A New Genetic Algorithm and Its Convergence for Constrained Optimization Problems

Constrained optimization problems are one of the most important mathematical programming problems frequently encountered in the disciplines of science and engineering applications. In this paper, a new approach is presented to handle constrained optimization problems. The new technique treats constrained optimization as a two-objective optimization and a new genetic algorithm with specifically designed genetic operators is proposed. The crossover operator adopts the idea of PSO but improves its search ability. To keep the diversity and generate the individuals near the boundary of the feasible region, the crossover is made between the individual taken part in the crossover and its farthest particle. As a necessary complement to crossover operator, the mutation operator is designed by using the shrinking chaotic technique and has strong local search ability. The selection operator is designed to prefer to the feasible solutions. Furthermore, the convergence of the algorithm is analyzed. At last, the computer simulation demonstrates the effectiveness of the proposed algorithm.