An Imperialist Competitive Algorithm and a Mixed Integer Programming Formulation for the Capacitated Vehicle Routing Problem

The Vehicle Routing Problem (VRP), a famous problem of operation research, holds a central place in combinatorial optimization problems. In this problem, a fleet vehicles with Q capacity start to move from depot and return after servicing to customers in which visit only ones each customer and load more than its capacity not at all. The objective is to minimize the number of used vehicles and total distance traversed. This paper presents an application of Imperialist Competitive Algorithm (ICA)) in VRP. Unlike other evolutionary optimization algorithms, ICA is inspired from a socio political process, the competition among imperialists and colonies. Comparison between this method and famous meta-heuristic algorithms shows the effectiveness of the proposed approach. Computational experience with two groups of instances involving from 50 to 200 confirms that proposed algorithm is competitive in compared to the famous meta-heuristic algorithms in terms of the quality of generated solutions. In addition, this algorithm finds closely the best known solutions (BKS) for most of the instances.