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We present the vehicle routing problem with potential demands and time windows (VRP-PDTW), which is a variation of the classical VRP. A homogenous fleet of vehicles originated in a central depot serves customers with soft time windows and deliveries from/to their locations, and split delivery is considered. Also, besides the initial demand in the order contract, the potential demand caused by conformity consuming behavior is also integrated and modeled in our problem. The objective of minimizing the cost traveled by the vehicles and penalized cost due to violating time windows is then constructed. We propose a heuristics-based parthenogenetic algorithm (HPGA) for successfully solving optimal solutions to the problem, in which heuristics is introduced to generate the initial solution. Computational experiments are reported for instances and the proposed algorithm is compared with genetic algorithm (GA) and heuristics-based genetic algorithm (HGA) from the literature. The comparison results show that our algorithm is quite competitive by considering the quality of solutions and computation time

A Heuristics-Based Parthenogenetic Algorithm for the VRP with Potential Demands and Time Windows