");
+  test_long_tetrahedron("data/long_tetrahedron.off");
+  test_compute_obb_evolution("data/random_unit_tetra.off");
+  test_compute_obb_mesh("data/elephant.off");
+  test_function_defaults_traits("data/random_unit_tetra.off", "data/elephant.off");
+
+  return 0;
+}
diff --git a/Polyhedron/demo/Polyhedron/Plugins/PCA/CMakeLists.txt b/Polyhedron/demo/Polyhedron/Plugins/PCA/CMakeLists.txt
index f86989e9000..d8ba5ededb3 100644
--- a/Polyhedron/demo/Polyhedron/Plugins/PCA/CMakeLists.txt
+++ b/Polyhedron/demo/Polyhedron/Plugins/PCA/CMakeLists.txt
@@ -17,6 +17,9 @@ target_link_libraries(clipping_box_plugin PUBLIC  scene_edit_box_item scene_basi
 polyhedron_demo_plugin(create_bbox_mesh_plugin Create_bbox_mesh_plugin)
 target_link_libraries(create_bbox_mesh_plugin PUBLIC scene_surface_mesh_item)
 
+polyhedron_demo_plugin(create_obb_mesh_plugin Create_obb_mesh_plugin)
+target_link_libraries(create_obb_mesh_plugin PUBLIC scene_surface_mesh_item scene_polyhedron_item scene_polyhedron_selection_item scene_points_with_normal_item)
+
 qt5_wrap_ui( volumesUI_FILES Basic_generator_widget.ui)
 polyhedron_demo_plugin(basic_generator_plugin Basic_generator_plugin ${volumesUI_FILES} KEYWORDS PolygonMesh PointSetProcessing)
 target_link_libraries(basic_generator_plugin PUBLIC scene_surface_mesh_item scene_points_with_normal_item scene_polylines_item)
diff --git a/Polyhedron/demo/Polyhedron/Plugins/PCA/Create_obb_mesh_plugin.cpp b/Polyhedron/demo/Polyhedron/Plugins/PCA/Create_obb_mesh_plugin.cpp
new file mode 100644
index 00000000000..444f0b2acc9
--- /dev/null
+++ b/Polyhedron/demo/Polyhedron/Plugins/PCA/Create_obb_mesh_plugin.cpp
@@ -0,0 +1,191 @@
+#include <QtCore/qglobal.h>
+#include <CGAL/Three/Scene_item.h>
+#include <CGAL/Three/Scene_interface.h>
+
+#include <QAction>
+#include <QMainWindow>
+#include <QApplication>
+
+#include "Scene_surface_mesh_item.h"
+#include "Polyhedron_type.h"
+#include "Scene_polyhedron_item.h"
+#include <CGAL/Three/Polyhedron_demo_plugin_interface.h>
+#include "Scene_polyhedron_selection_item.h"
+#include "Scene_points_with_normal_item.h"
+
+#include <boost/graph/graph_traits.hpp>
+#include <CGAL/Optimal_bounding_box/optimal_bounding_box.h>
+#include <CGAL/Eigen_linear_algebra_traits.h>
+
+//typedef Scene_surface_mesh_item Scene_facegraph_item;
+//typedef Scene_facegraph_item Scene_facegraph_item;
+
+typedef Scene_facegraph_item::Face_graph FaceGraph;
+typedef Polyhedron::Point_3 Point_3;
+using namespace CGAL::Three;
+
+class Create_obb_mesh_plugin :
+  public QObject,
+  public CGAL::Three::Polyhedron_demo_plugin_interface
+{
+  Q_OBJECT
+  Q_INTERFACES(CGAL::Three::Polyhedron_demo_plugin_interface)
+  Q_PLUGIN_METADATA(IID "com.geometryfactory.PolyhedronDemo.PluginInterface/1.0")
+
+public:
+  void init(QMainWindow* mainWindow, Scene_interface* scene_interface, Messages_interface*);
+  QList<QAction*> actions() const;
+
+  bool applicable(QAction*) const {
+
+    /*
+    if (scene->selectionIndices().size() == 1)
+    {
+    return qobject_cast<Scene_facegraph_item*>(scene->item(scene->mainSelectionIndex()))
+    || qobject_cast<Scene_polyhedron_selection_item*>(scene->item(scene->mainSelectionIndex()));
+    }
+
+    Q_FOREACH(int index, scene->selectionIndices())
+    {
+      if (qobject_cast<Scene_facegraph_item*>(scene->item(index)))
+        return true;
+    }
+    return false;
+    */
+
+    if(scene->mainSelectionIndex() != -1
+       && scene->item(scene->mainSelectionIndex())->isFinite())
+      return true;
+  return false;
+
+}
+
+protected:
+  void gather_mesh_points(std::vector<Point_3>& points);
+  void obb();
+
+public Q_SLOTS:
+  void createObb() {
+    QApplication::setOverrideCursor(Qt::WaitCursor);
+    obb();
+    QApplication::restoreOverrideCursor();
+  }
+
+private:
+  Scene_interface* scene;
+  QMainWindow* mw;
+  QAction* actionObb;
+
+}; // end Create_obb_mesh_plugin class
+
+
+
+void Create_obb_mesh_plugin::init(QMainWindow* mainWindow, Scene_interface* scene_interface, Messages_interface*)
+{
+  scene = scene_interface;
+  mw = mainWindow;
+  actionObb = new QAction(tr("Create &Optimal Bbox Mesh"), mainWindow);
+  actionObb->setObjectName("createObbMeshAction");
+  connect(actionObb, SIGNAL(triggered()), this, SLOT(createObb()));
+}
+
+QList<QAction*> Create_obb_mesh_plugin::actions() const {
+  return QList<QAction*>() << actionObb;
+}
+
+
+void Create_obb_mesh_plugin::gather_mesh_points(std::vector<Point_3>& points)
+{
+  const Scene_interface::Item_id index = scene->mainSelectionIndex();
+
+  Scene_facegraph_item* poly_item =
+    qobject_cast<Scene_facegraph_item*>(scene->item(index));
+
+  Scene_polyhedron_selection_item* selection_item =
+    qobject_cast<Scene_polyhedron_selection_item*>(scene->item(index));
+
+  Scene_points_with_normal_item* point_set_item =
+    qobject_cast<Scene_points_with_normal_item*>(scene->item(index));
+
+  if(poly_item || selection_item)
+  {
+    typedef typename boost::property_map<FaceGraph, boost::vertex_point_t>::type PointPMap;
+    typedef typename boost::graph_traits<FaceGraph>::vertex_descriptor vertex_descriptor;
+    typedef typename boost::graph_traits<FaceGraph>::face_descriptor face_descriptor;
+
+    std::vector<vertex_descriptor> selected_vertices;
+
+    if(poly_item != NULL)
+    {
+      FaceGraph& pmesh = *poly_item->polyhedron();
+      selected_vertices.assign(vertices(pmesh).begin(), vertices(pmesh).end());
+      PointPMap pmap = get(CGAL::vertex_point, pmesh);
+      BOOST_FOREACH(vertex_descriptor v, selected_vertices)
+        points.push_back(get(pmap, v));
+
+    }
+    else if(selection_item != NULL) // using selection of faces
+    {
+      FaceGraph& pmesh = *selection_item->polyhedron();
+      BOOST_FOREACH(face_descriptor f, selection_item->selected_facets)
+      {
+        BOOST_FOREACH(vertex_descriptor v, vertices_around_face(halfedge(f, pmesh), pmesh))
+        {
+          selected_vertices.push_back(v);
+        }
+      }
+
+      PointPMap pmap = get(CGAL::vertex_point, pmesh);
+      BOOST_FOREACH(vertex_descriptor v, selected_vertices)
+        points.push_back(get(pmap, v));
+    }
+    CGAL_assertion(points.size() >= 3);
+  }
+
+  if(point_set_item)
+  {
+    Point_set* points_set = point_set_item->point_set();
+    if(points_set == NULL)
+        return;
+
+    std::cout << "points_set->size()= " << points_set->size() << std::endl;
+    BOOST_FOREACH(Point_3 p, points_set->points())
+    {
+      points.push_back(p);
+    }
+  }
+
+}
+
+void Create_obb_mesh_plugin::obb()
+{
+  // gather point coordinates
+  std::vector<Point_3> points;
+  gather_mesh_points(points);
+
+  // find obb
+  CGAL::Eigen_linear_algebra_traits la_traits;
+  std::vector<Point_3> obb_points(8);
+  CGAL::Optimal_bounding_box::compute_optimal_bounding_box(points, obb_points, la_traits, true);
+
+  Scene_item* item;
+  if(mw->property("is_polyhedorn_mode").toBool())
+  {
+    Polyhedron* p = new Polyhedron;
+    CGAL::make_hexahedron(obb_points[0], obb_points[1], obb_points[2], obb_points[3],
+                          obb_points[4], obb_points[5], obb_points[6], obb_points[7], *p);
+    item = new Scene_polyhedron_item(p);
+  }
+  else {
+    SMesh* p = new SMesh;
+    CGAL::make_hexahedron(obb_points[0], obb_points[1], obb_points[2], obb_points[3],
+                          obb_points[4], obb_points[5], obb_points[6], obb_points[7], *p);
+    item = new Scene_surface_mesh_item(p);
+  }
+
+  item->setName("Optimal bbox mesh");
+  item->setRenderingMode(Wireframe);
+  scene->addItem(item);
+}
+
+#include "Create_obb_mesh_plugin.moc"
diff --git a/Solver_interface/include/CGAL/Eigen_linear_algebra_traits.h b/Solver_interface/include/CGAL/Eigen_linear_algebra_traits.h
new file mode 100644
index 00000000000..e56f1775f53
--- /dev/null
+++ b/Solver_interface/include/CGAL/Eigen_linear_algebra_traits.h
@@ -0,0 +1,326 @@
+// Copyright (c) 2018 GeometryFactory (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+// You can redistribute it and/or modify it under the terms of the GNU
+// General Public License as published by the Free Software Foundation,
+// either version 3 of the License, or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0+
+//
+//
+// Author(s)     : Konstantinos Katrioplas
+
+#ifndef CGAL_EIGEN_LINEAR_ALGEBRA_TRAITS_H
+#define CGAL_EIGEN_LINEAR_ALGEBRA_TRAITS_H
+
+#include <CGAL/basic.h>
+#include <Eigen/Dense>
+#include <Eigen/QR>
+
+
+namespace CGAL {
+
+
+template<typename T, int D = Eigen::Dynamic>
+class Eigen_dense_vector;
+
+/*!
+\ingroup PkgSolver
+
+The class `Eigen_dense_matrix` is a wrapper around \ref thirdpartyEigen "Eigen" matrix type
+<a href="http://eigen.tuxfamily.org/dox/classEigen_1_1SparseMatrix.html">`Eigen::DenseMatrix`</a>.
+
+\tparam T Number type.
+\tparam D1 Number of rows, or Dynamic.
+\tparam D1 Number of cols, or Dynamic.
+
+\sa `CGAL::Eigen_dense_vector<T, D>`
+\sa `CGAL::Eigen_linear_algebra_traits`
+*/
+template<typename T, int D1 = Eigen::Dynamic, int D2 = Eigen::Dynamic>
+class Eigen_dense_matrix
+{
+public:
+
+  /// The internal matrix type from \ref thirdpartyEigen "Eigen".
+  typedef Eigen::Matrix<T, D1, D2> EigenType;
+
+  /// Create a dense matrix
+  Eigen_dense_matrix(std::size_t nrows, std::size_t ncols)
+    : m_matrix(static_cast<int>(nrows), static_cast<int>(ncols))
+  {
+    CGAL_assertion(m_matrix.rows() > 0);
+    CGAL_assertion(m_matrix.cols() > 0);
+  }
+
+  /// Create a dense matrix
+  Eigen_dense_matrix(int nrows, int ncols)
+    : m_matrix(nrows, ncols)
+  {
+    CGAL_assertion(m_matrix.rows() > 0);
+    CGAL_assertion(m_matrix.cols() > 0);
+  }
+
+  /// Create a dense matrix out of a \ref thirdpartyEigen "Eigen" matrix type
+  Eigen_dense_matrix(const EigenType& eigen_mat)
+    : m_matrix(eigen_mat) {}
+
+  Eigen_dense_matrix() : m_matrix() {}
+
+  /// Read access to a matrix coefficient.
+  ///
+  /// \pre 0 <= i < row_dimension().
+  /// \pre 0 <= j < column_dimension().
+  T& operator() (int i_, int j_)
+  {
+    return m_matrix(i_, j_);
+  }
+
+  /// Write access to a matrix coefficient: a_ij <- val
+  ///
+  /// \pre 0 <= i < row_dimension().
+  /// \pre 0 <= j < column_dimension().
+  void set_coef(std::size_t i_, std::size_t j_, T val)
+  {
+    int i = static_cast<int>(i_);
+    int j = static_cast<int>(j_);
+    CGAL_precondition(i < m_matrix.rows());
+    CGAL_precondition(j < m_matrix.cols());
+
+    m_matrix.coeffRef(i,j) = val;
+  }
+
+  /// Return the matrix number of rows
+  std::size_t rows() const {return m_matrix.rows();}
+  /// Return the matrix number of cols
+  std::size_t cols() const {return m_matrix.cols();}
+
+  /// Resize to i rows and j cols
+  void resize(int i_, int j_) { m_matrix.resize(i_, j_);}
+
+  const T& coeff(int i_) const
+  {
+    return m_matrix.coeff(i_);
+  }
+
+  EigenType m_matrix;
+};
+
+/*!
+\ingroup PkgSolver
+
+The class `Eigen_vector` is a wrapper around \ref thirdpartyEigen "Eigen" dense vector
+type <a href="http://eigen.tuxfamily.org/dox/classEigen_1_1Matrix.html"> </a>,
+which is a simple array of numbers.
+
+\cgalModels `SvdTraits::Vector`
+\cgalModels `SparseLinearAlgebraTraits_d::Vector`.
+
+\tparam T Number type.
+\tparam D Number of colums, or Dynamic.
+
+\sa `CGAL::Eigen_dense_matrix<T>`
+\sa `CGAL::Eigen_linear_algebra_traits<T>`
+*/
+template <typename T, int D>
+class Eigen_dense_vector
+{
+private:
+
+  /// The internal vector type from \ref thirdpartyEigen "Eigen".
+  typedef Eigen::Matrix<T, D, 1> EigenType;
+
+public:
+
+  /// Create a dense vector out of a \ref thirdpartyEigen "Eigen" vector type
+  Eigen_dense_vector(const EigenType&  vec) : m_vector(vec) {}
+
+  /// Read and write and access to a vector coefficient: `a_i`
+  const T& coeff(std::size_t i)
+  {
+    CGAL_assertion(i >= 0);
+    CGAL_assertion(i < static_cast<std::size_t>(D));
+    return m_vector.coeff(i);
+  }
+
+  EigenType m_vector;
+};
+
+
+/*!
+\ingroup PkgSolver
+
+The class `Eigen_linear_algebra_traits` provides an interface to linear algebra functionalities of \ref thirdpartyEigen "Eigen".
+\ref thirdpartyEigen "Eigen" version 3.1 (or later) must be available on the system.
+
+\sa `CGAL::Eigen_dense_matrix<T, D1, D2>`
+\sa `CGAL::Eigen_dense_vector<T, D>`
+\sa http://eigen.tuxfamily.org
+
+Example
+-------------- 
+
+\code{.cpp}
+
+typedef CGAL::Eigen_linear_algebra_traits Linear_algebra_traits;
+
+// dynamic matrix at run time to store a large amount of data
+typedef Linear_algebra_traits::MatrixXd MatrixXd;
+
+// preallocated 3x3 matrix at compile time
+typedef Linear_algebra_traits::Matrix3d Matrix3d;
+
+// preallocated 3-cols vector at compile time
+typedef Linear_algebra_traits::Vector3d Vector3d;
+
+\endcode
+*/
+
+class Eigen_linear_algebra_traits
+{
+public:
+  typedef double NT;
+  typedef int Index;
+
+  // dynamic size at run time
+  typedef CGAL::Eigen_dense_matrix<NT> MatrixXd;
+
+  // dynamic rows in run time, fixed cols in compile time
+  typedef CGAL::Eigen_dense_matrix<NT, Eigen::Dynamic, 3> MatrixX3d;
+
+  // fixed at compile time
+  typedef CGAL::Eigen_dense_matrix<NT, 3, 3> Matrix3d;
+
+  // fixed at compile time
+  typedef CGAL::Eigen_dense_vector<NT, 3> Vector3d;
+
+  /// Get the transpose of a `CGAL::Eigen_dense_matrix<T, D1, D2>` matrix
+  template <class Matrix>
+  static Matrix transpose(const Matrix& mat)
+  {
+    return Matrix(mat.m_matrix.transpose());
+  }
+
+  /// Get the determinant of a `CGAL::Eigen_dense_matrix<T, D1, D2>` matrix
+  template <class Matrix>
+  static NT determinant(const Matrix& mat)
+  {
+    return mat.m_matrix.determinant();
+  }
+
+  /// Performs QR decomposition of matrix A to a unitary matrix and an upper triagonal 
+  /// and returns the unitary matrix.
+  template <class NT, int D1, int D2>
+  static CGAL::Eigen_dense_matrix<NT, D1, D2> qr_factorization(const CGAL::Eigen_dense_matrix<NT, D1, D2>& A)
+  {
+    Eigen::HouseholderQR<Eigen::Matrix<NT, D1, D2> > qr(A.m_matrix);
+    return CGAL::Eigen_dense_matrix<NT, D1, D2>(qr.householderQ());
+  }
+
+  template <class Matrix>
+  static void qr_factorization(std::vector<Matrix>& simplex)
+  {
+    for(std::size_t i = 0; i < simplex.size(); ++i)
+    {
+      Matrix mat = simplex[i].m_matrix;
+      simplex[i] = qr_factorization(mat);
+    }
+  }
+
+  // CGAL::Eigen_dense_vector<NT, D2> : the returned type with D2 may be -1 in compile time,
+  // and may not be equal to the expected type.
+  // Eigen manages to return a precompiled row out of a dynamic matrix but I don't know how.
+
+  /// Get the row vector out of a `CGAL::Eigen_dense_matrix<T, D1, D2>`. The result is stored in a 
+  /// preallocated at compile time 3-column `CGAL::Eigen_dense_vector<T, 3>`
+  template <class NT, int D1, int D2>
+  static CGAL::Eigen_dense_vector<NT, 3> row3(const CGAL::Eigen_dense_matrix<NT, D1, D2>& A,
+                                              int i)
+  {
+    return CGAL::Eigen_dense_vector<NT, 3>(A.m_matrix.row(i));
+  }
+
+};
+
+
+/// Matrix multiplication. If the columns of A and the rows of B are equal at compile time, 
+/// the product is stored at a preallocated at compile time `CGAL::Eigen_dense_matrix`. Otherwise, 
+/// the product is stored in a dynamic at run time matrix.
+template <class NT, int D1, int D2, int D3>
+const CGAL::Eigen_dense_matrix<NT, D1, D3> operator* (const CGAL::Eigen_dense_matrix<NT, D1, D2 >& A,
+                                                      const CGAL::Eigen_dense_matrix<NT, D2, D3 >& B)
+{
+  return CGAL::Eigen_dense_matrix<NT, D1, D3>(A.m_matrix * B.m_matrix);
+}
+
+// D2 and D3 may not be equal at compile time, but equal at run time!
+// This overload returns a dynamic matrix.
+template <class NT, int D1, int D2, int D3, int D4>
+const CGAL::Eigen_dense_matrix<NT> operator* (const CGAL::Eigen_dense_matrix<NT, D1, D2 >& A,
+                                              const CGAL::Eigen_dense_matrix<NT, D3, D4 >& B)
+{
+  return CGAL::Eigen_dense_matrix<NT>(A.m_matrix * B.m_matrix);
+}
+
+// scalar - matrix multiplication
+template <class NT, int D1, int D2>
+const CGAL::Eigen_dense_matrix<NT, D1, D2> operator* (const NT& scalar,
+                                                      const CGAL::Eigen_dense_matrix<NT, D1, D2>& B)
+{
+  return CGAL::Eigen_dense_matrix<NT, D1, D2>(scalar * B.m_matrix);
+}
+
+template <class NT, int D1, int D2>
+const CGAL::Eigen_dense_matrix<NT, D1, D2> operator* (const CGAL::Eigen_dense_matrix<NT, D1, D2>& A,
+                                                      const NT& scalar)
+{
+  return CGAL::Eigen_dense_matrix<NT, D1, D2>(A.m_matrix * scalar);
+}
+
+template <class NT, int D1, int D2>
+const CGAL::Eigen_dense_matrix<NT, D1, D2> operator/ (const CGAL::Eigen_dense_matrix<NT, D1, D2>& A,
+                                                      const double& scalar)
+{
+  return CGAL::Eigen_dense_matrix<NT, D1, D2>(A.m_matrix / scalar);
+}
+
+template <class NT, int D1, int D2>
+const CGAL::Eigen_dense_matrix<NT, D1, D2> operator/ (const double& scalar,
+                                                      const CGAL::Eigen_dense_matrix<NT, D1, D2> & A)
+{
+  return CGAL::Eigen_dense_matrix<NT, D1, D2> (scalar / A.m_matrix);
+}
+
+// addition
+template <class NT, int D1, int D2>
+const CGAL::Eigen_dense_matrix<NT, D1, D2> operator+ (const CGAL::Eigen_dense_matrix<NT, D1, D2> & A,
+                                                      const CGAL::Eigen_dense_matrix<NT, D1, D2> & B)
+{
+  return CGAL::Eigen_dense_matrix<NT, D1, D2> (A.m_matrix + B.m_matrix);
+}
+
+// vector - matrix multiplication
+template <class NT, int D1, int D2>
+const Eigen_dense_vector<NT, D1> operator* (const CGAL::Eigen_dense_matrix<NT, D1, D2>& A,
+                                            const CGAL::Eigen_dense_vector<NT, D2>& V)
+{
+  return Eigen_dense_vector<NT, D1>(A.m_matrix * V.m_vector);
+}
+
+
+
+}
+// end namespace
+
+
+
+#endif // CGAL_EIGEN_LINEAR_ALGEBRA_TRAITS_H