Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms

In trying to solve multiobjective optimization problems, many traditional methods scalar-ize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. Since genetic algorithms(GAs) work with a population of points, it seems natural to use GAs in multiobjec-tive optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaaer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias towards some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to nd multiple Pareto-optimal points simultaneously. The proof-of-principle results obtained on three problems used by Schaaer and others suggest that the proposed method can be extended to higher dimensional and more diicult multiobjective problems. A number of suggestions for extension and application of the algorithm is also discussed.