This repository contains the Matlab code of DirHV-EGO, EHVI-EGO, and KB&EHVI-EGO.
Liang Zhao and Qingfu Zhang. Hypervolume-Guided Decomposition for Parallel Expensive Multiobjective Optimization. IEEE Transactions on Evolutionary Computation, 28(2): 432-444, 2024. [Post-print PDF] [PDF]
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.
Matlab >= 2018a
- The
run_DirHV_EGO.m
provides the basic script to run experiments on ZDT and DTLZ.
- 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
:$11d-1$ .
- Default setting of
- 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.
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}
}
- This implementation is based on PlatEMO.
- For GP modeling, we leverage the DACE toolbox.