A genetic programming based reinforcement learning algorithm for dynamic hybrid flow shop scheduling with reworks under general queue time limits

This study addresses a hybrid flow shop scheduling problem in which each job with non-zero arrival time is reworked after a rework setup is done when one of its general queue time limits between two arbitrary stages is violated. The problem is to determine the allocations of jobs to machines at each stage and the start times of jobs and rework setups/operations, if occur, with the objective of minimizing total tardiness. After representing the problem as a mixed integer programming model, a genetic programming based deep reinforcement learning (GP-DRL) algorithm is proposed. The algorithm consists of two phases: (a) generation of superior hyper priority rules using a variable neighborhood search based genetic programming (VNS-GP) algorithm; and (b) construction of a complete schedule by applying one of the superior hyper rules at each scheduling point by a Deep Q-network with state features, actions and rewards designed using the characteristics of the problem. Simulation experiments were done on a number of test instances, and the results can be summarized as follows. First, the superior hyper priority rules generated by the VNS-GP algorithm outperform the conventional ones in overall averages. Second, the superior hyper rule based GP-DRL algorithm dominates the conventional rule based DRL algorithm.