Solving the Single-Source Capacitated Facility Location Problem Using a Crow Search-Based Hybrid Method

The Single Source Capacitated Facility Location Problem (SSCFLP) stands as a pivotal yet highly complex challenge in facility location science, underpinning real-world supply chains where single-sourcing constraints are critical for service quality and operational efficiency. This study introduces a hybrid solution framework that merges a Binary Crow Search Algorithm (BinCSA) with an exact method, leveraging XOR logic, bit-flip mechanisms, and a dynamic awareness probability (AP) scheme to prevent premature convergence. Across medium-, large-, and extreme-scale benchmark instances, the enhanced BinCSA demonstrates accelerated convergence relative to the original BinCSA. By decomposing the SSCFLP into two subproblems, the proposed approach eases the burden on the exact solver and circumvents the need for transfer functions. A Markov chain analysis underpins BinCSA’s theoretical convergence guarantees, supported by computational results that confirm irreducibility and convergence within a finite solution space. Experiments on benchmark datasets show that BinCSA yields high-quality solutions with efficient runtimes, performing competitively against existing heuristics as well as a CPLEX baseline. To the best of our knowledge, although the Crow Search Algorithm (CSA) has been applied to uncapacitated facility location problems (UFLP), the present work is among the first to adapt CSA-based methods to SSCFLP, thereby extending the algorithm’s scope of applicability. Overall, these findings highlight BinCSA’s robustness and efficiency in tackling large-scale, NP-hard optimization problems, paving the way for broader applications in supply chain design, telecommunication networks, and other high-tech domains.