A Convex Reformulation and an Outer Approximation for a Large Class of Binary Quadratic Programs

• 成果类型: Article
• 署名作者: Rostami, Borzou; Errico, Fausto; Lodi, Andrea
• 署名单位: Wilfrid Laurier University; Universite de Montreal; Polytechnique Montreal; University of Quebec; Ecole de Technologie Superieure - Canada; Cornell University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.2241
• 发表日期: 2023
• 页码: 471-486
• 关键词: hub location-problems; linearization technique; polynomial algorithm; cutting-plane; Lower bounds; formulations; relaxation; recipe

摘要

In this paper, we propose a general modeling and solving framework for a large class of binary quadratic programs subject to variable partitioning constraints. Problems in this class have a wide range of applications as many binary quadratic programs with linear constraints can be represented in this form. By exploiting the structure of the partitioning constraints, we propose mixed-integer nonlinear programming (MINLP) and mixedinteger linear programming (MILP) reformulations and show the relationship between the two models in terms of the relaxation strength. Our solution methodology relies on a convex reformulation of the proposedMINLP and a branch-and-cut algorithm based on outer approximation cuts, in which the cuts are generated on the fly by efficiently solving separation subproblems. To evaluate the robustness and efficiency of our solution method, we perform extensive computational experiments on various quadratic combinatorial optimization problems. The results show that our approach outperforms the state-of-the-art solver applied to differentMILP reformulations of the corresponding problems.