Hybrid bi-objective gray wolf optimization algorithm for a truck scheduling problem in the automotive industry

Abstract This paper investigates a bi-objective truck scheduling problem (BTSP) in the automotive industry, where a set of containers are transported in batches from a cross-dock to an assembly manufacturer. Each container is characterized by an arbitrary size, an unequal release time and a due date. The problem is to assign containers into batches and schedule these batches on identical trucks so as to minimize the makespan and the total weighted earliness and tardiness cost. A mixed integer linear programming (MILP) model is developed for solving BTSP to optimality via an epsilon-constraint method. Due to NP-hardness of the considered problem, a hybrid bi-objective gray wolf optimization (HBGWO) algorithm is proposed by combining the decomposition framework and the gray wolf optimizer (GWO) metaheuristic. A new solution representation scheme is developed to accommodate the problem characteristic. In addition, the Gaussian mutation (GM) and a tailored local search are introduced to enhance the algorithm’s convergence ability and exploitation performance, respectively. Computational results indicate that the proposed hybrid algorithm is effective and efficient in solving BTSP with different scales.