Applying VNPSO Algorithm to Solve the Many-to-Many Hub Location-Routing Problem in a Large scale

One way to increase the companies’ performance and reducing their costs is to concern the transportation industry. Many-to-many hub location-routing problem (MMHLRP) is one of the problems that can affect the process of transportation costs. The problem of MMHLRP is one of the NP-HARD problems. Hence, solving it by exact methods is not affordable; however it was first solved by Benders decomposition algorithm. Modeling and the solving algorithm is able to solve the problem with 100 nodes. In this study, using VNPSO (a combination of the two methods VNS and PSO) was suggested to solve MMHLRP in large-scale. Given high similarity of the results obtained in small scale, using a random sample confirmed that the proposed method was able to solve problem MMHLRP with 300 nodes and acceptable accuracy and speed