This paper presents a hybrid Particle Swarm Optimization (PSO) for solving Vehicle Routing Problem with Time Windows (VRPTW). Three versions of the algorithm were implemented. The first version is a traditional PSO. In this case, the initialization is random and the best insertion for each customer on the route is evaluated. The second version is a combination of Greedy Randomized Adaptive Search Procedure (GRASP) and Push-Forward Insertion Heuristic (PFIH) with PSO. The last version, in addition to the previous characteristics, features a mutation operator after updating speed and position of each particle. For computational experiments, the 56 Solomon's instances are used and the results obtained in each version are compared with the best known results from literature. A statistical analysis indicates that the third version has a better performance than the other versions.
ResumoEste artigo apresenta um Algoritmo Memético Híbrido para a solução do Problema de Roteamento de Veículos com Janela de Tempo (PRVJT). A hibridização está caracterizada na combinação entre PFIH e GRASP, utilizada para gerar a população inicial do algoritmo proposto. O meme inserido no processo evolutivo visa não somente alcançar bons resultados, mas economizar tempo de execução. Para os experimentos computacionais, as 56 instâncias de Solomon foram utilizadas. Os resultados obtidos são comparados com os melhores resultados conhecidos na literatura e com algoritmos similares ao proposto neste trabalho. Uma análise empírica, uma avaliação do tempo de execução e uma análise estatística foram realizadas. Os resultados indicam que o algoritmo alcançou resultados melhores em um tempo de execução razoável, considerando a inserção do meme.
Palavras-Chaves:Problema de Roteamento de Veículos com Janela de Tempo; Algoritmos Meméticos; Algoritmos Híbridos.
Abstract
This article presents a Hybrid Memetic Algorithm for solving the Vehicle Routing Problem with Time Windows (VRPTW). The hybridization is characterized by the combination between the Push Forward Insertion Heuristic (PFIH) and the GreedyRandomized Adaptive Search Procedure (GRASP). This combination is used to generate the initial population of the proposed algorithm. The meme inserted into the evolutionary process aims not only achieve good results, but save runtime. The 56 Solomon instances were used for computational experiments. The obtained results are compared with the best results known in the literature and with similar algorithms to the proposed in this work. An empirical analysis, an evaluation of the run time and a statistical analysis was performed. The results indicate that the algorithm has achieved the best results at a reasonable execution time considering the insertion of the meme.
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