Effects of Discretization of Decision and Objective Spaces on the Performance of Evolutionary Multiobjective Optimization Algorithms
This work addresses performance tuning for evolutionary algorithms in multi-objective optimization, but it is incremental as it extends prior studies on discretization.
The paper investigates how discretizing decision and objective spaces affects evolutionary multi-objective optimization algorithms, finding that decision space discretization improves performance on large-scale problems, objective space discretization helps on many-objective problems, and simultaneous discretization benefits large-scale many-objective problems.
Recently, the discretization of decision and objective spaces has been discussed in the literature. In some studies, it is shown that the decision space discretization improves the performance of evolutionary multi-objective optimization (EMO) algorithms on continuous multi-objective test problems. In other studies, it is shown that the objective space discretization improves the performance on combinatorial multi-objective problems. However, the effect of the simultaneous discretization of both spaces has not been examined in the literature. In this paper, we examine the effects of the decision space discretization, objective space discretization and simultaneous discretization on the performance of NSGA-II through computational experiments on the DTLZ and WFG problems. Using various settings about the number of decision variables and the number of objectives, our experiments are performed on four types of problems: standard problems, large-scale problems, many-objective problems, and large-scale many-objective problems. We show that the decision space discretization has a positive effect for large-scale problems and the objective space discretization has a positive effect for many-objective problems. We also show the discretization of both spaces is useful for large-scale many-objective problems.