Abstract
Evolutionary algorithms have proved to be efficient approaches in pursuing optimum solutions of multiobjective optimization problems with the number of objectives equal to or less than three. However, the searching performance degenerates in high-dimensional objective optimizations. In this paper we propose an algorithm for many-objective optimization with particle swarm optimization as the underlying metaheuristic technique. In the proposed algorithm, the objectives are decomposed and reconstructed using discrete decoupling strategy, and the subgroup procedures are integrated into unified coevolution strategy. The proposed algorithm consists of inner and outer evolutionary processes, together with adaptive factor μ, to maintain convergence and diversity. At the same time, a designed repository reconstruction strategy and improved leader selection techniques of MOPSO are introduced. The comparative experimental results prove that the proposed UMOPSO-D outperforms the other six algorithms, including four common used algorithms and two newly proposed algorithms based on decomposition, especially in high-dimensional targets.
Highlights
Many-objective optimization problems (MaOPs) refer to the optimizations which consisted of a larger number of objectives
On Generational Distance (GD) metric, first of all, we focus on the comparison between UMOPSO-D and the peer algorithms
The statistical records show that UMOPSO-D is associated with poorer performance in DTLZ3 as compared to other DTLZs in all dimensions, with the relatively higher GD value from other comparison algorithms; this indicates the difficulty in searching the Pareto front (PF) for DTLZ3
Summary
Many-objective optimization problems (MaOPs) refer to the optimizations which consisted of a larger number of objectives. The commonly used evolutionary algorithms such as NSGA-II, SPEA2, MOPSO, and their improved or integrating methods are devoted to finding the solutions with uniform distribution to the Pareto front (PF) and maintaining the group diversity during the evolution as well [1,2,3,4]. None of these classical methods meet high level when facing the many-objective problems, because the process of Pareto dominance makes the individuals nondominated with each other at early generations [5]. The computational complexity rises to execute searching in high-dimensional space results in long-time search procedure, poor convergence, and incomplete solution set
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