A Bi-criteria Ant Colony Optimization for Minimizing Fuel Consumption and Cost of The Traveling Salesman Problem With Time Windows

We investigate in this paper a Green Travelling Salesman Problem with Time Windows (GTSPTW), a bi-criteria variant of the classical TSPTW. The proposed GTSPTW consists of determining the vehicle's speed in order to minimize the fuel consumption and resulting emission costs. The problem can model numerous industries as service companies and post office. We propose a linear mixed integer mathematical model for the GTSPTW. Due to the NP-hardness of the problem, we develop a hybrid bi-criteria ant colony optimization starts from a local search solution, then performs numerous neighborhoods. We compare the ability of the proposed algorithm with the exact solution using CPLEX on benchmark instances in the literature. In order to demonstrate the performance of our proposed approach, we apply it on a real case within the city of Gafsa in the south of Tunisia.