A many-objective evolutionary algorithm with estimating the convexity-concavity of Pareto fronts and clustering

Abstract

Many real-world applications involve several conflicting objectives that can be solved using multiobjective evolutionary algorithms (MOEAs). Nevertheless, when considering the convexity-concavity of Pareto fronts (PFs), which is not common in the existing MOEAs, it may improve the performance of MOEAs. Spurred by this advantage, we propose a many-objective evolutionary algorithm with estimating the Convexity-Concavity of PFs and Clustering, named MaOEA-3C. Specifically, the convexity-concavity of PF is estimated according to a well-converged and well-distributed elitist archive that is updated periodically using non-dominated sorting and a niche-based method. Then, the solution fitness is computed according to the estimation result, enhancing the selection pressure and promoting the convergence when the Pareto dominance fails to select solutions. Additionally, the solutions in the elitist archive guide evolving directions for the current population by clustering, acting like reference vectors in decomposition-based algorithms, thus maintaining the diversity of solutions. The performance of MaOEA-3C is compared with seven state-of-the-art algorithms, and the results demonstrate the effectiveness and competitiveness of MaOEA-3C on many-objective optimization problems.