Application of coevolutionary genetic algorithms for multiobjective optimization

Abstract

Multiobjective optimization is clearly one of the most important classes of problems in science and engineering. The solution of real problem involved in multiobjective optimization must satisfy all optimization objectives simultaneously, and in general the solution is a set of indeterminacy points. The task of multiobjective optimization is to estimate the distribution of this solution set, then to find the satisfying solution in it. Many methods solving multiobjective optimization using genetic algorithm have been proposed in recent twenty years. But these approaches tend to work negatively, causing that the population converges to small number of solutions due to the random genetic drift. To avoid this phenomenon, a multiobjective coevolutionary genetic algorithm (MoCGA) for multiobjective optimization is proposed. The primary design goal of the proposed approach is to produce a reasonably good approximation of the true Pareto front of a problem. In the algorithms, each objective corresponds to a population. At each generation, these populations compete among themselves. An ecological population density competition equation is used for reference to describe the relation between multiple objectives and to direct the adjustment over the relation at individual and population levels. The proposed approach store the Pareto optimal point obtained along the evolutionary process into external set. The proposed approach is validated using Schaffer's test function f₂ and it is compared with the Niched Pareto GA (nPGA). Simulation experiments prove that the algorithm has a better performance in finding the Pareto solutions, and the MoCGA can have advantages over the other algorithms under consideration in convergence to the Pareto-optimal front.