Although cooperative coevolutionary algorithms are developed for large-scale dynamic optimization via subspace decomposition, they still face difficulties in reacting to environmental changes, in the presence of multiple peaks in the fitness functions and unevenness of subproblems. The resource allocation mechanisms among subproblems in the existing algorithms rely mainly on the fitness improvements already made but not potential ones. On the one hand, there is a lack of sufficient computing resources to achieve potential fitness improvements for some hard subproblems. On the other hand, the existing algorithms waste computing resources aiming to find most of the local optima of problems. In this article, we propose a cooperative particle swarm optimization algorithm to address these issues by introducing a bilevel balanceable resource allocation mechanism. A search strategy in the lower level is introduced to select some promising solutions from an archive based on solution diversity and quality to identify new peaks in every subproblem. A resource allocation strategy in the upper level is introduced to balance the coevolution of multiple subproblems by referring to their historical improvements and more computing resources are allocated for solving the subproblems that perform poorly but are expected to make great fitness improvements. Experimental results demonstrate that the proposed algorithm is competitive with the state-of-the-art algorithms in terms of objective function values and response efficiency with respect to environmental changes.

中文翻译：

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用于大规模动态优化的双层资源分配机制的合作粒子群优化

尽管合作协同进化算法是为通过子空间分解进行大规模动态优化而开发的，但在适应度函数中存在多个峰值和子问题不均匀的情况下，它们仍然面临着对环境变化做出反应的困难。现有算法中子问题之间的资源分配机制主要依赖于已经做出的适应度改进，而不是潜在的改进。一方面，缺乏足够的计算资源来实现某些困难子问题的潜在适应度改进。另一方面，现有算法浪费了计算资源，旨在找到问题的大部分局部最优值。在本文中，我们提出了一种合作粒子群优化算法，通过引入双层平衡资源分配机制来解决这些问题。引入了较低级别的搜索策略，根据解决方案的多样性和质量从存档中选择一些有前途的解决方案，以识别每个子问题中的新峰值。上层引入了资源分配策略，通过参考子问题的历史改进来平衡多个子问题的协同演化，分配更多的计算资源来解决性能较差但有望获得较大适应度改进的子问题。实验结果表明，所提出的算法在目标函数值和对环境变化的响应效率方面与最先进的算法具有竞争力。