This paper proposes a two-archive algorithm with decomposition and fitness allocation for multi-modal multi-objective optimization problems which have more than one Pareto-optimal solution set corresponding to the same objective vector. The general framework of the proposed method uses two archives, the convergence archive (CA) and the diversity archive (DA), which focus on the convergence and diversity of population, respectively. Both archives are based on a decomposition-based framework. In CA, the population update strategy adopts a fitness scheme, which is designed according to the change state of population during evolution, combining the convergence of the objective space with the diversity of the decision space. In DA, we use the crowding distance strategy to ensure the diversity of the decision space. Moreover, different neighborhood criteria are used to ensure the convergence and diversity of population for two archives. The algorithm is shown to not only locate and maintain a larger number of Pareto-optimal sets, but also to obtain good diversity and convergence in both the decision and objective spaces. In addition, the proposed algorithm is empirically compared with five state-of-the-art evolutionary algorithms on two series of test functions. Comparison results show that the proposed algorithm has better performance than the competing algorithms.

针对具有多个帕累托最优解集对应同一目标向量的多模态多目标优化问题，本文提出了一种具有分解和适应度分配的二存档算法。所提出方法的一般框架使用两个档案，收敛档案（CA）和多样性档案（DA），分别关注种群的收敛性和多样性。这两个档案都基于一个基于分解的框架。在CA中，种群更新策略采用适应度方案，该方案根据种群在进化过程中的变化状态设计，结合目标空间的收敛性和决策空间的多样性。在DA中，我们使用拥挤距离策略来保证决策空间的多样性。而且，不同的邻里标准被用来确保两个档案馆的人口趋同和多样性。该算法不仅可以定位和维护大量的帕累托最优集，而且在决策空间和目标空间中都获得了良好的多样性和收敛性。此外，所提出的算法在两个系列的测试函数上与五种最先进的进化算法进行了经验比较。比较结果表明，所提出的算法比竞争算法具有更好的性能。在两个系列的测试函数上，将所提出的算法与五种最先进的进化算法进行了经验比较。比较结果表明，所提出的算法比竞争算法具有更好的性能。在两个系列的测试函数上，将所提出的算法与五种最先进的进化算法进行了经验比较。比较结果表明，所提出的算法比竞争算法具有更好的性能。