• DOI:10.48550/arXiv.2208.03685
• Corpus ID: 251402761

A Parallel Technique for Multi-objective Bayesian Global Optimization: Using a Batch Selection of Probability of Improvement

@article{Yang2022APT,
  title={A Parallel Technique for Multi-objective Bayesian Global Optimization: Using a Batch Selection of Probability of Improvement},
  author={Kaifeng Yang and Guozhi Dong and Michael Affenzeller},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.03685}
}

• Kaifeng Yang, Guozhi Dong, M. Affenzeller
• Published 7 August 2022
• Computer Science
• ArXiv

Bayesian global optimization (BGO) is an efficient surrogate-assisted technique for problems involving expensive evaluations. A parallel technique can be used to parallelly evaluate the true-expensive objective functions in one iteration to boost the execution time. An effective and straightforward approach is to design an acquisition function that can evaluate the performance of a bath of multiple solutions, instead of a single point/solution, in one iteration. This paper proposes five alternatives of Probability of Improvement (PoI) with multiple points in a batch (q-PoI) for multi-objective Bayesian global optimization (MOBGO), taking the covariance among multiple points into account. Both exact computational formulas and the Monte Carlo approximation algorithms for all proposed q-PoIs are provided. Based on the distribution of the multiple points relevant to the Pareto-front, the position-dependent behavior of the five q-PoIs is investigated. Moreover, the five q-PoIs are compared with the other nine state-of-the-art and recently proposed batch MOBGO algorithms on twenty bio-objective benchmarks. The empirical experiments on different variety of benchmarks are conducted to demonstrate the effectiveness of two greedy q-PoIs (q-PoI best and q-PoI all) on low-dimensional problems and the effectiveness of two explorative q-PoIs (q-PoI one and q-PoI worst) on high-dimensional problems with difficult-to-approximate Pareto front boundaries.