Interactive Evolutionary Multi-Objective Optimization Algorithm Using Cone Dominance

As the number of objectives increases, the performance of the Pareto dominance-based Evolutionary Multi-objective Optimization (EMO) algorithms such as NSGA-II, SPEA2 severely deteriorates due to the drastic increase in the Pareto-incomparable solutions. We propose a sorting method which classifies these incomparable solutions into several ordered classes by using the decision maker's (DM) preference information. This is accomplished by designing an interactive evolutionary algorithm and constructing convex cones. This method allows the DMs to drive the search process toward a preferred region of the Pareto optimal front. The performance of the proposed algorithm is assessed for two, three, and four-objective knapsack problems. The results demonstrate the algorithm's ability to converge to the most preferred point. The evaluation and comparison of the results indicate that the proposed approach gives better solutions than that of NSGA-II. In addition, the approach is more efficient compared to NSGA-II in terms of the number of generations required to reach the preferred point.