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The vehicle routing problem is the basic problem of distribution planning which seeks to find the best route with minimum displacement cost considering the number of customers, their constraints, and number and capacity of the available vehicles. In this study, the traveling salesman problem and vehicle routing models are firstly described and, after that, the multi objective vehicle routing model is proposed to consider the Precedence constraints among customers. There are different meta-heuristic algorithms that can solve such NP-hard problems. In the present study, a solver algorithm is proposed which is based on a combination of the particle swarm optimization and the artificial bee colony algorithms. Additionally, by presenting an operational sample, using data of customers in a region, considering different constraints of the problem and its functions, and using penalty method as well as additional segmentation constraint method, the best vehicle route is obtained and the results of each algorithm together with its hybrid algorithm are demonstrated.
Sedighizadeh et al. (Mon,) studied this question.