HORL_2OPT: A Hybrid Reinforcement Learning and Hippopotamus Optimization Algorithm for Bottled Water Delivery Route Optimization
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This study presents HORL_2OPT, a hybrid optimization framework developed to address the bottled water delivery routing problem modeled as a Traveling Salesman Problem (TSP). The framework aims to minimize travel distance, enhance computational efficiency, and ensure consistent solutions. HORL_2OPT combines three key components: 𝑄-learning for guided initialization, the Hippopotamus Optimization Algorithm (HOA) for global exploration, and a 2-opt heuristic for local route refinement. Tested on 15 TSPLIB benchmarks and 26 real-world cases from a bottled water distributor in southern Thailand, HORL_2OPT consistently produced the best or near-best results. For instance, it achieved a total distance of 8,034.2 in the berlin52 problem, outperforming HOA (12,953.2), DE (25,215.2), and PSO (23,187.0); and in lin318, it achieved 56,695.0 compared to HOA’s 85,286.2 and DFA’s 122,910.4. In real applications, it generated the shortest or equally optimal routes in 18 of 26 cases, occasionally surpassing LINGO, with most runs completed within 20 seconds. By integrating machine learning, metaheuristics, and local search, HORL_2OPT delivers robust, high-quality solutions suitable for practical logistics and dynamic routing scenarios.
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