A particle swarm optimisation algorithm for the capacitated location-routing problem

This article presents a particle swarm optimisation algorithm for solving a capacitated location routing problem (LRP). Based on the framework of particle swarm optimisation with multiple social learning terms (GLNPSO), a solution representation is designed as a multi‐dimensional particle representing depot element and customer element. Each particle is decoded into a solution by using the position of a particle to determine depot location, customer assignment, and route construction. The proposed algorithm is evaluated using a set of benchmark problem instances. The results show that the solution quality is good for large problem instances and a total of nine new best solutions are found. Additional performance indices are also proposed as additional indicators to assess the operational performance of the location selection and route forming decisions.