A Memetic Algorithm with Population Management (MA|PM) for the Periodic Location-Routing Problem

A generalization of the well-known Vehicle Routing Problem (VRP) has been developed toward tactical or strategic decision levels of companies but not both. The tactical extension or Periodic VRP (PVRP) plans a set of trips over a multiperiod horizon, subject to frequency constraints. The strategic extension is motivated by interdependent depot location and routing decisions in most distribution systems. Low-quality solutions are obtained if depots are located first, regardless the future routes. In the Location-Routing Problem (LRP), location and routing decisions are simultaneously tackled. The goal here is to combine the PVRP and LRP into an even more realistic problem covering all decision levels: the Periodic LRP or PLRP. An evolutionary algorithm called Memetic Algorithm with Population Management (MA|PM) is proposed to solve large size instances of the PLRP. First, a population is randomly generated. Every individual represents a feasible solution using the same combination of visit days on each customers. The evolution is operated by a memetic mechanism and the offsprings must satisfy a distance test before entering the population. Information about better customer assignment to visit days is collected on the offsprings, and is used to create a new population of solutions. The algorithm stops when a given number of regenerations of the population is reached. The method is evaluated on three sets of instances and solutions are compared to the literature on particular cases such as one-day horizons (LRP) or one depot (PVRP). This metaheuristic outperforms the previous method for the PLRP.