A Study on the Performance of Substitute Distance Based Approaches for Evolutionary Many Objective Optimization

Non-dominated Sorting Genetic Algorithm (NSGA-II) [1] and the Strength Pareto Evolutionary Algorithm (SPEA2) [2] are the two most widely used evolutionary multi-objective optimization algorithms. Although, they have been quite successful so far in solving a wide variety of real life optimization problems mostly 2 or 3 objective in nature, their performance is known to deteriorate significantly with an increasing number of objectives. The term

many objective optimization

refers to problems with number of objectives significantly larger than two or three. In this paper, we provide an overview of the challenges involved in solving many objective optimization problems and provide an in depth study on the performance of recently proposed substitute distance based approaches, viz. Subvector dominance, -eps-dominance, Fuzzy Pareto Dominance and Sub-objective dominance count for NSGA-II to deal with many objective optimization problems. The present study has been conducted on scalable benchmark functions (DTLZ2-DTLZ3) and the recently proposed P* problem [3] since their convergence and diversity measures can be compared conveniently. An alternative substitute distance approach is introduced in this paper and compared with existing ones on the set of benchmark problems.