MOMBI: A new metaheuristic for many-objective optimization based on the R2 indicator

Abstract

The incorporation of performance indicators as the selection mechanism of a multi-objective evolutionary algorithm (MOEA) is a topic that has attracted increasing interest in the last few years. This has been mainly motivated by the fact that Pareto-based selection schemes do not perform properly when solving problems with four or more objectives. The indicator that has been most commonly used for being incorporated in the selection mechanism of a MOEA has been the hypervolume. Here, however, we explore the use of the R2 indicator, which presents some advantages with respect to the hypervolume, the main one being its low computational cost. In this paper, we propose a new MOEA called Many-Objective Metaheuristic Based on the R2 Indicator (MOMBI), which ranks individuals using a utility function. The proposed approach is compared with respect to MOEA/D (based on scalarization) and SMS-EMOA (based on hypervolume) using several benchmark problems. Our preliminary experimental results indicate that MOMBI obtains results of similar quality to those produced by SMS-EMOA, but at a much lower computational cost. Additionally, MOMBI outperforms MOEA/D in most of the test instances adopted, particularly when dealing with high-dimensional problems having complicated Pareto fronts. Thus, we believe that our proposed approach is a viable alternative for solving many-objective optimization problems. 1 The Hypervolume (also known as the S metric or the Lebesgue Measure) of a set of solutions measures the size of the portion of objective space that is dominated by those solutions collectively [6].

Many-Objective Evolutionary Algorithms

“…The empirical results on DTLZ with up to 10 objectives indicate that these algorithms can outperform SMS-EMOA by using much less computational time. Another algorithm based on the R2 indicator, namely many-objective metaheuristic based on R2 indicator (MOMBI), achieved similar performance [Gómez and Coello 2013] (Table X).…”

An Indicator-Based Multiobjective Evolutionary Algorithm With Reference Point Adaptation for Better Versatility

“…For example, Trautmann et al developed an R2 indicator in [34] for solving MOPs, and Gómez and Coello Coello proposed two extensions of R2 based MOEAs for solving MaOPs, termed MOMBI [35] and MOMBI-II [21], respectively; Menchaca-Mendez and Coello Coello proposed a GD indicator based MOEA, termed GD-MOEA [36], and an improved version GDE-MOEA [20] by incorporating the ϵ-dominance into the GD-MOEA algorithm; Rudolph et al [37] developed an MOEA based on the ∆ p indictor, termed AS-MOEA, where ∆ p is a modified composition of GD and IGD [38]- [40].…”

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

“…R2 indicator is associated with less computational cost. Therefore, our main concern is to focus on this operator [46,47]. R2 [48] indicator is defined as:…”