This paper introduces a novel set of benchmark problems aimed at advancing research in both single and multi-objective optimization, with a specific focus on the design of human-powered aircraft (HPA). These benchmark problems are unique in that they incorporate real-world design considerations such as fluid dynamics and material mechanics, providing a more realistic simulation of engineering design optimization. We propose three difficulty levels and a wing segmentation parameter in these problems, allowing for scalable complexity to suit various research needs. The problems are designed to be computationally reasonable, ensuring short evaluation times, while still capturing the moderate multimodality of engineering design problems. Our extensive experiments using popular evolutionary algorithms for multi-objective problems demonstrate that the proposed benchmarks effectively replicate the diverse Pareto front shapes observed in real-world problems, including convex, linear, concave, and degenerated forms. The benchmarks and their Python source codes are made publicly available for broader use in the optimization research community.

翻译：本文提出一组新颖的基准问题，旨在推动单目标和多目标优化的研究，特别聚焦于人力飞行器（HPA）的设计。这些基准问题的独特之处在于融合了流体动力学和材料力学等实际设计考量，为工程设计优化提供了更真实的模拟。我们在这些问题中提出了三个难度级别和一个机翼分段参数，使复杂度可扩展以适应不同研究需求。问题设计注重计算合理性，确保评估时间短，同时保留了工程设计问题特有的适度多模态性。我们使用主流的进化算法对多目标问题进行了广泛实验，结果表明所提出的基准能够有效复现实际应用中常见的帕累托前沿形状，包括凸形、线性、凹形和退化形态。这些基准及其Python源代码已公开发布，供优化研究社区广泛使用。