Preference-based NSGA-II for many-objective knapsack problems

Many-objective optimization has attracted increasing attention in the evolutionary multi-objective optimization (EMO) community. It has been repeatedly demonstrated that many-objective optimization problems with four or more objectives are very difficult to solve for EMO algorithms. Whereas a number of performance improvement attempts have been proposed, many-objective optimization is still difficult for EMO algorithms. In our previous study, we proposed a preference-based approach where Gaussian functions on a hyperplane in the objective space are used for preference representation. In this paper, we examine the behavior of our approach in the handling of combinatorial many-objective problems. Through computational experiments on multi-objective knapsack problems with 2-10 objectives, a set of well-distributed solutions over the preferred regions is obtained for each test problem. A trade-off relation between convergence and diversity for the preferred regions is also observed through computational experiments.