Multi-objective capacitated multiple allocation hub location problem (MOCMAHLP) is a variation of classic hub location problem, which deals with network design, considering both the number and the location of the hubs and the connections between hubs and spokes, as well as routing of flow on the network. In this study, we offer two meta-heuristic approaches based on the non-dominated sorting genetic algorithm (NSGA-II) and archived multi-objective simulated annealing method (AMOSA) to solve MOCMAHLP. We attuned AMOSA based approach to obtain feasible solutions for the problem and developed five different neighborhood operators in this approach. Moreover, for NSGA-II based approach, we developed two novel problem-specific mutation operators. To statistically analyze the behavior of both algorithms, we conducted experiments on two well-known data sets, namely Turkish and Australian Post (AP). Hypervolume indicator is used as the performance metric to measure the effectiveness of both approaches on the given data sets. In the experimental study, thorough tests are conducted to fine-tune the proposed mutation types for NSGA-II and proposed neighborhood operators for AMOSA. Fine-tuning tests reveal that for NSGA-II, mutation probability does not have a real effect on Turkish data set, whereas lower mutation probabilities are slightly better for AP data set. Moreover, among the AMOSA based neighborhood operators, the one which adds/removes a specific number of links according to temperature (NS-5) performs better than the others for both data sets. After analyzing different operators for both algorithms, a comparison between our NSGA-II based and AMOSA based approaches is performed with the best settings. As a result, we conclude that both of our algorithms are able to find feasible solutions of the problem. Moreover, NSGA-II performs better for larger, whereas AMOSA performs better for smaller size networks.

多目标容量多分配集线器位置问题 (MOCMAHLP) 是经典集线器位置问题的变体，它涉及网络设计，同时考虑集线器的数量和位置以及集线器和辐条之间的连接，以及在网络上流动。在这项研究中，我们提供了两种基于非支配排序遗传算法 (NSGA-II) 和存档多目标模拟退火方法 (AMOSA) 的元启发式方法来解决 MOCMAHLP。我们调整了基于 AMOSA 的方法以获得问题的可行解决方案，并在这种方法中开发了五种不同的邻域算子。此外，对于基于 NSGA-II 的方法，我们开发了两个新的特定于问题的变异算子。为了统计分析两种算法的行为，我们对两个著名的数据集进行了实验，即土耳其和澳大利亚邮政 (AP)。Hypervolume 指标用作性能指标来衡量两种方法在给定数据集上的有效性。在实验研究中，进行了彻底的测试以微调 NSGA-II 的拟议突变类型和 AMOSA 的拟议邻域算子。微调测试表明，对于 NSGA-II，突变概率对土耳其语数据集没有真正的影响，而对于 AP 数据集，较低的突变概率稍微好一些。此外，在基于 AMOSA 的邻域算子中，根据温度 (NS-5) 添加/删除特定数量链接的算子在两个数据集上的性能都优于其他算子。在分析了两种算法的不同算子后，使用最佳设置对我们基于 NSGA-II 的方法和基于 AMOSA 的方法进行比较。因此，我们得出结论，我们的两种算法都能够找到问题的可行解决方案。此外，NSGA-II 对于较大的网络表现更好，而 AMOSA 对于较小规模的网络表现更好。