Applications of Metaheuristics Inspired by Nature in a Specific Optimisation Problem of a Postal Distribution Sector

Abstract

This paper presents a logistics problem, related to the transport of goods, which can be applied in practice, for example, in postal or courier services. Two mathematical models are presented as problems occurring in a logistics network. The main objective of the optimisation problem presented is to minimise capital resources (Capex), such as cars or containers. Three methods are proposed to solve this problem. The first is a method based on mixed integer programming (MIP) and available through the CPLEX solver. This method is the reference method for us because, as an exact method, it is guaranteed to find the optimal solution as long as the problem is not too large. However, the logistic problem under consideration belongs to the class of NP-complete problems and therefore, for larger problems, i.e., for networks of large size, the MIP method does not find any integer solution in a reasonable computational time. Therefore, two nature-inspired heuristic methods have been proposed. The first is the evolutionary algorithm and the second is the artificial bee colony algorithm. Results indicate that the heuristics methods solve instances of large size, giving suboptimal solutions and therefore, enabling their application to real-life scenarios.