Optimization Overview

Abstract

This first chapter of Part IV of the book begins a discussion of optimization within the context of its application in modelling and simulation projects. This chapter provides a broad overview of some of the important notions in this area of study. It is noted that the main feature is the specification of a criterion function, J, whose value is dependent on a specified parameter vector, p, of dimension m. The objective of the optimization process is to locate a value for p which yields a minimum value for J (the alternative of seeking a maximum value for J can be accommodated by undertaking the minimization of −J). The simplest case of the problem occurs when the search space (namely the domain of admissible values allowed for p) is the entire space of real valued m-vectors. Constraints on the allowable values for p are common and this understandably introduces complexity in search procedures. A common occurrence within the modelling and simulation context is the case where only integer values are allowed for some, or possibly all, components of p. A common approach for classifying optimization methods relates to their dependence upon the gradient of the criterion function, J. Thus there are gradient dependent methods and heuristic methods; i.e., methods that do not depend of gradient information. Examples of both of these categories are provided.