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An Improved Whale Optimization Algorithm for Vehicle Routing Problem with Time Windows

Sirichai Yodwangjai, Kittipong Malampong


The vehicle routing problem with time windows (VRPTW) is a pivotal problem in logistics operation management which attempts to establish routes for vehicles to deliver goods to customers. The objective of VRPTW is to find the optimal set of routes for a fleet of vehicles in order to serve a given set of customers within time window constraints. As the VRPTW is known to be NP-hard combinatorial problem, it is hard to be solved in reasonable computational time. Therefore, this paper proposes the modification of the whale optimization algorithm with local search to solve the VRPTW. The local search comprised 2-Operator and single insertion for solution improvement. Furthermore, the 2-Operator is used after the exploration phase and single insertion in the exploitation phase. The computational experiments were applied to Solomon’s instance that included small to large size problems. The experiment results show that the average gap of the total distance between the Best Known Solution (BKS) and the proposed solutions is within 5.82%. In addition, the best solution was found 29 out of 56 instances that is better than the PSO at 1.09%. This shows that this proposed provides a minimum value and outperforms other metaheuristics approaches.


Whale Optimization Algorithm; Vehicle Routing Problem; Time Constraints

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DOI: 10.14416/


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