DirHV-EGO

This repository contains the Matlab code of DirHV-EGO. The Python implementation is available at LibMOON.

Liang Zhao and Qingfu Zhang. Hypervolume-Guided Decomposition for Parallel Expensive Multiobjective Optimization. IEEE Transactions on Evolutionary Computation, 28(2): 432-444, 2024. [PDF] [Supplementary]

Direction-based Hypervolume Improvement (DirHVI)

• It is designed under the MOEA/D framework to support parallel expensive multiobjective optimization.
• It only measures the hypervolume improvement within each axis-parallel box induced by the modified Tchebycheff scalarization.
• It can be regarded as an unbiased estimation of a weighted hypervolume improvement.

Expected Direction-based Hypervolume Improvement (DirHV-EI)

• It is defined as the expectation of DirHVI over the Gaussian process (GP) posterior $p(\boldsymbol{y}|\boldsymbol{x},\mathcal{D})$.
• It has a simple closed-form expression and is very cheap to compute.

Usage

Matlab >= 2018a

Quick Start

• The run_DirHV_EGO.m provides the basic script to run experiments on ZDT and DTLZ.

Advanced usage

• Download PlatEMO (version 4.6, Matlab >= 2018a) and read PlatEMO's User Manual to familiarize yourself with how to use this platform.
• Copy the folders within "Algorithms" into the directory at "PlatEMO/Algorithms/". Next, add all of the subfolders contained within the "PlatEMO" directory to the MATLAB search path.
• In the MATLAB command window, type platemo() to run PlatEMO using the GUI.
• Select the label "expensive" and choose the algorithm "DirHV-EGO".
  • Default setting of batch size: 5.
  • Default setting of number of initial samples: $11d-1$.
• Select a problem and set appropriate parameters.
  • e.g., ZDT1, N=200, M=2, D=8, maxFE=200.
  • e.g., Inverted DTLZ2, N=210, M=3, D=6, maxFE=300.

If you have any questions or feedback, please feel free to contact liazhao5-c@my.cityu.edu.hk and qingfu.zhang@cityu.edu.hk.

Citation

If you find our work is helpful to your research, please cite our paper:

@article{zhao2024hypervolume,
  author={Zhao, Liang and Zhang, Qingfu},
  journal={IEEE Transactions on Evolutionary Computation}, 
  title={Hypervolume-Guided Decomposition for Parallel Expensive Multiobjective Optimization}, 
  year={2024},
  volume={28},
  number={2},
  pages={432-444},
  doi={10.1109/TEVC.2023.3265347}
  }

Acknowledgements

• This implementation is based on PlatEMO.
• For GP modeling, we leverage the DACE toolbox.