High-Dimensional Multi-Objective Bayesian Optimization With Block Coordinate Updates: Case Studies in Intelligent Transportation System

Many transportation system problems can be formulated as high-dimensional expensive multi-objective problems. They are challenging for Gaussian process-based Bayesian optimization methods to find the Pareto fronts due to the curse of dimensionality and the boundary issue in the acquisition function...

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Published in:	IEEE transactions on intelligent transportation systems Vol. 25; no. 1; pp. 1 - 12
Main Authors:	Wang, Hongyan, Xu, Hua, Zhang, Zeqiu
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.01.2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
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ISSN:	1524-9050, 1558-0016
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Abstract	Many transportation system problems can be formulated as high-dimensional expensive multi-objective problems. They are challenging for Gaussian process-based Bayesian optimization methods to find the Pareto fronts due to the curse of dimensionality and the boundary issue in the acquisition function optimization. This paper presents a multi-objective Bayesian optimization method with block coordinate updates, Block-MOBO, to solve high-dimensional expensive multi-objective problems. Block-MOBO first partitions the decision variable space into different blocks, each of which includes a low-dimensional multi-objective problem. At each iteration, one block is considered and the decision variables not in this block are approximated by context-vector generation embedded with the Pareto prior knowledge thus promoting convergence. To tackle the boundary issue, we present <inline-formula> <tex-math notation="LaTeX">\epsilon</tex-math> </inline-formula>-greedy acquisition function in a Bayesian and multi-objective fashion, which recommends candidates either from the exploitation-exploration trade-off perspective or with probability <inline-formula> <tex-math notation="LaTeX">\epsilon</tex-math> </inline-formula> from the Pareto dominance relationship perspective. We verify the effectiveness of Block-MOBO by comparing it with other multi-objective Bayesian methods on two real-world optimization problems in transportation system and three multi-objective synthetic test suites. The experimental results show that Block-MOBO can find more evenly distributed and non-dominated solutions in the whole search space with lower complexity compared with other state-of-the-art approaches. Our analyses illustrate that block coordinate updates and <inline-formula> <tex-math notation="LaTeX">\epsilon</tex-math> </inline-formula>-greedy acquisition function contribute to computational complexity reduction and convergence-diversity trade-offs, respectively.
AbstractList	Many transportation system problems can be formulated as high-dimensional expensive multi-objective problems. They are challenging for Gaussian process-based Bayesian optimization methods to find the Pareto fronts due to the curse of dimensionality and the boundary issue in the acquisition function optimization. This paper presents a multi-objective Bayesian optimization method with block coordinate updates, Block-MOBO, to solve high-dimensional expensive multi-objective problems. Block-MOBO first partitions the decision variable space into different blocks, each of which includes a low-dimensional multi-objective problem. At each iteration, one block is considered and the decision variables not in this block are approximated by context-vector generation embedded with the Pareto prior knowledge thus promoting convergence. To tackle the boundary issue, we present [Formula Omitted]-greedy acquisition function in a Bayesian and multi-objective fashion, which recommends candidates either from the exploitation-exploration trade-off perspective or with probability [Formula Omitted] from the Pareto dominance relationship perspective. We verify the effectiveness of Block-MOBO by comparing it with other multi-objective Bayesian methods on two real-world optimization problems in transportation system and three multi-objective synthetic test suites. The experimental results show that Block-MOBO can find more evenly distributed and non-dominated solutions in the whole search space with lower complexity compared with other state-of-the-art approaches. Our analyses illustrate that block coordinate updates and [Formula Omitted]-greedy acquisition function contribute to computational complexity reduction and convergence-diversity trade-offs, respectively. Many transportation system problems can be formulated as high-dimensional expensive multi-objective problems. They are challenging for Gaussian process-based Bayesian optimization methods to find the Pareto fronts due to the curse of dimensionality and the boundary issue in the acquisition function optimization. This paper presents a multi-objective Bayesian optimization method with block coordinate updates, Block-MOBO, to solve high-dimensional expensive multi-objective problems. Block-MOBO first partitions the decision variable space into different blocks, each of which includes a low-dimensional multi-objective problem. At each iteration, one block is considered and the decision variables not in this block are approximated by context-vector generation embedded with the Pareto prior knowledge thus promoting convergence. To tackle the boundary issue, we present <inline-formula> <tex-math notation="LaTeX">\epsilon</tex-math> </inline-formula>-greedy acquisition function in a Bayesian and multi-objective fashion, which recommends candidates either from the exploitation-exploration trade-off perspective or with probability <inline-formula> <tex-math notation="LaTeX">\epsilon</tex-math> </inline-formula> from the Pareto dominance relationship perspective. We verify the effectiveness of Block-MOBO by comparing it with other multi-objective Bayesian methods on two real-world optimization problems in transportation system and three multi-objective synthetic test suites. The experimental results show that Block-MOBO can find more evenly distributed and non-dominated solutions in the whole search space with lower complexity compared with other state-of-the-art approaches. Our analyses illustrate that block coordinate updates and <inline-formula> <tex-math notation="LaTeX">\epsilon</tex-math> </inline-formula>-greedy acquisition function contribute to computational complexity reduction and convergence-diversity trade-offs, respectively.
Author	Zhang, Zeqiu Xu, Hua Wang, Hongyan
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Title	High-Dimensional Multi-Objective Bayesian Optimization With Block Coordinate Updates: Case Studies in Intelligent Transportation System
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