设施布局问题中基于语言模式的经济与空间均匀性准则优化
Linguistic Pattern Based Optimization of Economic and Spatial Uniformity Criteria in Facility Layout Problems
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中文总结 AI 辅助
本文扩展LP Alinks框架，引入NCS空间均匀性准则，通过实验揭示结构与语言参数对布局的影响，推导参数选择矩阵，对比显示其在成本与均匀性权衡上表现更优。
中文摘要 AI 辅助
本文扩展了此前基于语言模式的设施布局优化工作，通过引入显式空间均匀性准则对LP Alinks框架进行增强。早期研究表明，语言模式可有效编码专家知识并指导智能体生成布局，但其优化范围仅限于成本导向目标。为解决这一缺口，我们提出归一化覆盖度（NCS），这是一种经尺度调整的空间均匀性度量，可补充经典的流量距离经济目标，实现成本-均匀性权衡的系统探索。包含324种条件的全因子实验评估了问题规模、链接密度、虚拟力缩放以及两类隶属函数对两个目标的综合影响。五因素和嵌套三因素方差分析（ANOVA）显示，结构因素（对象数量和链接密度）对经济性能和空间均匀性均起主导基准影响；不过，经济成本主要受这些结构特征支配，而均匀性对语言模式参数更为敏感，这些参数控制着结构约束内生成布局的分散-压缩动态。基于这些交互作用，我们推导了参数选择矩阵，为成本最小化、均匀性最大化或平衡折中规定设置。与Drezner方法、MDS及非度量MDS的对比分析表明，扩展后的LP Alinks框架在保持具有竞争力的经济性能的同时，始终实现更优的均匀性，成为早期设施布局设计中一种可靠且可解释的决策支持工具。
英文摘要
This paper extends prior work on linguistic pattern based facility layout optimization by enhancing the LP Alinks framework with an explicit spatial uniformity criterion. While earlier studies demonstrated that linguistic patterns can effectively encode expert knowledge and guide agent based layout emergence, their optimization scope remained limited to cost oriented objectives. To address this gap, we introduce the Normalized Coverage Score (NCS), a scale adjusted measure of spatial evenness that complements the classical flow distance economic objective and enables systematic exploration of cost uniformity trade offs. A full factorial experiment comprising 324 conditions evaluates the combined effects of problem size, link density, virtual force scaling, and two families of membership functions on both objectives. Five way and nested three way ANOVAs reveal that structural factors (number of objects and link density) exert a dominant baseline influence on both economic performance and spatial uniformity. However, while economic cost is overwhelmingly governed by these structural characteristics, uniformity is substantially more sensitive to the linguistic pattern parameters, which control the dispersion compaction dynamics of the emerging layouts within the structural constraints. Based on these interactions, we derive a parameter-selection matrix that prescribes settings for cost minimization, uniformity maximization, or balanced compromise. Comparative analyses with Drezner's method, MDS, and non metric MDS demonstrate that the extended LP Alinks framework consistently attains superior uniformity while maintaining competitive economic performance, making it a robust and interpretable decision support tool for early stage facility layout design.
