Demand-Weighted Initialization for Network-Based Uncapacitated Facility Location Problem: Enhancing Neighborhood Search and Scalability in Large-Scale Networks

Optimizing networks under large-scale, multidimensional, and dynamic demand presents a significant challenge. This complexity is further amplified when solving network-based Uncapacitated Facility Location Problems (UFLP), which are well-known for their NP-hardness. Current large-scale analytical approaches, such as Neighborhood Search (NS) and Variable Neighborhood Search (VNS), face limitations in either solution quality or computational efficiency, predominantly due to their reliance on either unstable Random Initialization (RI) or computationally expensive Greedy Initialization (GI). Considering demand intensity and network topology, this research proposes the Demand-Weighted Roulette Wheel Initialization (DWRWI) strategy. This novel initialization method strategically prioritizes high-demand and centrally located network nodes, thereby creating high-potential initial facility configurations for improvement algorithms. Scenario-based testing demonstrates several distinctive strengths of DWRWI: Compared to RI and GI, DWRWI better identifies high-demand, central network nodes, yielding superior initial solutions early in optimization. For example, in the large-scale network, DWRWI-initialized NS achieved a higher Silhouette score (0.3859) than RI (0.3833) and GI (0.3752). Additionally, DWRWI reduces computation time by about 28% compared to Greedy-initialized NS while maintaining competitive costs. By integrating demand-weighted distance and stochastic optimization theory, DWRWI significantly reduces computation time while ensures more uniform customer-to-facility assignments aligned closely with spatial demand distributions.