A novel membrane algorithm for capacitated vehicle routing problem

This study is focused on solving the capacitated vehicle routing problem (CVRP) by applying a novel membrane algorithm based on ant colony optimization (MA_ACO). The effect of non-determinism on the performance of the membrane algorithm is also studied in this work. In this approximate approach model, a membrane system is considered to be a non-deterministic distributed parallel framework, and ant colony optimization (ACO) is used as a sub-algorithm of elementary membranes. With the purpose of maintaining balance between the convergence rate and the population diversity, MA_ACO supports sub-algorithms for elementary membranes based on two types of ACO. The elementary membranes send their best solutions to the skin membrane. In the next step, the best one in the skin membrane is sent back to every inner membrane with a fixed probability. All of the elementary membranes have thus a chance to receive the best result and make changes to the current search direction. Thirty benchmark problems of CVRP are utilized to confirm the effectiveness of the proposed membrane algorithm. Experimental results show that compared with other algorithms proposed in the previous literature, our algorithm is very competitive. The new best solutions for seven instances are also listed.