A Two-phase Framework with a Bezier Simplex-based Interpolation Method for Computationally Expensive Multi-objective Optimization

This repository provides the code to reproduce results shown in the following paper.

Ryoji Tanabe, Youhei Akimoto, Ken Kobayashi, Hiroshi Umeki, Shinichi Shirakawa, Naoki Hamada, A Two-phase Framework with a Bezier Simplex-based Interpolation Method for Computationally Expensive Multi-objective Optimization, accepted for GECCO2022, pdf

The code highly depends on the COCO software:

Nikolaus Hansen, Anne Auger, Raymond Ros, Olaf Mersmann, Tea Tusar, and Dimo Brockhoff, COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting, Optimization Methods and Software, 36(1): 114-144 (2021), link

Requirements

This code require Python (=>3.8), numpy, cocoex, pygmo, pybobyqa, click, torch, and torch_bsf.

This repository also provides code to run optimizers implemented in optuna and PlatEMO on the bi-objective BBOB problems. Each software is optionally needed to run the code.

gpus=0 in the following line in tpb.py can cause an error in pytorch-bsf. The argument auto_select_gpus=True in line 215 in bezier_simplex.py should be auto_select_gpus=False when the option gpus is set to 0.

bs = torch_bsf.fit(params=ts, values=xs, degree=bez_degree, max_epochs=100, gpus=0)

Usage

The following command runs a TPB with a default parameter setting on the 55 bi-objective BBOB problems with 2, 3, 5, 10, and 20 objectives:

python tpb.py

The parameter setting can be given to the code of TPB as follows:

python tpb.py --budget_multiplier 20 --n_weights 3 --opt_budget_rate 0.9 --optimizer bobyqa --bez_degree 2 --scalarizing_fun ws --interpolator bez

Usage of other code

MOTPE in optuna

Simply, the following command runs MOTPE on the 55 bi-objective TPB problems:

python optuna_bbob.py

EMO algorithms in PlatEMO

First, you need to copy all Matlab files in the example to your PlatEMO code in this directory. Then, you need to copy dummyFun.m, dummyFun1.m, dummyFun2.m, and platemo_bbob.py to the same directory. The use of the PlatEMO code in the COCO software require a trick as in dummyFun.m, dummyFun1.m, and dummyFun2.m. The following command runs K-RVEA on the 55 bi-objective TPB problems. Of course, you can run the code on the GUI environment.

matlab -batch platemo_bbob.m