Enhanced branch-and-bound algorithm for chance constrained programs with Gaussian mixture models

Jinxiang Wei (), Zhaolin Hu (), Jun Luo () and Shushang Zhu ()
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Jinxiang Wei: Tongji University
Zhaolin Hu: Tongji University
Jun Luo: Shanghai Jiao Tong University
Shushang Zhu: Sun Yat-Sen University

Annals of Operations Research, 2024, vol. 338, issue 2, No 17, 1283-1315

Abstract: Abstract We study a class of chance constrained programs (CCPs) where the underlying distribution is modeled by a Gaussian mixture model. As the original work, Hu et al. (IISE Trans 54(12):1117–1130, 2022. https://doi.org/10.1080/24725854.2021.2001608 ) developed a spatial branch-and-bound (B &B) algorithm to solve the problems. In this paper, we propose an enhanced procedure to speed up the computation of B &B algorithm. We design an enhanced pruning strategy that explores high-potential domains and an augmented branching strategy that prevents redundant computations. We integrate the new strategies into original framework to develop an enhanced B &B algorithm, and illustrate how the enhanced algorithm improves on the original approach. Furthermore, we extend the enhanced B &B framework to handle the CCPs with multiple chance constraints, which is not considered in the previous work. We evaluate the performance of our new algorithm through extensive numerical experiments and apply it to solve a real-world portfolio selection problem.

Keywords: Chance constrained program; Gaussian mixture model; Branch-and-bound algorithm; Enhanced strategies; Multiple chance constraints (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-024-05947-0

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