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5

Genetic Algorithms: Mimicking Evolution and
Natural Selection in Optimization Models

Tammy Drezner and Zvi Drezner

CONTENTS
5.1 Introduction .......................................................................................................................................... 157
5.1.1 Common Metaheuristic Methods ........................................................................................... 158
5.2 The Framework of Genetic Algorithms............................................................................................... 159
5.3 Modifications of the Genetic Algorithm Framework .......................................................................... 160
5.3.1 Parallel Genetic Algorithms ................................................................................................... 161
5.3.2 Compounded Genetic Algorithms .......................................................................................... 161
5.3.3 Hybrid Genetic Algorithms .................................................................................................... 162
5.3.4 Mutations ................................................................................................................................ 162
5.3.5 Invasions ................................................................................................................................. 162
5.3.6 Gender..................................................................................................................................... 163
5.3.7 Distance-Based Parent Selection ............................................................................................ 163
5.3.8 Removal of Population Members........................................................................................... 164
5.4 An Illustration ...................................................................................................................................... 164
5.4.1 The Genetic Algorithm Process.............................................................................................. 167
5.4.2 Illustrating the Steepest Descent Algorithm........................................................................... 168
5.4.3 Illustrating a Mutation ............................................................................................................ 168
5.4.4 Calculating Diversity .............................................................................................................. 169
5.5 Application: Balancing a Turbine Engine ........................................................................................... 169
5.5.1 A Turbine Balancing Example ............................................................................................... 171
5.6 Discussion............................................................................................................................................. 172
References....................................................................................................................................................... 174

5.1 INTRODUCTION

Optimization problems are defined by an objective function. The objective function is a
dependent variable, i.e., it is a function of several independent variables. The objective is to find
the best combination of the independent variables such that the objective function is either
minimized or maximized (for clarity of the discussion we assume in this chapter that the problem
is minimization). Typically, the objective function is subject to a set of constraints that must
be satisfied.

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