Modelling and multi-objective scheduling of an energy-efficient hybrid flow shop with multiple heating-forging cycles

This study addresses the characteristics of forging production scheduling and investigates an energy-efficient hybrid flow shop scheduling problem considering multiple heating-forging cycles (EEHFSP-MHFC). The problem is formulated as a multi-objective optimisation problem with two objectives: minimising the makespan and minimising the total energy consumption. A mathematical description model is proposed by considering the characteristics of forging production, including multi-resource constraints, mixed production modes, and multiple heating-forging cycles. A dual-archive hybrid cultural genetic algorithm with knowledge transfer (DAHCGA) is developed to solve the scheduling problem, building upon the Memetic Algorithm framework and NSGA-II. It adopts two hybrid initialisation rules and a dual-archive mechanism to achieve coordinated optimisation of solution-set convergence and diversity. The effectiveness of the proposed model and algorithm is demonstrated through experiments on instances of different scales, as well as comparative analyses and numerical evaluations against alternative algorithms.