An Adaptive Spiking Neural P System for Solving Vehicle Routing Problems

The capabilities of membrane computing frameworks in solving multi-objective constrained optimization problems have invited many researchers to focus their efforts on developing new methods and computational paradigms. Getting motivated from the computational completeness of membrane computing systems (P systems), this paper proposes a new way of solving vehicle routing problems (VRP) using one of the most eminent membrane computing frameworks called spiking neural P systems (SNPS). A new model for SNPS has been recommended both for finding the optimal solutions and for optimizing the parameters that are used in the calculation of minimum feasible insertion cost of the customer insertion phase of VRP without using any heuristic operators. The SNPS suggested here is an adaptive SNPS in which some potentials (ATSNPS) with learning and training facilities are incorporated. Being an NP-hard problem with numerous applications in many areas such as gas distribution management, postal delivery, and truck dispatching, the benefits of this study are far-reaching. Here, a variant of VRP called VRP with time windows (VRPTW) has been used in the proposed system. Since this is the first attempt to find solutions of VRP using ATSNPS, a comparison has been made with the algorithms used over VRPTW. The analysis of results proved that the proposed ATSNPS is substantially superior to the state-of-the-art algorithms in terms of computational time and optimizing the attributes such as the average number of vehicles used and the total distance traveled.