Vertical distance-based clonal selection mechanism for the multiobjective immune algorithm

Abstract

Traditional multiobjective immune algorithms (MOIAs) widely use the domination relationship and crowding distance metric to run the cloning operator, which places more attention on nondominated solutions with larger crowding distance values. This “convergence-first” cloning principle may hamper population diversity. To better maintain population diversity in most traditional MOIAs, we propose a novel vertical distance-based clonal selection mechanism for MOIAs, called VD-MOIA in this paper, which arranges the cloning numbers for each solution based on the vertical distance value between the solution and its corresponding weight vector. First, the decomposition approach is used to decompose the target MOP into a set of subproblems, which are then optimized cooperatively and simultaneously. Second, the vertical distance-based clonal selection mechanism is performed, which puts more emphasis on the solutions with small vertical distance values. A large number of clones is allocated to the solutions that show good performance in terms of diversity, as these solutions are closer to their corresponding weight vectors than solutions that result in poor diversity. Moreover, the aggregated values quantified by the Chebyshev function are used to ensure convergence, while differential evolution (DE) is employed to strengthen the exploration ability of the algorithm, which further improves the population diversity as well. To validate the effectiveness of our proposed algorithm, twenty-eight multiobjective benchmark problems are adopted with complicated Pareto-optimal sets and fronts. The experimental comparison results validate the superiority of our proposed VD-MOIA when compared with four competitive MOIAs and four state-of-the-art multiobjective evolutionary algorithms.