A two-level evolutionary algorithm for solving the petrol station replenishment problem with periodicity constraints and service choice

This paper addresses the petrol station replenishment problem with periodicity constraints and introduces the frequency service choice as a decision variable. We present a mathematical optimization model for the problem and we develop first a simple heuristic method that is able to handle the complexity of the problem and then two metaheuristic approaches based on a novel two-level evolutionary algorithm. The first level deals with the periodicity and frequency selection of the visits to the petrol stations. The second level of evolution assigns the stations to the tank-trucks such that the total traveled distance is minimized. The effectiveness of the proposed approaches has been tested by means of a comprehensive experimental study by using first a set of randomly generated test cases and then a real-life problem.