Meta-harmony search algorithm for the vehicle routing problem with time windows

Abstract

It has been proven that the hybridization of the harmony search algorithm with a local search algorithm (LS) is essential to compensate for the inadequacy of its exploitation. However, the success of this hybridization relies on the achievement of a proper balance between HSA exploration and LS exploitation. The question is can we obtain this balance by adaptively selecting (i) HSA parameter values, (ii) LS and its parameters and (iii) the LS neighborhood structures? To address these issues, this work proposes a meta-harmony search algorithm (meta-HSA) that uses two HSA algorithms, an HSA-optimizer and HSA-solver. The HSA-optimizer will adaptively adjust the components and the configurations of the HSA-solver based on the search status. The HSA-solver, which is a hybridization of HSA and LS, takes the configuration generated by the HSA-optimizer as input and then solves the given problem instance. That is, the HSA-optimizer operates on the components and the configurations of the HSA-solver, while the HSA-solver operates directly on the given problem instance (the solution search space). The proposed meta-HSA was applied to Solomon’s vehicle routing problem with time windows benchmark to verify its effectiveness compared with standard HSA and the state-of-the art methods. The results of the comparison confirmed that the meta-HSA produces competitive results with respect to the other methods. Therefore, we can conclude that the meta-optimization technique does assist the hybrid HSA in obtaining the appropriate selection of its components and configurations during the search process. This demonstrates that the meta-HSA can provide a proper balance between exploration and exploitation by adaptively selecting (i) HSA parameter values, (ii) LS and its parameters and (iii) the LS neighborhood structures. Moreover, the meta-HSA optimizer decreases the effort exerted by the user in tuning these components and configurations.