Surrogate-assisted metaheuristics for the facility location problem with distributed demands on network edges

This study aims to develop a time-efficient yet high-performance solution algorithm to address a facility location problem with uniformly distributed demand along the network edges. On the premise that demands are assigned to their closest open facilities, the optimal locations for opening facilities are determined such that the customers’ aggregate traveling time is minimized. Since the closest facilities to the endpoints of any network edges may be different, each network edge may be decomposed into two segments, each assigned to its closest open facilities. The decision variables encompass the determination of both facility locations and positions of edge-decomposing points. Given the general NP-hardness of location problems and the additional complexity introduced by edge decomposition, solving the problem using metaheuristics would be inevitable. Nevertheless, metaheuristics often require a substantial number of function evaluations to attain desired results, incurring significant costs for such a computationally expensive problem. This becomes especially pronounced in scenarios where prompt results are essential or when the problem needs to be solved repeatedly. This study addresses this challenge by emphasizing the integration of well-established and cost-effective surrogate models with state-of-the-art metaheuristics. To assess the effectiveness of the proposed surrogate-assisted metaheuristics, experiments are conducted on several benchmark functions with varying sizes and specifications. The results are then compared to those obtained using the base metaheuristics. The findings indicate that the proposed surrogate-assisted solution methods determine high-quality solutions for all benchmark problems in significantly less computational time. •Adoption of meta-heuristics to tackle the edge-based Facility Location Problem.•Interplay of machine learning tools in optimization.•Using surrogate models to improve the efficiency of optimization algorithms in solving expensive problems.•Introduce new realistic benchmarks problems with different sizes and specifications.•Develop surrogate-assisted new algorithms to solve the introduced problems.