Abstract
Problem statement: In this study, we considered the application of a g enetic algorithm to vehicle routing problem with time windows where a set of vehicles with limits on capacity and travel time are available to service a set of customers wi th demands and earliest and latest time for serving . The objective is to find routes for the vehicles to service all the customers at a minimal cost withou t violating the capacity and travel time constraints of the vehicles and the time window constraints set by the customers. Approach: We proposed a genetic algorithm using an optimized crossover operator designed by a complete undirected bipartite graph t hat finds an optimal set of delivery routes satisfy ing the requirements and giving minimal total cost. Var ious techniques have also been introduced into the proposed algorithm to further enhance the solutions quality. Results: We tested our algorithm with benchmark instances and compared it with some other heuristics in the literature. The results showed that the proposed algorithm is competitive in terms of the quality of the solutions found. Conclusion/Recommendations: This study presented a genetic algorithm for solvi ng vehicle routing problem with time windows using an optimized crossover operator. From the results, it can be concluded that the proposed algorithm is competitiv e when compared with other heuristics in the literature.
Highlights
The Vehicle Routing Problem with Time Windows (VRPTW) which is an extension of Vehicle Routing Problems (VRPs) arises in a wide array of practical decision making problems
The VRPTW consists in determining a set of a maximum of K routes (i) of minimum total cost (Eq 1); (ii) starting and ending at the depot denoted with customer 0 and such that (iii) each customer is visited exactly once by exactly one vehicle; subject to the restrictions (iv) the total demand of any route Rk does not exceed qk; (v) each route Rk must be completed within a total route time, which is essentially the time
Optimized crossover: We propose an optimized crossover operator within a Genetic Algorithm (GA) for the VRPTW
Summary
The Vehicle Routing Problem with Time Windows (VRPTW) which is an extension of Vehicle Routing Problems (VRPs) arises in a wide array of practical decision making problems. A solution for the VRPTW would be a partition R1,R2,..., RK , representing the routes of the vehicles, each route Rk is a permutation of the customers in C specifying the order of visiting them, starting and ending at the depot. The VRPTW consists in determining a set of a maximum of K routes (i) of minimum total cost (Eq 1); (ii) starting and ending at the depot denoted with customer 0 and such that (iii) each customer is visited exactly once by exactly one vehicle; subject to the restrictions (iv) the total demand of any route Rk does not exceed qk; (v) each route Rk must be completed within a total route time, which is essentially the time. We consider the vehicle routing problem with time windows and propose an Optimized Crossover Genetic Algorithm (OCGA) for this problem
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