量子启发进化优化在256个连续函数上的景观极限
Landscape Limits of Quantum-Inspired Evolutionary Optimization across 256 continuous functions
- BosonQ Psi Corporation（BosonQ Psi 公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过256个连续函数系统评估量子启发进化优化（QIEO）的性能极限，对比三种QIEO变体、两种遗传算法编码和CMA-ES，揭示其独立变量表示的局限及适用条件。
AI中文摘要：
量子启发进化优化（QIEO）将设计变量表示为一组量子比特，并通过旋转量子比特的振幅对来搜索连续、多维的景观。每一代都将这些振幅向一个单一精英个体旋转，该精英个体对应当代的最优解。该更新过程计算成本低、几乎无需参数调整，并且非常适合大规模并行实现，这促进了其在工程、设计和规划应用中的采用。然而，该公式存在关键问题，主要是将设计变量视为独立的概率分量，使其无法利用局部曲率、各向异性或变量耦合信息。尽管如此，QIEO被认为具有前景，并已被广泛用于解决实际问题，与其经典对应算法——遗传算法（GA）相比，具有显著的定性和计算优势。从先前的研究中选取了256个（实际上为508个；256个未平移+252个平移，4个无法平移）连续函数，这些函数代表了十一种景观特征，即连续性、可微性、可分离性、可扩展性、多模态性、凸性、条件数、对称性、最大维度、维度依赖性和设计变量的耦合模式。随后，使用三种QIEO变体、两种GA编码和Hansen的协方差矩阵自适应进化策略（CMA-ES）求解这些函数。结果根据计算成本、求解精度和跨景观特征的专门化程度进行评估。研究确定了QIEO提供有竞争力性能的条件，阐明了其独立变量表示在何处成为限制因素，并确定了特定QIEO变体是否针对特定景观特征提供优势。
英文摘要：
Quantum-inspired evolutionary optimization (QIEO) represents design variables as a set of qubits and searches a continuous, multi-dimensional landscape through rotation of the qubit's amplitude pair. Every generation rotates those amplitudes toward a single elite, which corresponds to that generation's best. The update is cheap, almost parameter-free, and well-suited for massive parallel implementation, which has encouraged its adoption in engineering, design, and planning applications. However, there are critical issues with this formulation, principally, the treatment of design variables as independent probability components which make it incapable of exploiting local curvature, anisotropy, or variable coupling. Despite this, QIEO is believed to hold promise, and has been used extensively to solve real-world problems, with significant qualitative and computational advantage over its classical counterpart, Genetic Algorithm (GA). A collection of 256 (actually 508; 256 unshifted + 252 shifted, 4 could not be shifted) continuous function are selected from the prior works, in such a way that they represent eleven landscape characteristics, namely continuity, differentiability, separability, scalability, modality, convexity, conditioning, symmetry, maximum dimensionality, dimension dependency, and the coupling pattern of the design variables. These functions are then solved by three QIEO variants, two GA encodings and Hansen's Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The results are evaluated in terms of computational cost, solution precision, and specialization across landscape characteristics. They identify the conditions under which QIEO provides competitive performance, clarify where its independent-variable representation becomes limiting, and establish whether particular QIEO variants offer advantages for specific landscape characteristics.
