Improving discrete model representations via symmetry considerations

• 成果类型: Article
• 署名作者: Sherali, HD; Smith, JC
• 署名单位: Virginia Polytechnic Institute & State University; University of Arizona
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.47.10.1396.10265
• 发表日期: 2001
• 页码: 1396-1407
• 关键词: integer programming; Modeling; tight representation; symmetry; REFORMULATION

摘要

In this paper, we focus on a useful modeling concept that is frequently ignored while formulating discrete optimization problems. Very often, there exists a natural symmetry inherent in the problem itself that, if propagated to the model, can hopelessly mire a branch-and-bound solver by burdening it to explore and eliminate such alternative symmetric solutions. We discuss three applications where such a symmetry arises: a telecommunications network design problem, a noise pollution problem, and a machine procurement and operation problem. For each case, we identify the indistinguishable objects in the model that create the problem symmetry and show how imposing certain decision hierarchies within the model significantly enhances its solvability, while using a popular modern-day commercial branch-and-cut software (CPLEX 6.5).