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In this paper, multi-vehicles, multi-depots pick-up and delivery problems with time windows (m-MDPDPTW) is presented as a multi-criteria optimization problem. The m-MDPDPTW is a variant of pick-up and delivery problem (PDP) and a challenging problem in the field of vehicle routing problem (VRP). The aim is to discover a set of satisfying solutions (routes) minimizing total travel distance, total tardiness time and the total number of vehicles. These routes satisfy transportation requests without contravening any of the instance specific constraints (precedence, capacity and time window constraints). In our problem each request is transported by one of the vehicles between paired pick-up and delivery locations. Such that, the depot does not retain the goods. In this paper, we assume that all vehicles have the same capacity and depart from and return to the same depot. The new encoding and structure algorithm on which this contribution is based uses a genetic algorithm, a selection process using ranking with several Pareto fronts and an elitist selection strategy for replacement. An improved encoding chromosome path representation is given to simulate the process of evolution using several types of populations in different sizes. The performance of the new algorithm is tested on data sets instances of Li & Lim's PDPTW benchmark problems. The results indicate that the proposed algorithm gives good results.

Genetic Algorithm for Multi-Criteria Optimization of Multi-Depots Pick-up and Delivery Problems with Time Windows and Multi-Vehicles