Benders decomposition for the large-scale probabilistic set covering problem

IF 4.1 2区 工程技术 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computers & Operations Research Pub Date : 2025-01-30 DOI:10.1016/j.cor.2025.106994
Jie Liang , Cheng-Yang Yu , Wei Lv , Wei-Kun Chen , Yu-Hong Dai
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引用次数: 0

Abstract

In this paper, we consider a probabilistic set covering problem (PSCP) in which each 0-1 row of the constraint matrix is random with a finite discrete distribution, and the objective is to minimize the total cost of the selected columns such that each row is covered with a prespecified probability. We develop an effective decomposition algorithm for the PSCP based on the Benders reformulation of a standard mixed integer programming (MIP) formulation. The proposed Benders decomposition (BD) algorithm enjoys two key advantages: (i) the number of variables in the underlying Benders reformulation is equal to the number of columns but independent of the number of scenarios of the random data; and (ii) the Benders feasibility cuts can be separated by an efficient polynomial-time algorithm, which makes it particularly suitable for solving large-scale PSCPs. We enhance the BD algorithm by using initial cuts to strengthen the relaxed master problem, implementing an effective heuristic procedure to find high-quality feasible solutions, and adding mixed integer rounding enhanced Benders feasibility cuts to tighten the problem formulation. Numerical results demonstrate the efficiency of the proposed BD algorithm over a state-of-the-art MIP solver. Moreover, the proposed BD algorithm can efficiently identify optimal solutions for instances with up to 500 rows, 5000 columns, and 2000 scenarios of the random rows.
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来源期刊
Computers & Operations Research
Computers & Operations Research 工程技术-工程:工业
CiteScore
8.60
自引率
8.70%
发文量
292
审稿时长
8.5 months
期刊介绍: Operations research and computers meet in a large number of scientific fields, many of which are of vital current concern to our troubled society. These include, among others, ecology, transportation, safety, reliability, urban planning, economics, inventory control, investment strategy and logistics (including reverse logistics). Computers & Operations Research provides an international forum for the application of computers and operations research techniques to problems in these and related fields.
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