Linguistic Pattern Based Optimization of Economic and Spatial Uniformity Criteria in Facility Layout Problems

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.