4 Experiments This section examines the effectiveness of the proposed IFCS-MOEA framework. First, Section 4.1 presents the experimental settings. Second, Section 4.2 examines the effect of IFCS on MOEA/D-DE. Then, Section 4.3 compares the performance of IFCS-MOEA/D-DE with five state-of-the-art MOEAs on 19 test problems. Finally, Section 4.4 compares the performance of IFCS-MOEA/D-DE with five state-of-the-art MOEAs on four real-world application problems. 4.1 Experimental Settings MOEA/D-DE [23] is integrated with the proposed framework for experiments, and the resulting algorithm is named IFCS-MOEA/D-DE. Five surrogate-based MOEAs, i.e., FCS-MOEA/D-DE [39], CPS-MOEA [41], CSEA [29], MOEA/DEGO [43] and EDN-ARM-OEA [12] are used for comparison. UF1–10, LZ1–9 test problems [44, 23] with complicated PSs are used for experiments. Among them, UF1–7, LZ1–5, and LZ7–9 have 2 objectives, UF8–10, and LZ6 have 3 objectives. UF1–10, LZ1–5, and LZ9 are with 30 decision variables, and LZ6–8 are with 10 decision variables. The population size N is set to 45 for all compared algorithms. The maximum number of FEs is set as 500 since the problems are viewed as expensive MOPs [39]. For each test problem, each algorithm is executed 21 times independently. For IFCS-MOEA/D-DE, wmax is set to 30 and η is set to 5. For the other algorithms, we use the settings suggested in their papers. The IGD [6] metric is used to evaluate the performance of each algorithm. All algorithms are examined on PlatEMO [34] platform.

4 实验
本节将研究所提出的IFCS-MOEA框架的有效性。首先，在第4.1节中介绍实验设置。其次，在第4.2节中研究IFCS对MOEA/D-DE的影响。然后，在第4.3节中，将IFCS-MOEA/D-DE与19个测试问题上的五种最先进的MOEA进行比较。最后，在第4.4节中，将IFCS-MOEA/D-DE与四种真实世界应用问题上的五种最先进的MOEA进行比较。

4.1 实验设置
实验中将MOEA/D-DE [23]与所提出的框架集成，得到的算法称为IFCS-MOEA/D-DE。比较使用了五种基于代理的MOEA，即FCS-MOEA/D-DE [39]，CPS-MOEA [41]，CSEA [29]，MOEA/D-EGO [43]和EDN-ARM-OEA [12]。使用了具有复杂PS的UF1-10、LZ1-9测试问题[44，23]。其中，UF1-7、LZ1-5和LZ7-9具有2个目标，UF8-10和LZ6具有3个目标。UF1-10、LZ1-5和LZ9具有30个决策变量，LZ6-8具有10个决策变量。所有比较算法的种群大小N都设置为45。由于这些问题被视为昂贵的MOP [39]，所以最大FE的数量设置为500。对于每个测试问题，每个算法都独立运行21次。对于IFCS-MOEA/D-DE，将wmax设置为30，将η设置为5。对于其他算法，我们使用其论文中建议的设置。使用IGD [6]指标评估每个算法的性能。所有算法都在PlatEMO [34]平台上进行检验。