Abstract

Abstract A novel algorithm combining bidirectional recurrent neural networks (BiRNNs) with temporal difference is proposed for multi‐objective energy‐efficient non‐permutation flow‐shop scheduling problem (NFSP). The objectives of this problem involve minimising both the makespan and total energy consumption. To begin, a mathematical model is formulated to represent the energy‐efficient NFSP. Subsequently, the NFSP is transformed into a Markov decision process, where an action space comprising 28 scheduling rules is constructed. Considering the global and local features of NFSP, a set of 15 state features is extracted. Different reward functions are then defined to correspond to the specific objectives. Furthermore, the state features of NFSP are extracted using a multi‐layer perceptron model based on BiRNNs. By utilising the TD( λ ) algorithm to calculate the state value function, various policies are generated. In order to evaluate the proposed algorithm, a new test set for the energy‐efficient NFSP is constructed, building upon classic benchmark problems. Finally, comparison experiments are conducted to demonstrate the effectiveness and efficiency of the proposed algorithm.