MOIFA with dynamic position update and variable neighborhood search for multi-objective scheduling optimization in lithium battery workshops

Abstract This study addresses an energy-aware hybrid flow shop scheduling problem in lithium-ion battery equipment workshops, with the simultaneous objectives of minimizing makespan and total energy consumption. An improved multi-objective firefly algorithm, termed MOIFA, is proposed to handle the coupled decisions of process sequencing and equipment speed allocation. MOIFA integrates a two-layer process-speed encoding scheme, gray entropy correlation-based Pareto guidance, dynamic position update, and multi-structure variable neighborhood search. Benchmark experiments, FA-based variant comparisons, and practical workshop tests are conducted to evaluate the proposed method. The results show that MOIFA obtains better Pareto-front quality than the comparison algorithms in terms of NP, SM, generational distance (GD), and inverted generational distance (IGD). On 20 benchmark instances, MOIFA achieves the highest average NP and the lowest average SM, GD, and IGD among the FA-based variants. In the practical workshop case, MOIFA obtains an average NP of 12.1, GD of 0.04351, and IGD of 0.03429. Additional scaled workshop cases further indicate that MOIFA maintains competitive solution quality as the number of jobs increases, although it requires moderately higher runtime due to its enhanced search mechanisms. These findings demonstrate that MOIFA can provide diverse and energy-efficient scheduling schemes for lithium-ion battery equipment workshops.