Data-driven spatial branch-and-bound algorithms for box-constrained simulation-based optimization

• Published in: Journal of global optimization Vol. 82; no. 1; pp. 21 - 50
• Main Authors: Zhai, Jianyuan, Boukouvala, Fani
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2022; Springer; Springer Nature B.V
• Subjects: Algorithms; Complexity; Computer Science; Computer simulation; Computer-generated environments; Decision analysis; Decision making; First principles; Mathematical optimization; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Optimization techniques; Real Functions; Simulation; Spatial data; Branch-and-bound; Simulation-optimization; Convex underestimators; Global optimization; Black-box optimization
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-021-01045-8

The ability to use complex computer simulations in quantitative analysis and decision-making is highly desired in science and engineering, at the same rate as computation capabilities and first-principle knowledge advance. Due to the complexity of simulation models, direct embedding of equation-based optimization solvers may be impractical and data-driven optimization techniques are often needed. In this work, we present a novel data-driven spatial branch-and-bound algorithm for simulation-based optimization problems with box constraints, aiming for consistent globally convergent solutions. The main contribution of this paper is the introduction of the concept data-driven convex underestimators of data and surrogate functions, which are employed within a spatial branch-and-bound algorithm. The algorithm is showcased by an illustrative example and is then extensively studied via computational experiments on a large set of benchmark problems.