An improved artificial bee colony algorithm with path relinking strategy for the integrated distributed no-wait flow-shop scheduling and vehicle routing problem

The coordinated optimization of production and transportation ensures that enterprises can lower the total cost of the supply chain while providing high-quality products to consumers, thereby increasing company profits. The integrated distributed no-wait flow-shop scheduling and vehicle routing problem (DNFSVRP) is considered for a make-to-order (MTO) manufacturer. A mathematical model with the objective of minimizing the maximum delivery time is established. For the DNFSVRP, three vectors are designed to represent the solution encoding and an improved artificial bee colony (IABC) algorithm with problem-specific knowledge is proposed. Firstly, an efficient initialization method is developed to generate high-quality initial solutions. Secondly, in the employed bee phase, eight neighborhood structures are designed to expand the search space. Moreover, in the onlooker bee phase, a path relinking strategy is adopted to fully utilize the information of the best solution and accelerate the convergence speed. Furthermore, in the scout bee phase, a destruction and reconstruction approach based on problem-specific knowledge is designed to effectively balance the breadth and depth of the search. Finally, five sets of comparative experiments are conducted, and the results demonstrate the effectiveness of the IABC algorithm in addressing the DNFSVRP.