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Block-MOBO

This repository contains Matlab implementation of the algorithm framework for Block-MOBO in the research paper High-dimensional Multi-objective Bayesian Optimization with Block Coordinate Updates: Case Studies in Intelligent Transportation System (Accepted by IEEE Transactions on Intelligent Transportation Systems 2023).

Algorithm Preparation

We use PlatEMO-V2.9.0, an evolutionary multi-objective optimization platform, to implement all the related experiments. Details on how to use PlatEMO can be found in manual.pdf. Before starting our methods, we recommend to carefully study how to use the PlatEMO platform.

Get Started

We recommend runing all the related experiments with GUI of PlatEMO. To invoke the interface, use the function:

main()

More details can be found in manual.pdf.

Baselines

The baseline methods in Block-MOBO include random search, NSGA-II [1], SMS-EMOA [2], ParEGO [3], MOEA/D-EGO [4], ReMO [5], Multi-LineBO, K-RVEA [6] and MOEA/D-ASS [7]. ReMO is an optimization architecture that can be equiped with any well known derivative-free MO algorithm. We equip ReMO with ParEGO in this paper to make comparisons with EGO-based methods. Multi-LineBO is a version of single-objective LineBO [8].

Algorithm Name Characteristics Published
NSGA-II Multi-objective, low-dimensional IEEE Transactions on Evolutionary Computation 2002
SMS-EMOA Multi-objective, low-dimensional European Journal of Operational Research 2007
ParEGO Multi-objective, low-dimensional IEEE Transactions on Evolutionary Computation 2006
MOEA/D-EGO Multi-objective, low-dimensional IEEE Transactions on Evolutionary Computation 2010
ReMO Multi-objective, high-dimensional AAAI 2017
Multi-LineBO Multi-objective, high-dimensional ICML 2019
K-RVEA Many-objective, low-dimensional IEEE Transactions on Evolutionary Computation 2016
MOEA/D-ASS Multi-objective, low-dimensional IEEE Transactions on Cybernetics 2023

Benchmark Problems

Benchmark problems contain six three-objective benchmark problems taken from the DTLZ test suite [9], four three-objective benchmark problems from WFG test suite [10], four three-objective benchmark problems from mDTLZ test suite [11] and two optimization problems in transportation systems, including car side impact problem [12] and car cab design with preference information [13].

Problem M D Descriptions
DTLZ 3 10,20,30,40,50 DTLZ11, DTLZ2, DTLZ3,DTLZ5, DTLZ6, DTLZ7
WFG 3 10,20,30,40,50 WFG1-4
mDTLZ 3 10,20 mDTLZ1-4
Car Side Impact Problem 4 7 -
car cab design with preference information 2 11 -

Citation

Please cite our paper if you find our work useful for your research:

@article{WANG2023,
title = {High-Dimensional Multi-Objective Bayesian Optimization With Block Coordinate Updates: Case Studies in Intelligent Transportation System},
author = {Hongyan Wang, Hua Xu and Zeqiu Zhang},
journal = {IEEE Transactions on Intelligent Transportation Systems},
year = {2023},
doi = {10.1109/TITS.2023.3241069},
}

If there's any question, please feel free to contact [email protected] and [email protected].

References

[1] K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197, April 2002.

[2] N.Beume,B.Naujoks,andM.Emmerich, SMS-EMOA: Multiobjective selection based on dominated hypervolume, European Journal of Operational Research, vol. 181, no. 3, pp. 1653–1669, 2007.

[3] J. Knowles, ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multi-objective optimization problems, IEEE Transactions on Evolutionary Computation 10 (1) (2006) 50–66.

[4] Q. Zhang, W. Liu, E. Tsang, B. Virginas, Expensive multi-objective optimization by MOEA/D with Gaussian process model, IEEE Transactions on Evolutionary Computation 14 (3) (2010) 456–474.

[5] H. Qian, Y. Yu, Solving high-dimensional multi-objective optimization problems with low effective di- mensions, in: Proceedings of the 31st AAAI Conference on Artificial Intelligence, AAAI’17, AAAI Press, 2017, p. 875–881.

[6] T. Chugh, Y. Jin, K. Miettinen, J. Hakanen, and K. Sindhya, A surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive many-objective optimization, IEEE Transactions on Evolutionary Computation, vol. 22, no. 1, pp. 129–142, Feb. 2018.

[7] Z. Wang, Q. Zhang, Y.-S. Ong, S. Yao, H. Liu, and J. Luo, Choose appropriate subproblems for collaborative modeling in expensive multiobjective optimization, IEEE Transactions on Cybernetics, vol. 53, no. 1, pp. 483–496, Jan. 2023.

[8] J. Kirschner, M. Mutny, N. Hiller, R. Ischebeck, A. Krause, Adaptive and safe bayesian optimization in high dimensions via one-dimensional subspaces, Proceedings of the 36th International Conference on Machine Learning, Vol. 97 of ICML’19, PMLR, Long Beach, California, USA, 2019, pp. 3429–3438.

[9] K. Deb, L. Thiele, M. Laumanns, E. Zitzler, Scalable Test Problems for Evolutionary Multiobjective Optimization, Springer London, London, 2005, pp. 105–145.

[10] Huband, S., Barone, L., While, L., Hingston, P. A Scalable Multi-objective Test Problem Toolkit. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds) Evolutionary Multi-Criterion Optimization. EMO 2005.

[11] Z. Wang, Y.-S. Ong, and H. Ishibuchi, On scalable multiobjective test problems with hardly dominated boundaries, IEEE Transactions on Evolutionary Computation, vol. 23, no. 2, pp. 217–231, Apr. 2018.

[12] H. Jain and K. Deb, An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, Part II: Handling constraints and extending to an adaptive approach, IEEE Transactions on Evolutionary Computation, vol. 18, no. 4, pp. 602–622, Aug. 2014.

[13] K. Deb, S. Gupta, D. Daum, J. Branke, A. K. Mall, and D. Padmanabhan, Reliability-based optimization using evolutionary algorithms, IEEE Transactions on Evolutionary Computation, vol. 13, no. 5, pp. 1054–1074, Oct. 2009.

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