The large-scale multiobjective optimization problem (LSMOP) is characterized by simultaneously optimizing multiple conflicting objectives and involving hundreds of decision variables. Many real-world applications in engineering fields can be modeled as LSMOPs; simultaneously, engineering applications require insensitivity in performance. This requirement usually means that the results from the algorithm runs should not only be good for every run in terms of performance but also that the performance of multiple runs should not fluctuate too much, i.e., the algorithm shows good insensitivity. Considering that substantial computational resources are requested for each run, it is essential to improve upon the performance of the large-scale multiobjective optimization algorithm, as well as the insensitivity of the algorithm. However, existing large-scale multiobjective optimization algorithms solely focus on improving the performance of the algorithms, leaving the insensitivity characteristics unattended. In this work, we propose an evolutionary algorithm for solving LSMOPs based on Monte Carlo tree search, the so-called LMMOCTS, which aims to improve the performance and insensitivity for large-scale multiobjective optimization problems. The proposed method samples the decision variables to construct new nodes on the Monte Carlo tree for optimization and evaluation. It selects nodes with good evaluation for further search to reduce the performance sensitivity caused by large-scale decision variables. We compare the proposed algorithm with several state-of-the-art designs on different benchmark functions. We also propose two metrics to measure the sensitivity of the algorithm. The experimental results confirm the effectiveness and performance insensitivity of the proposed design for solving large-scale multiobjective optimization problems.

翻译：大规模多目标优化问题（LSMOP）以同时优化多个相互冲突的目标并涉及数百个决策变量为特征。工程领域的许多实际应用可建模为LSMOP；同时，工程应用要求性能具有不敏感性。这一要求通常意味着算法运行结果不仅应在每次执行时表现良好，而且多次运行的性能不应波动过大，即算法表现出良好的不敏感性。考虑到每次运行需要大量计算资源，在提升大规模多目标优化算法性能的同时增强其不敏感性至关重要。然而，现有大规模多目标优化算法仅关注算法性能的提升，忽视了不敏感性特性。本文提出一种基于蒙特卡洛树搜索的求解LSMOP的进化算法——LMMOCTS，旨在提升大规模多目标优化问题的性能与不敏感性。该方法对决策变量进行采样，在蒙特卡洛树上构建新节点以进行优化与评估，并选择评估结果良好的节点进行深入搜索，从而减少大规模决策变量导致的性能敏感性。我们将所提算法与多种最新设计在不同基准函数上进行比较，同时提出两种度量算法敏感性的指标。实验结果验证了所提设计在求解大规模多目标优化问题中的有效性与性能不敏感性。