7.1 Introduction

Optimization deals with problems of minimizing or maximizing a function with several variables usually subject to equality and/or inequality constraints. It plays a central role in operations research, management science and engineering design. Many industrial engineering design problems are very complex and difficult to solve using conventional optimization techniques. In recent years, genetic algorithms have received considerable attention regarding their potential as a novel optimization technique. Based on their simplicity, ease of operation, minimal requirements and parallel and global perspective, genetic algorithms have been widely applied in a variety of problems. A brief introduction to genetic optimization techniques and their application is described in this section, including major fields of optimization, such as fuzzy, combinatorial and multi objective optimizations.

7.2 Fuzzy Optimization Problems

Fuzzy optimization describes an optimization problem with fuzzy objective function and fuzzy constraints. The results obtained from classical methods of optimization involving deterministic variables exhibit various shortcomings. In particular, the effects of the uncertainty attached to input information is often ignored altogether or only taken into account to a limited degree. The classical deterministic optimization problem according to

is considered under the aspect of uncertainty, and extended. For the objective function z(x, e) the optimum solution x _OPT from the set of design variables X (design space) is determined under compliance with the equality constraints h _j(x, e) and the inequality constraints g _i(x, e). Input parameters such as geometrical parameters, material parameters, external load parameters, reliability parameters and economic parameters are...