A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization

• Published in: IEEE transactions on evolutionary computation Vol. 10; no. 6; pp. 658 - 675
• Main Authors: Cai, Zixing, Wang, Yong
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acceleration; Algorithm design and analysis; Algorithms; Applied sciences; Archiving; Artificial intelligence; Benchmark testing; Computer aided instruction; Computer science; control theory; systems; Constrained optimization; Constraint optimization; Constraints; evolutionary algorithm (EA); Evolutionary algorithms; Evolutionary computation; Exact sciences and technology; Inequalities; Information science; Learning and adaptive systems; Mathematical analysis; Mathematical models; multiobjective optimization; nondominated individuals; Optimization; Robustness; Studies; Information system; Evolutionary algorithm; Multiobjective programming; evolutionary algorithm (EA); Replacement; Modeling; Constrained optimization; multiobjective optimization; Value function; Inequality constraint; Equality constraint; Population dynamics; Standard deviation; Objective function; Mathematical programming; nondominated individuals
• ISSN: 1089-778X; 1941-0026
• DOI: 10.1109/TEVC.2006.872344

A considerable number of constrained optimization evolutionary algorithms (COEAs) have been proposed due to increasing interest in solving constrained optimization problems (COPs) by evolutionary algorithms (EAs). In this paper, we first review existing COEAs. Then, a novel EA for constrained optimization is presented. In the process of population evolution, our algorithm is based on multiobjective optimization techniques, i.e., an individual in the parent population may be replaced if it is dominated by a nondominated individual in the offspring population. In addition, three models of a population-based algorithm-generator and an infeasible solution archiving and replacement mechanism are introduced. Furthermore, the simplex crossover is used as a recombination operator to enrich the exploration and exploitation abilities of the approach proposed. The new approach is tested on 13 well-known benchmark functions, and the empirical evidence suggests that it is robust, efficient, and generic when handling linear/nonlinear equality/inequality constraints. Compared with some other state-of-the-art algorithms, our algorithm remarkably outperforms them in terms of the best, mean, and worst objective function values and the standard deviations. It is noteworthy that our algorithm does not require the transformation of equality constraints into inequality constraints