Constrained optimization by α constrained genetic algorithm (αGA)

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Abstract
In this study, α constrained genetic algorithm (αGA) which solves constrained optimization problems is proposed. Constrained optimization problems, where the objective functions are minimized under given constraints, are very important and frequently appear in the real world. Recently, researches on constrained optimization using genetic algorithm (GA) have been widely carried out, and their results are equivalent to those by existing mathematical methods. αGA is a method which combines the α constrained method with GA. In the α constrained method, the satisfaction level of constraints to express how much a search point satisfies the constraints is introduced. The α level comparison which compares the search points based on the satisfaction level of constraints is also introduced. The α constrained method can convert constrained problems to unconstrained problems using α level comparison. In αGA, the individuals who satisfy the constraints will evolve to optimize the objective function and the individuals who do not satisfy the constraints will evolve to satisfy the constraints, naturally. In this paper, the effectiveness of αGA is shown by comparing αGA with GENOCOP 5.0 on various types of test problems, such as a linear programming problem, nonlinear programming problems, and problems with nonconvex constraints. © 2004 Wiley Periodicals, Inc. Syst Comp Jpn, 35(5): 11–22, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10562