The new optimization algorithm for the vehicle routing problem with time windows using multi-objective discrete learnable evolution model

This paper presents a new multi-objective discreet learnable evolution model (MODLEM) to address the vehicle routing problem with time windows (VRPTW). Learnable evolution model (LEM) includes a machine learning algorithm, like the decision trees, that can discover the correct directions of the evolution leading to significant improvements in the fitness of the individuals. We incorporate a robust strength Pareto evolutionary algorithm in the LEM presented here to govern the multi-objective property of this approach. A new priority-based encoding scheme for chromosome representation in the LEM as well as corresponding routing scheme is introduced. To improve the quality and the diversity of the initial population, we propose a novel heuristic manner which leads to a good approximation of the Pareto fronts within a reasonable computational time. Moreover, a new heuristic operator is employed in the instantiating process to confront incomplete chromosome formation. Our proposed MODLEM is tested on the problem instances of Solomon's VRPTW benchmark. The performance of this proposed MODLEM for the VRPTW is assessed against the state-of-the-art approaches in terms of both the quality of solutions and the computational time. Experimental results and comparisons indicate the effectiveness and efficiency of our proposed intelligent routing approach.