A multi-objective optimization of Multi-depot Fleet Size and Mix Vehicle Routing Problem with time window

In this paper, Multi-depot Fleet Size Mix Vehicle Routing Problem with time window (MD-FSMVRP-TW) is presented as a multi-criteria optimization problem. For this purpose, we propose in this study a decision support system which aims 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: schedules requests from clients, the heterogeneous capacity of vehicles... 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. Computational experiments with the benchmark test instances confirm that our approach produces acceptable quality solutions compared with previous results in similar problems in terms of generated solutions and processing time. Experimental results prove that the method of genetic algorithm heuristics is effective in solving the MD-FSMVRP-TW problem and hence has a great potential.