Balancing and scheduling of transfer lines for cycle time and peak power minimisation: a learning-enhanced multi-objective variable neighbourhood search

As global electricity demand surges due to industrial electrification and digitalisation, peak power (PP) management has emerged as a critical challenge in energy-intensive manufacturing, affecting operational costs and grid capacity. PP is defined as the maximum instantaneous total power demand across all workstations during the production cycle, and its minimisation is essential for reducing demand charges and avoiding grid overloads. This study introduces the balancing and scheduling of machining transfer lines as a bi-objective optimisation problem that simultaneously minimises cycle time (CT) and PP under precedence, inclusion/exclusion, and technological compatibility constraints. A multi-objective constraint programming (CP) model is formulated and solved via a bidirectional ε-constraint method, generating high-quality Pareto sets for small-scale instances. To overcome the computational intractability of CP for medium- and large-scale problems, a multi-objective variable neighbourhood search (MOVNS) enhanced with deep reinforcement learning (NN_MOVNS) is proposed, in which a Deep Q-Network adaptively guides neighbourhood operator selection throughout the search. Computational experiments on 55 benchmark instances demonstrate that NN_MOVNS consistently outperforms competing algorithms across all problem scales, with improvements becoming increasingly pronounced on larger instances, as confirmed by statistical significance tests. Peak shaving experiments confirm PP reductions ranging from 33% to 73% with modest CT increases averaging 5.7%. An industrial-scale test instance of a 148-task automotive cylinder head production line achieves an 11.8% CT reduction and a 63.1% PP reduction, lowering the peak-to-average power ratio from 2.35 to 1.49.