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. 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 inverted triangular forms. The benchmark problems' source codes are publicly available for wider application in the optimization research community.

翻译：本文提出一组新颖的基准测试问题，旨在推动单目标和多目标优化领域的相关研究，特别聚焦于人力驱动飞机的设计问题。这些基准问题的独特性在于融合了流体动力学与材料力学等实际工程设计考量因素，从而更真实地模拟工程设计优化过程。我们在这些问题中设置了三个难度等级及机翼分段参数，使复杂度具有可扩展性，以满足不同研究需求。问题设计强调计算合理性，确保评估耗时较短，同时仍能体现工程设计问题中常见的适度多模态特性。基于主流多目标进化算法的广泛实验表明，该基准测试能有效复现实际工程问题中观测到的各类帕累托前沿形态，包括凸形、线性、凹形及倒三角前沿。该基准问题的源代码已公开，可供优化研究领域广泛应用。