Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models

• 成果类型: Article
• 署名作者: Nakagawa, Yuji; James, Ross J. W.; Rego, Cesar; Edirisinghe, Chanaka
• 署名单位: Kansai University; University of Canterbury; University of Mississippi; University of Tennessee System; University of Tennessee Knoxville
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2013.1772
• 发表日期: 2014
• 页码: 695-707
• 关键词: multidimensional nonlinear knapsack; separable discrete optimization; Combinatorial Optimization; surrogate constraints; problem difficulty estimation; entropy

摘要

This paper develops a new way to help solve difficult linear and nonlinear discrete-optimization decision models more efficiently by introducing a problem-difficulty metric that uses the concept of entropy from information theory. Our entropy metric is employed to devise rules for problem partitioning within an implicit enumeration method, where branching is accomplished based on the subproblem complexity. The only requirement for applying our metric is the availability of (upper) bounds on branching subproblems, which are often computed within most implicit enumeration methods such as branch-and-bound (or cutting-plane-based) methods. Focusing on problems with a relatively small number of constraints, but with a large number of variables, we develop a hybrid partitioning and enumeration solution scheme by combining the entropic approach with the recently developed improved surrogate constraint (ISC) method to produce the new method we call ISCENT. Our computational results indicate that ISCENT can be an order of magnitude more efficient than commercial solvers, such as CPLEX, for convex instances with no more than eight constraints. Furthermore, for nonconvex instances, ISCENT is shown to be significantly more efficient than other standard global solvers.