Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models

Type of content
Journal Article
Thesis discipline
Degree name
Publisher
University of Canterbury. Management, Marketing, and Entrepreneurship
Journal Title
Journal ISSN
Volume Title
Language
Date
2014
Authors
Nakagawa, Y.
James, R.J.W.
Rego, C.
Edirisinghe, C.
Abstract

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.

Description
Citation
Nakagawa, Y., James, R.J.W., Rego, C., Edirisinghe, C. (2014) Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models. Management Science, 30(3), pp. 695-707.
Keywords
multidimensional nonlinear knapsack, separable discrete optimization, combinatorial optimization, surrogate constraints, problem difficulty estimation, entropy
Ngā upoko tukutuku/Māori subject headings
ANZSRC fields of research
Fields of Research::35 - Commerce, management, tourism and services::3507 - Strategy, management and organisational behaviour::350709 - Organisation and management theory
Fields of Research::49 - Mathematical sciences::4903 - Numerical and computational mathematics::490304 - Optimisation
Field of Research::08 - Information and Computing Sciences::0802 - Computation Theory and Mathematics::080201 - Analysis of Algorithms and Complexity
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