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Adaptive Random-key Particle Swarm Optimization with DC-closure Local Search for a Two-stage Fixed-charge Transportation Benchmark

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This study introduces ARK-PSO-CLS, an adaptive random-key particle swarm optimization with local search for a two-stage fixed-charge transportation problem, achieving statistically significant improvements over baseline methods, with average ranks of 1.75 compared to 2.28 for RK-PSO and 3.19 for RK-GA across 149 benchmark instances.

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This paper addresses the two-stage fixed-charge transportation problem with distribution-center (DC) opening costs.We propose adaptive random-key particle swarm optimization with DC-closure local search (ARK-PSO-CLS), a random-key particle swarm optimization (PSO) method with adaptive coefficient scheduling, stagnationtriggered partial restart, and a DC-closure local search, combined with a feasibility-preserving decoder.Experiments are conducted on 149 public benchmark instances from Mendeley Data (50 small, 50 medium, 49 large).For small instances, exact optima are obtained by mixed-integer linear programming (MILP) solved with HiGHS, enabling true optimality gaps; for medium and large instances, gaps are computed relative to the best value found within the compared set.Using swarm size N = 10 and T = 10 iterations, results show statistically significant improvements over greedy construction, random-key PSO (RK-PSO), and random-key genetic algorithm (RK-GA) baselines, while accounting for the additional evaluation cost of local search.Average ranks (lower is better) are 1.75 for ARK-PSO-CLS, 2.28 for RK-PSO, 2.78 for Greedy, and 3.19 for RK-GA.

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