IT-CEMOP: An iterative co-evolutionary algorithm for multiobjective optimization problem with nonlinear constraints M.S. Osman a , Mahmoud A. Abo-Sinna b , A.A. Mousa b, * a High Institute of Technology, 10th Ramadan city, Egypt b Department of Basic Engineering Science, Faculty of Engineering, Shebin El-Kom, Menoufia University, Egypt Abstract Over the past few years, researchers have developed a number of multiobjective evolutionary algorithms (MOEAs). Although most studies concentrate on solving unconstrained optimization problems, there exit a few studies where MOEAs have been extended to solve constrained optimization problems. Most of them were based on penalty functions for handling nonlinear constraints by genetic algorithms. However the performance of these methods is highly problem- dependent, many methods require additional tuning of several parameters. In this paper, we present a new optimization algorithm, which is based on concept of co-evolution and repair algorithm for handling nonlinear constraints. The algorithm maintains a finite-sized archive of nondominated solutions which gets iteratively updated in the presence of new solutions based on the concept of e-dominance. The use of e-dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto set approximation by choosing an appropriate e value, which guarantees convergence and diversity. The results, provided by the proposed algorithm for six benchmark problems, are promising when compared with exiting well-known algorithms. Also, our results suggest that our algorithm is better applicable for solving real-world application problems. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Multiobjective nonlinear programming; Multiobjective evolutionary algorithms; Genetic algorithms; e-Dominance 1. Introduction When attempting to optimize a decision in industrial and scientific applications, the designer is frequently faced with the problem of achieving several design targets, some of which may be conflicting and noncommen- surable and wherein a gain in one objective is at the expense of another. This problem can be generally reduced to multiobjective optimization problems (MOPs) in operational description, which has been in the spotlight of operations research communities over years. Usually, there is no unique optimal solution, but rather a set of 0096-3003/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2006.05.095 * Corresponding author. E-mail address: A_mousa15@yahoo.com (A.A. Mousa). Applied Mathematics and Computation 183 (2006) 373–389 www.elsevier.com/locate/amc