Many-objective harmony search for integrated order planning in steelmaking-continuous casting-hot rolling production of multi-plants

This paper investigates a challenging problem of integrated order planning (IOP) in steelmaking-continuous casting-hot rolling production of multiple plants with consideration of four conflicting objectives. The objective functions refer to the earliness/tardiness ratio, the non-hot charge ratio and the imbalance ratio of production capacity utilisation corresponding to SCC plants and HR Plants. The IOP guided by the integration strategy, which includes the vertical integration of production stages and the horizontal integration of steel plants, is regarded as a large-scale many-objective optimisation problem. To deal with the difficulty of large-scale decision variables, we introduce a new concept named ‘order-set’ for modelling. In addition, a novel knee point-driven many-objective global-best harmony search (KGHS) algorithm, mainly integrating a KGHS process and a new knee point-driven Pareto optimisation, is developed to tackle this many-objective problem. The proposed model and algorithm were tested with benchmarks and real production data. Experiments demonstrate that the proposed approach generates effective solutions superior to those generated by the other popular many-objective optimisation methods.