Many-Objective Evolutionary Algorithm: Objective Space Reduction and Diversity Improvement

Abstract

Evolutionary algorithms have been successfully applied for exploring both converged and diversified approximate Pareto-optimal fronts in multiobjective optimization problems, two-or three-objective in general. However, when solving problems with many objectives, nearly all algorithms perform poorly due to the loss of selection pressure in fitness evaluation. An extremely large objective space could inadvertently deteriorate the effect of an evolutionary operator. In this paper, we propose a new approach to directly handle the challenges to solve many-objective optimization problems. This novel design includes two stages: first, the whole population quickly approaches a small number of "target" points near the true Pareto front; then, the proposed diversity improvement strategy is applied to facilitate these individuals to spread and distribute well. As a case study, the proposed algorithm based on this design is compared with five state-of-the-art algorithms. Experimental results show that the proposed method exhibits improved performance in both convergence and diversity for solving many-objective optimization problems. IndexTerms-Objective space reduction, diversity improvement strategy, many-objective optimization problems, many-objective evolutionary algorithms 1089-778X (c)

PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum]

“…MaOEA-R&D [50] 2016 Many-objective evolutionary algorithm based on objective space reduction and diversity improvement RPEA [51] 2016 Reference points-based evolutionary algorithm RVEA [52] 2016 Reference vector guided evolutionary algorithm RVEA* [52] 2016 RVEA embedded with the reference vector regeneration strategy SPEA/R [53] 2016 Strength Pareto evolutionary algorithm based on reference direction θ-DEA [54] 2016 θ-dominance based evolutionary algorithm…”

A mutation operator guided by preferred regions for set-based many-objective evolutionary optimization

“…Bandyopadhyay and Mukherjee [12] developed an algorithm for MaOPs that periodically orders objectives based on the correlation and selects a subset of conflicting objectives. In the method proposed by He and Yen [13], a scheme of reducing the objective space and a strategy of improving the diversity of a population are employed to address the following two issues: a large search space and an ineffective Pareto-optimal set. Cheung et al [14] proposed a method of extracting objectives that minimizes the correlation between reduced objectives using a linear combination of the original objectives.…”

“…As a result, MaOPs are very challenging and have received a lot of attention in the evolutionary optimization community in recent years [4][5][6][7][8][9][10]. At present, approaches for solving MaOPs can be grouped into the following four categories: (1) increasing the selection pressure via novel Pareto dominance relations [5][6][7][8][9]; (2) deleting redundant objectives according to certain principles [11][12][13][14]; (3) transforming an MaOP into one or several single-objective optimization problems by weighting or decomposing objectives [15][16][17][18][19][20]; (4) utilizing a certain performance indicator to evaluate individuals [21,22]; (5) taking a set of solutions and performance indicators as the variable and objectives of a new optimization problem, respectively, and utilizing set-based evolutionary operators to solve the new problem [23][24][25][26].…”

Evolutionary Many-Objective Optimization of Hybrid Electric Vehicle Control: From General Optimization to Preference Articulation

“…For example, a shift-based density estimation strategy is proposed to penalize poorly converged solutions that cannot be distinguished by Pareto dominance [20]; a knee point based secondary selection is introduced on top of non-dominated sorting to enhance convergence pressure in the recently proposed knee point driven evolutionary algorithm (KnEA) [21]. Some other recent work along this line includes the two-archive algorithm for many-objective optimization (Two Arch2) [22], manyobjective evolutionary algorithm based on both objective space reduction and diversity enhancement (MaOEA-R&D) [23], and the recently proposed bi-criterion evolutionary algorithm (BCE) [24].…”