Abstract:

Replacing expensive objective function evaluations with computationally inexpensive surrogate models to assist evolutionary algorithms in solving expensive black-box multi-objective optimization problems has garnered significant attention in recent years. Model accuracy plays a critical role in surrogate-assisted Multi-Objective Evolutionary Algorithms （MOEAs）； particularly when dealing with numerous objective functions， inaccurate models may misguide the search direction. However， due to the high cost of objective function evaluation， obtaining sufficient training samples to build high-quality surrogate models remains challenging. To address this issue， a Two-stage Infill Sampling-based Semi-supervised Expensive Multi-objective Optimization Algorithm （TISS-EMOA） was proposed. Semi-supervised techniques were introduced to augment the training dataset by selecting partial unlabeled data， thereby improving model accuracy. Simultaneously， a two-stage infill sampling criterion was introduced to acquire high-quality solutions for expensive multi-objective optimization problems under limited evaluation budgets. To validate the effectiveness of TISS-EMOA， experiments were conducted on the DTLZ1 - DTLZ7 benchmark problems and a real-world vehicle frontal structure optimization design. Compared with five State-Of-The-Art （SOTA） surrogate-assisted multi-objective evolutionary algorithms， TISS-EMOA achieves 25， 28， 28，24， 23 optimal or equal Modified Inverted Generational Distance （IGD⁺） results in 28 benchmark problems.

Key words: semi-supervised learning, multi-objective optimization, infill sampling criterion, surrogate model, vehicle frontal structure

摘要：

利用计算成本低廉的代理模型替换昂贵目标函数评价，以辅助进化算法对昂贵黑盒多目标优化问题的求解，近年来受到广泛关注。模型的准确度在代理模型辅助的多目标进化算法（MOEA）中发挥着重要作用，特别是当目标函数数量较多时，不准确的模型很容易引导算法朝错误的方向搜索；但目标函数评价昂贵，很难获得充裕的样本训练高质量的代理模型。因此，提出一种两阶段填充采样的半监督昂贵多目标优化算法（TISS-EMOA）。该算法引入半监督技术，选择部分无标签数据扩充训练数据集，从而提升模型的准确性；同时，提出两阶段选点的填充采样准则，以期在评价次数有限的情况下获得昂贵多目标优化问题的较优解集。为验证TISS-EMOA的有效性，在DTLZ1~DTLZ7基准测试问题以及车辆正面结构优化设计上进行了实验。与当前具有代表性的5种代理模型辅助进化多目标算法的对比结果显示，TISS-EMOA在28个基准测试问题中获得了25、28、28、24、23个更好或相当的改进的反转世代近距离（IGD⁺）。

关键词: 半监督学习, 多目标优化, 填充采样准则, 代理模型, 车辆正面结构