可变制造公差下弹簧设计的鲁棒优化

中文摘要 AI 辅助

对优化器鲁棒性的可靠评估需要跟踪参数的受控变化，以识别算法弱点的来源。这种方法被应用于设计拉伸/压缩弹簧的问题，该问题涉及三个描述弹簧几何形状的连续变量。另外三个独立的二元参数反映了材料变异性、与制造相关的几何偏差以及额外的安全裕度。在不扩展决策空间的情况下，这些参数可以以八种方式组合，生成允许直接比较的变体。在本研究中，我们区分了鲁棒性效应和问题的维度，这允许在保持标称质量目标不变的同时跟踪可行性的变化。七种优化方法及其八种混合变体被用于分析。混合机制应用了第3节中提出的预测程序所选择的算子。所有方法在相同的实验条件下进行评估。每种方法对每个变体运行三十次，每次运行允许最多30000次函数评估。最终质量评估考虑了可行性区域的几何形状、搜索轨迹、跨景观的性能变化以及固定目标的计算成本。这些因素共同使我们能够确定解决方案的质量、可重复性、可行性控制以及优化的有效性。一个有趣的观察是，混合可以减轻与特定配置相关的成本或可行性损失。虽然它补偿了底层机制中的特定弱点，但它并不能提供普遍的韧性。

英文摘要

A reliable assessment of an optimizer robustness requires tracking controlled changes in parameters to identify sources of algorithmic weakness. Such an approach was applied to the problem of designing tension/compression springs with three continuous variables describing the spring geometry. Three additional independent binary parameters reflect material variability, manufacturing-related geometric deviations, and an additional safety margin. Without expanding the decision space, these parameters can be combined in eight ways to generate variants that allow for direct comparison. In this study we distinguish between robustness effects and the dimension of the problem, which allows tracking changes in feasibility while keeping the nominal mass objective constant. Seven optimization methods and eight hybridized their variants are used for the analysis. The hybridization mechanism applies the operator selected by the prediction procedure presented in Section 3. All methods are evaluated under the same experimental conditions. Each method is run thirty times for each variant, with a maximum of 30000 function evaluations permitted per run. The final quality assessment takes into account the geometry of the feasibility region, search trajectories, performance variations across landscapes and the computational cost of fixed objectives. Together, these factors allow us to determine the quality of the solution, reproducibility, feasibility control, and the effectiveness of optimization. An interesting observation was that hybridization can mitigate cost or feasibility losses associated with a specific configuration. While it compensates for a specific weakness in the underlying mechanism, it does not provide universal resilience.

发表机构

• Rzeszów University of Technology（热舒夫理工大学）
• Polish Academy of Sciences（波兰科学院）

机构由 AI 辅助整理，请以论文原文为准。