A Grid-Based Evolutionary Algorithm for Many-Objective Optimization

Abstract

Balancing convergence and diversity plays a key role in evolutionary multiobjective optimization (EMO). Most current EMO algorithms perform well on problems with two or three objectives, but encounter difficulties in their scalability to many-objective optimization. This paper proposes a Gridbased Evolutionary Algorithm (GrEA) to solve many-objective optimization problems. Our aim is to exploit the potential of the grid-based approach to strengthen the selection pressure towards the optimal direction while maintaining an extensive and uniform distribution among solutions. To this end, two concepts-grid dominance and grid difference-are introduced to determine the mutual relationship of individuals in a grid environment. Three grid-based criteria, i.e., grid ranking, grid crowding distance, and grid coordinate point distance, are incorporated into the fitness of individuals to distinguish them in both the mating and environmental selection processes. Moreover, a fitness adjustment strategy is developed by adaptively punishing individuals based on the neighborhood and grid dominance relations in order to avoid partial overcrowding as well as guide the search towards different directions in the archive. Six state-of-the-art EMO algorithms are selected as the peer algorithms to validate GrEA. A series of extensive experiments is conducted on 52 instances of 9 test problems taken from 3 test suites. The experimental results show the effectiveness and competitiveness of the proposed GrEA in balancing convergence and diversity. The solution set obtained by GrEA can achieve a better coverage of the Pareto front than that obtained by other algorithms on most of the tested problems. Additionally, a parametric study reveals interesting insights of the division parameter in grid and also indicates useful values for problems with different characteristics.

A Strengthened Dominance Relation Considering Convergence and Diversity for Evolutionary Many-Objective Optimization

“…The second category of dominance relations is based on the gridding of the objective space, such as ϵ-dominance [8], paϵ-dominance [26], cone ϵ-dominance [27], and grid dominance [9]. In the (c) Self-CDAS (S-CDAS) grid dominance relation, the grid coordinate g(…”

“…There exist many techniques for developing new dominance relations in the literature, such as expanding the dominance area [6], [7], gridding the objective space [8], [9], adopting the fuzzy logic [10], [11], and defining the dominance relation by weight vectors [12], [13].…”

“…3) The performance of the proposed SDR is also assessed by embedding it in two existing MOEAs developed for solving MOPs, namely, SPEA2 [20] and PESA-II [21], and three existing MOEAs tailored for handling MaOPs, namely, GrEA [9], KnEA [14], and VaEA [15]. Experimental results demonstrate that the proposed SDR maintains a good balance between convergence and diversity, which can considerably improve the performance of the MOEAs.…”

A benchmark test suite for evolutionary many-objective optimization

“…In recent years, a number of new algorithms have been proposed for dealing with MaOPs [1], including the convergence enhancement based algorithms such as the grid-dominancebased evolutionary algorithm (GrEA) [2], the knee pointdriven evolutionary algorithm (KnEA) [3], the two-archive algorithm (Two_Arch2) [4]; the decomposition-based algorithms such as the NSGA-III [5], and the evolutionary algorithms based on both dominance and decomposition (MOEA/DD) [6], and the reference vector-guided evolutionary algorithm (RVEA) [7]; the performance indicator-based algorithms such as the fast hypervolume-based evolutionary algorithm (HypE) [8]. In spite of the various algorithms proposed for dealing with MaOPs, the literature still lacks a benchmark test suite for evolutionary many-objective optimization.…”

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

“…As for MaOPs, non-dominated sorting has also been favored by researchers in developing MOEAs despite that its effectiveness considerably deteriorates on MaOPs due to the Pareto dominance resistance phenomenon [19]. Some representative MOEAs that directly adopted non-dominated sorting to handle MaOPs include GrEA [20], NSGA-III [21], KnEA [22], and LMEA [23]. There are also some recent works reported that non-dominated sorting is also an effective strategy to which did not use non-dominated sorting in their original versions, e.g., decomposition-based MOEAs with dominance, MOEA/DD [24], and BCE-MOEA/D [25].…”