Ranking Methods for Many-Objective Optimization

Abstract

Abstract. An important issue with Evolutionary Algorithms (EAs) is the way to identify the best solutions in order to guide the search process. Fitness comparisons among solutions in single-objective optimization is straightforward, but when dealing with multiple objectives, it becomes a non-trivial task. Pareto dominance has been the most commonly adopted relation to compare solutions in a multiobjective optimization context. However, it has been shown that as the number of objectives increases, the convergence ability of approaches based on Pareto dominance decreases. In this paper, we propose three novel fitness assignment methods for many-objective optimization. We also perform a comparative study in order to investigate how effective are the proposed approaches to guide the search in high-dimensional objective spaces. Results indicate that our approaches behave better than six state-of-the-art fitness assignment methods.

Evolutionary many-objective optimization: A quick-start guide

“…An increase in the number of objectives causes a large portion of a randomly generated population to become non-dominated [28]. Having a population which is largely composed of non-dominated solutions does not give room for creating new solutions in every generation [3,13].…”

“…Most of the EMO algorithms use the concept of Pareto Dominance in order to compare and identify the best solutions [28]. An increase in the number of objectives causes a large portion of a randomly generated population to become non-dominated [28].…”

Evolutionary many-objective optimization by MO-NSGA-II with enhanced mating selection

“…The experimental results showed that average ranking is a good method. Garza-Fabre et al [26] proposed three ranking methods, two based on the difference of objective values between individuals and one based on the distance to the ideal point.…”

“…The second direction is to improve the weak selective pressure of dominance-based selection when facing the large number of non-dominated solutions in the population. The techniques may modify Pareto dominance or assign different ranks to non-dominated solutions [20]− [26]. The third direction is to try selection mechanisms other than dominance-based ones, such as adopting performance indicators (e.g.…”

Many Objective Particle Swarm Optimization

“…The ranking method is called global detriment (GD) and has been proposed by the same authors of the CEGA in[17]. The global detriment is a ranking method based on distances objective-wise between the individual and the others individuals of the population.…”