Evolutionary algorithms via decomposition, namely, DEAs, decompose the original challenging problem and evolve a number of subproblems/subspaces concurrently in a cooperative fashion. Adaptive computational resource allocation (CRA) strategy is able to identify the efficiency of different subspaces and invest search effort on them accordingly in an online manner. A crucial issue for CRA is to measure the efficiency of subspaces. Unfortunately, existing approaches for efficiency measurement are either fitness improvement oriented or contribution oriented, which struggle to capture the potentials of subspaces accurately. To mitigate such drawback, we present an ensemble method for CRA, based on the recent fitness contribution rates (FCRs) and fitness improvement rates (FIRs) of subspaces simultaneously. In order to dynamically track the potential of each subregion, we adopt two memory matrices to record FIR and FCR for multiple subspaces over recent generations, respectively. Afterward, an aptitude vector indicating the potentials of subspaces is defined by exploiting FCR and FIR with memory and decaying scheme. On the basis of above strategies, an ensemble CRA (ECRA) scheme is designed, which is then embedded into an adaptive objective space partition-based DEA, termed ECRA-DEA, for solving the multi/many-objective optimization. Extensive experimental studies for ECRA-DEA on various types of challenging problems have been carried out and the results confirm that ECRA is effective. Besides, the competence of ECRA-DEA is empirically validated in comparison with state-of-the-art designs. The proposed ECRA paves a new way to leverage the capability of DEAs on handling complex problems.

中文翻译：

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用于基于分解的多目标优化的动态资源分配策略集合

通过分解的进化算法，即 DEA，分解原始具有挑战性的问题，并以协作的方式同时进化多个子问题/子空间。自适应计算资源分配 (CRA) 策略能够识别不同子空间的效率，并以在线方式相应地对它们进行搜索。CRA 的一个关键问题是测量子空间的效率。不幸的是，现有的效率测量方法要么以适应度改进为导向，要么以贡献为导向，难以准确捕捉子空间的潜力。为了减轻这种缺点，我们提出了一种 CRA 的集成方法，基于最近的子空间的适应度贡献率（FCR）和适应度改善率（FIR）。为了动态跟踪每个子区域的潜力，我们采用两个存储矩阵分别记录最近几代多个子空间的 FIR 和 FCR。然后，通过利用具有记忆和衰减方案的 FCR 和 FIR 来定义指示子空间势的能力向量。在上述策略的基础上，设计了一种集成 CRA（ECRA）方案，然后将其嵌入到基于自适应目标空间分区的 DEA 中，称为 ECRA-DEA，用于解决多目标/多目标优化问题。已经对 ECRA-DEA 对各种具有挑战性的问题进行了广泛的实验研究，结果证实 ECRA 是有效的。此外，与最先进的设计相比，ECRA-DEA 的能力得到了经验验证。