The trade-offs between different mechanical properties of materials pose fundamental challenges in engineering material design, such as balancing stiffness versus toughness, weight versus energy-absorbing capacity, and among the various elastic coefficients. Although gradient-based topology optimization approaches have been effective in finding specific designs and properties, they are not efficient tools for surveying the vast design space of metamaterials, and thus unable to reveal the attainable bound of interdependent material properties. Other common methods, such as parametric design or data-driven approaches, are limited by either the lack of diversity in geometry or the difficulty to extrapolate from known data, respectively. In this work, we formulate the simultaneous exploration of multiple competing material properties as a multi-objective optimization (MOO) problem and employ a neuroevolution algorithm to efficiently solve it. The Compositional Pattern-Producing Networks (CPPNs) is used as the generative model for unit cell designs, which provide very compact yet lossless encoding of geometry. A modified Neuroevolution of Augmenting Topologies (NEAT) algorithm is employed to evolve the CPPNs such that they create metamaterial designs on the Pareto front of the MOO problem, revealing empirical bounds of different combinations of elastic properties. Looking ahead, our method serves as a universal framework for the computational discovery of diverse metamaterials across a range of fields, including robotics, biomedicine, thermal engineering, and photonics.

翻译：材料不同力学性能之间的权衡关系给工程材料设计带来了根本性挑战，例如刚度与韧性的平衡、重量与能量吸收能力的权衡，以及各弹性系数之间的制约关系。尽管基于梯度的拓扑优化方法在寻找特定设计和性能方面卓有成效，但其并非探索超材料广阔设计空间的有效工具，因而无法揭示相互依存材料性能的可达边界。其他常用方法（如参数化设计或数据驱动方法）则分别受限于几何多样性不足或难以从已知数据外推的缺陷。本研究将多个竞争性材料性能的同步探索构建为多目标优化问题，并采用神经进化算法进行高效求解。我们使用组合模式生成网络作为单胞设计的生成模型，该模型能以极其紧凑且无损的方式编码几何信息。通过改进的增强拓扑结构神经进化算法对CPPN进行演化，使其能在MOO问题的帕累托前沿上生成超材料设计，从而揭示不同弹性性能组合的经验边界。展望未来，本方法可作为跨机器人学、生物医学、热工程及光子学等多领域实现多样化超材料计算发现的通用框架。