The memetic self-organizing map approach to the vehicle routing problem

The paper presents an extension of the self- organizing map (SOM) by embedding it into an evolutionary algorithm to solve the Vehicle Routing Problem (VRP). We call it the memetic SOM. The approach is based on the standard SOM algorithm used as a main operator in a population based search. This operator is combined with other derived operators specifically dedicated for greedy insertion moves, a fitness evaluation and a selection operator. The main operators have a similar structure based on the closest point findings and local moves performed in the plane. They can be interpreted as performing parallels and massive insertions, simulating the behavior of agents which interact continuously, having localized and limited abilities. This self-organizing process is intended to allow adaptation to noisy data as well as to confer robustness according to demand fluctuation. Selection is intended to guide the population based search toward useful solution compromises. We show that the approach performs better, with respect to solution quality and/or computation time, than other neural network applications to the VRP presented in the literature. As well, it substantially reduces the gap to classical Operations Research heuristics, specifically on the large VRP instances with time duration constraint.