Controlling Dominance Area of Solutions and Its Impact on the Performance of MOEAs

Abstract

Abstract. This work proposes a method to control the dominance area of solutions in order to induce appropriate ranking of solutions for the problem at hand, enhance selection, and improve the performance of MOEAs on combinatorial optimization problems. The proposed method can control the degree of expansion or contraction of the dominance area of solutions using a user-defined parameter S. Modifying the dominance area of solutions changes their dominance relation inducing a ranking of solutions that is different to conventional dominance. In this work we use 0/1 multiobjective knapsack problems to analyze the effects on solutions ranking caused by contracting and expanding the dominance area of solutions and its impact on the search performance of a multiobjective optimizer when the number of objectives, the size of the search space, and the complexity of the problems vary. We show that either convergence or diversity can be emphasized by contracting or expanding the dominance area. Also, we show that the optimal value of the area of dominance depends strongly on all factors analyzed here: number of objectives, size of the search space, and complexity of the problems.

Effectiveness and efficiency of non-dominated sorting for evolutionary multi- and many-objective optimization

“…For two random solutions with M objectives, the probability that one solution dominates the other one is ( 1 2 ) M−1 , and hence, it is rare for one solution to dominate the other one in high-dimensional space. The controlling dominance area of solutions (CDAS) method [39] expands the dominance area of each solution by a specified angle on each objective, and thus, the probability of dominance and the selection pressure increase. An adaptive version of CDAS was suggested in [40], where the expanding angle was adaptively estimated according to the extreme solutions.…”

Objective reduction based on nonlinear correlation information entropy

“…Much work aims to modify the original dominance relation (Köppen et al 2005;Kukkonen and Lampinen 2007;Sato et al 2007;Farina and Amato 2002;Dai et al 2015), but their performance is still less than satisfactory. -Decomposition-based MOEAs The main idea is to solve MaOPs by aggregation functions with a series of weight vectors to obtain several single-objective optimization problems (Zhang and Li 2007;Ma et al 2014), but it suffers from poor performance on MaOPs with highly correlated objectives (Ishibuchi et al 2009) because of the unsuitable arrangement of weight vectors (Ishibuchi et al 2011a, b).…”

PSA Based Multi Objective Evolutionary Algorithms

“…The underlying principle of ε-dominance is that two solutions are not allowed to be non-dominated to each other, if the difference between them is less than a properly chosen value. Extensions based on this idea are the CDAS [21], where the user can control the size of a solution's dominated area and the cone ε-dominance [18], where the shape of the dominated area is a cone.…”