Imitation Learning-Assisted Evolutionary Algorithm for Energy-Efficient Flexible Job Shop Scheduling Problem With Automated Guided Vehicles

The flexible job shop scheduling problem with limited automatic guided vehicles (FJSP-AGV) is prevalent in manufacturing enterprises. To improve production efficiency and reduce energy consumption, this paper investigates the energy-efficient FJSP-AGV (EFJSP-AGV), aiming to minimize both the makespan and total energy consumption. To address EFJSP-AGV, both exact and approximate methods were developed. The exact method employs a novel mixed integer linear programming (MILP) model, capable of producing optimal Pareto solutions for small-sized instances using the epsilon method. EFJSP-AGV is an NP-hard problem that involves three subproblems: operation sequencing, machine selection, and AGV selection. To overcome these challenges, a novel approximate method called imitation learning (IL)-assisted multi-population evolutionary algorithm (ILMPEA) was proposed. The multi-population evolutionary framework assigns distinct search regions to populations to improve the efficiency of solution space exploration. To further enhance search accuracy, IL is applied to select search operators, guiding the Pareto front toward a better approximation of the true front. Experimental results demonstrated the effectiveness of both the MILP model and ILMPEA.