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| Maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms (EAs). However, traditional multi-objective evolutionary algorithms, which have demonstrated their competitive performance in a variety of practical problems involving two or three objectives, face significant challenges in many-objective optimization problems (MaOPs). This paper proposes a dynamic convergence-diversity guided evolutionary algorithm (DCDG-EA) for MaOPs by employing decomposition technique. The objective space of MaOPs is divided into $K$ subspaces by a set of uniformly distributed reference vectors. Each subspace has its own subpopulation and evolves in parallel with the other subspaces. In DCDG-EA, the balance between convergence and diversity is achieved through convergence-diversity based operator selection (CDOS) strategy and convergence-diversity based individual selection (CDIS) strategy. In CDOS, each operator in a set of operators is assigned a selection probability which is related to its convergence and diversity reward. On the basis of selection probability, an appropriate operator is selected to generate offspring. Furthermore, CDIS greatly overcomes the inefficiency of Pareto dominance. It updates each subpopulation by using two independent distance measures that respectively represent convergence and control diversity. The experimental results on DTLZ benchmark problems with up to 15 objectives show that our algorithm is highly competitive in comparison with the selected four state-of-the-art evolutionary algorithms in terms of convergence and diversity. |
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| Keywords:Many-objective optimization, convergence, diversity, decomposition, evolutionary algorithm, Pareto optimality. |
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