Ship replenishment path planning has always been a critical concern for researchers in the field of security. This study proposes a modified whale optimization algorithm (MWOA) to address single-task ship replenishment path planning problems. To ensure high-quality initial solutions and maintain population diversity, a hybrid approach combining the nearest neighbor search with random search is employed for initial population generation. Additionally, crossover operations and destroy and repair operators are integrated to update the whale’s position, significantly enhancing the algorithm’s search efficiency and optimization performance. Furthermore, variable neighborhood search is utilized for local optimization to refine the solutions. The proposed MWOA has been tested against several algorithms, including the original whale optimization algorithm, genetic algorithm, ant colony optimization, hybrid particle swarm optimization, and simulated annealing, using traveling salesman problems as benchmarks. Results demonstrate that MWOA outperforms these algorithms in both solution quality and stability. Moreover, when applied to ship replenishment path planning problems of varying scales, MWOA consistently achieves superior performance compared to the other algorithms. The proposed algorithm demonstrates high adaptability in addressing diverse ship replenishment path planning problems, delivering efficient, high-quality, and reliable solutions.

Ship replenishment path planning is a critical problem in the field of maritime logistics. This study proposes a novel synergistic hybrid optimization algorithm (SHOA) that effectively integrates ant colony optimization (ACO), the Clarke–Wright algorithm (CW), and the genetic algorithm (GA) to solve the capacitated multi-ship replenishment path planning problem (CMSRPPP). The proposed methodology employs a three-stage optimization framework: (1) initial path generation via parallel execution of the CW and ACO; (2) population initialization for the GA by strategically combining optimal solutions from ACO and the CW with randomized solutions; (3) iterative refinement using an enhanced GA featuring an embedded evolutionary reversal operation for local intensification. To evaluate performance, the SHOA is benchmarked against ACO, the GA, the particle swarm optimization algorithm, and the simulated annealing algorithm for the capacitated vehicle routing problem. Finally, the SHOA is applied to diverse CMSRPPP instances, demonstrating high adaptability, robust planning capabilities, and promising practical potential.