MilaNedic / moarchiving

This repository contains the description and corresponding files for the "Computing and updating Hypervolume" project

Incrementally Computing the Hypervolume of a Set of n-D Points for n=3 and 4

This repository contains the description and corresponding files for the "Incrementally computing the hypervolume of a set of n-D points for n=3 and 4" project.

This is a project for the master's subject "Matematika z računalnikom" at University of Ljubljana, Faculty of Mathematics and Physics.

Description

The hypervolume of a set of n-D points is often used in multi-objective optimization and serves as a measure of tracking the progress of optimization algorithms.

The goal of this project is to transfer the most computationally efficient implementation of the incremental hypervolume computation for 3-D and 4-D spaces, which is written in C, into Python.

Repository Structure

The repository is structured as follows:

• The moarchiving folder consists of my implementation of the hypervolume problem in three and four dimensions in Python.
  • The hv_plus.py contains all the auxiliary funtions as well as the main functions for computing the hypervolume in both three and four dimensions.
  • Example tests for the auxiliary functions are written in the hv_plus_tests.py file, which can be run by simply downloading both files into the same folder and then running the hv_plus_tests.py file.
  • Additional tests for the hyperovlume in four dimensions are available in hv4d_test.py and are executed by running the file.
  • An example test for the three dimensional case, which can be found at [https://github.com/apguerreiro/HVC], is implemented in hv3d_test_original.py. After running this Python file, the computed hypervolume is printed in the terminal (and equals to the original result from C). A visual representation for this example can be found in the visualization folder (one can either run the hv3d_example_original.m script or simply open the MATLAB figure hv3d_example_original.fig).
  • Additional three dimensional examples are available in hv3d_test_01.py, hv3d_test_02.py, ..., hv3d_test_10.py. A visual representation of hv3d_test_01.py is available in the visualization folder (by opening either hv3d_example_01.m or hv3d_example_01.fig).
  • Tests for time-efficiency for the three and four dimensional case are available in hv3d_test_time.py (for hv3dplus) and hv4d_test_time_R.py (for hv4dplus-R)/hv4d_test_time_U.py(for hv4dplus-U), respectively. Plots are saved in the plots subfolder. Test files are generated using generate_points.py and are saved in the tests subfolder.
• The related folder is a copy of the HVC repository, available at [https://github.com/apguerreiro/HVC]. Here, the original implementation is available as well as example cases (additional examples have been aded to the examples folder). The code has been slightly modified for testing purposes and comparing my Python implementation to the original one.
• The final report for the project can be found in the final_report folder (the project has not been yet completed at the time of writing the final report).

Requirements

• Python (version 3.12.0 has been used) with the following libraries: numpy, sortedcontainers and functools.
• C (for testing/comparison purposes only).