Logic-based modeling and solution of nonlinear discrete/continuous optimization problems

Logic-based modeling and solution of nonlinear discrete/continuous optimization problems

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Article ID: iaor20061009
Country: Netherlands
Volume: 139
Issue: 1
Start Page Number: 267
End Page Number: 288
Publication Date: Oct 2005
Journal: Annals of Operations Research
Authors: ,
Keywords: programming: integer
Abstract:

This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations have some limitations such as difficulty of formulation and numerical singularities for the nonlinear case, we consider logic-based modeling as an alternative approach, particularly Generalized Disjunctive Programming (GDP), which the authors have extensively investigated over the last few years. Solution strategies for GDP models are reviewed, including the continuous relaxation of the disjunctive constraints. Also, we briefly review a hybrid model that integrates disjunctive programming and mixed-integer programming. Finally, the global optimization of nonconvex GDP problems is discussed through a two-level branch and bound procedure.

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