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The complexity of the Vehicle Routing Problems (VRPs) and their applications in our day to day life has garnered a lot of attentions in the area of optimization. Recently, attentions have turned to multi-objective VRPs with Multi-Objective Genetic Algorithms (MOGAs). MOGAs, thanks to its genetic operators such as selection, crossover, and/or mutation, constantly modify a population of solutions in order to find optimal solutions. However, given the complexity of VRPs, conventional crossover operators have major drawbacks. The Best Cost Route Crossover is lately gaining popularity in solving multi-objective VRPs. It employs a brute force approach to generate new children. Such approach may be unacceptable when presented with a relatively large problem instance. In this paper, we introduce a new crossover operator, called Partially Optimized Cyclic Shift Crossover (POCSX). A comparative study, between a MOGA based on POCSX, and a MOGA which is based on the Best Cost Route Crossover affirms the level of competitiveness of the former.

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