A validation and verification tool for global optimization solvers

Abstract

Linearly constrained optimization models based on a systems description often possess multiple local optima. Therefore, there are a broad variety of problems in which the property of unique solution cannot be simply postulate or verified. The aim of global optimization (GO) is to find the best possible solution of multi-extremal problems. This paper illustrates the applicability of GO modeling techniques and solution strategies to real-world problems. In this paper we propose an enumeration approach for solving the linearly constrained optimization problem with continuous but general objective function. The method uses a parametric but unconstrained representation of the problem in terms of the vertices (and the extreme rays) of the feasible region. The unconstrained problem is then solved by the classical unconstrained continuous optimization procedure. Our aim is to propose a new introduction to optimization, the design of a general solution algorithm that is easy for the user to understand and provides useful information such as global bounding of the objective function. For illustrative and comparative purposes, the algorithm and its applications are presented in the context of applied problems solved by other solution algorithms.