Optimization of Scalarizing Functions Through Evolutionary Multiobjective Optimization

Abstract

Abstract. This paper proposes an idea of using evolutionary multiobjective optimization (EMO) to optimize scalarizing functions. We assume that a scalarizing function to be optimized has already been generated from an original multiobjective problem. Our task is to optimize the given scalarizing function. In order to efficiently search for its optimal solution without getting stuck in local optima, we generate a new multiobjective problem to which an EMO algorithm is applied. The point is to specify multiple objectives, which are similar to but different from the scalarizing function, so that the location of the optimal solution is near the center of the Pareto front of the generated multiobjective problem. The use of EMO algorithms helps escape from local optima. It also helps find a number of alternative solutions around the optimal solution. Difficulties of Pareto ranking-based EMO algorithms in the handling of many objectives are avoided by the use of similar objectives. In this paper, we first demonstrate that the performance of EMO algorithms as single-objective optimizers of scalarizing functions highly depends on the choice of multiple objectives. Based on this observation, we propose a specification method of multiple objectives for the optimization of a weighted sum fitness function. Experimental results show that our approach works very well in the search for not only a single optimal solution but also a number of good alternative solutions around the optimal solution. Next we evaluate the performance of our approach in comparison with a hybrid EMO algorithm where a single-objective fitness evaluation scheme is probabilistically used in an EMO algorithm. Then we show that our approach can be also used to optimize other scalarizing functions (e.g., those based on constraint conditions and reference solutions). Finally we show that our approach is applicable not only to scalarizing functions but also other single-objective optimization problems.

Performance evaluation of evolutionary multiobjective optimization algorithms for multiobjective fuzzy genetics-based machine learning

“…Whereas very good experimental results of EMO algorithms on a number of test problems have been reported in the literature, they do not always work well on multiobjective combinatorial optimization problems. For example, it was pointed out in some studies (Ishibuchi and Nojima 2007b;Jaszkiewicz 2002Jaszkiewicz , 2004Sato et al 2007) that well-known and frequently used EMO algorithms such as NSGA-II (Deb et al 2002), SPEA (Zitzler and Thiele 1999) and SPEA2 (Zitzler et al 2001) could not find a set of non-dominated solutions that approximate the entire Pareto front of a two-objective 0-1 knapsack problem very well.…”

Swarm Intelligence in Multiple and Many Objectives Optimization: A Survey and Topical Study on EEG Signal Analysis

“…Non-Pareto dominance based approach include techniques like indicator function [24-26, 28-30, 175], scalarizing function (a kind of weighted sum approach) [31][32][33][34][35][36][37], and preference information [27,[38][39][40][41][42][43][44]. Out of the above three approaches indicator function approach is widely used.…”

“…iv. Use of scalarizing function [142]: In this technique weighted sum of multiple objectives are calculated even though the number of objectives is large. There are many scalarizing functions available in the literature like weighted sum, reference vector etc.…”

Adaptive ε-Ranking on many-objective problems

“…Recently, there is a growing interest on applying EMOs to solve many-objective optimization problems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], where the number of objectives to optimize simultaneously is more than three. However, on many-objective problems the number of Pareto non-dominated solutions could increase substantially with the dimensionality of the objective space [4,8].…”