A solution algorithm for chance-constrained problems with integer second-stage recourse decisions

• 成果类型: Article
• 署名作者: Lodi, Andrea; Malaguti, Enrico; Monaci, Michele; Nannicini, Giacomo; Paronuzzi, Paolo
• 署名单位: Technion Israel Institute of Technology; University of Bologna; University of Southern California
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-023-01984-y
• 发表日期: 2024
• 页码: 269-301
• 关键词: 2-stage stochastic programs; mixed-binary 1st; decomposition algorithms; nonlinear programs; branch; relaxations

摘要

We study a class of chance-constrained two-stage stochastic optimization problems where the second-stage recourse decisions belong to mixed-integer convex sets. Due to the nonconvexity of the second-stage feasible sets, standard decomposition approaches cannot be applied. We develop a provably convergent branch-and-cut scheme that iteratively generates valid inequalities for the convex hull of the second-stage feasible sets, resorting to spatial branching when cutting no longer suffices. We show that this algorithm attains an approximate notion of convergence, whereby the feasible sets are relaxed by some positive tolerance e. Computational results on chance-constrained resource planning problems indicate that our implementation of the proposed algorithm is highly effective in solving this class of problems, compared to a state-of-the-art MIP solver and to a naive decomposition scheme.