A Decomposition-Based Many-Objective Evolutionary Algorithm with Local Iterative Update

TL;DR

This paper introduces a decomposition-based many-objective evolutionary algorithm with local iterative update (LIU) that enhances population diversity and solution quality by selectively replacing solutions and iteratively refining subproblem assignments.

Contribution

The proposed LIU strategy improves population diversity and efficiency in MOEAs, with lower time complexity and better performance on benchmark problems compared to existing methods.

Findings

Maintains population diversity effectively on DTLZ4.

Outperforms other MOEAs in solution quality and runtime.

Lower computational complexity similar to MOEA/D.

Abstract

Existing studies have shown that the conventional multi-objective evolutionary algorithms (MOEAs) based on decomposition may lose the population diversity when solving some many-objective optimization problems. In this paper, a simple decomposition-based MOEA with local iterative update (LIU) is proposed. The LIU strategy has two features that are expected to drive the population to approximate the Pareto Front with good distribution. One is that only the worst solution in the current neighborhood is swapped out by the newly generated offspring, preventing the population from being occupied by copies of a few individuals. The other is that its iterative process helps to assign better solutions to subproblems, which is beneficial to make full use of the similarity of solutions to neighboring subproblems and explore local areas in the search space. In addition, the time complexity of the proposed algorithm is the same as that of MOEA/D, and lower than that of other known MOEAs, since it considers only individuals within the current neighborhood at each update. The algorithm is compared with several of the best MOEAs on problems chosen from two famous test suites DTLZ and WFG. Experimental results demonstrate that only a handful of running instances of the algorithm on DTLZ4 lose their population diversity. What's more, the algorithm wins in most of the test instances in terms of both running time and solution quality, indicating that it is very effective in solving MaOPs.