Balancing Convergence and Diversity in Multiobjective Immune Algorithm

Recently, multiobjective immune algorithms (MOIAs) become popular, which are designed for multiobjective optimization problems (MOPs). However, most existing MOIAs put more attention on maintaining diversity as the used clonal selection strategy will allocate more cloning for the sparse areas, which may hamper the convergence to speed to the optimal Pareto front, especially for some complicated MOPs. To alleviate the phenomenon mentioned above, we propose a dynamic mechanism into traditional MOIAs in this paper, aiming to balance convergence and diversity, called BCD-MOIA. First, MOP will be decomposed into several single subproblems by decomposition method, and then these subproblems will be optimized simultaneously. Second, we propose a novel measure metric instead of the crowding distance to assign the clone number for each solution, which includes two main parts. The first part focuses on the diversity performance, i.e., the perpendicular distance between solution and its associated weight vectors. The second part uses the aggregated function values quantified by the decomposition method, which is more efficient for accelerating the convergence speed and maintaining diversity as well. Moreover, a dynamic mechanism is performed during the whole evolutionary process, focusing on diversity and convergence at different stages. By this way, our proposed algorithm can tradeoff the performance on convergence and diversity dynamically. The effectiveness of our proposed algorithm BCD-MOIA is validated by comparing with three competitive MOIAs and three multi-objective evolutionary algorithms for tackling two sets of complicated problems.