The integrated charge planning (ICP) problem based on flexible jobs in an integrated steel plant is extremely difficult and valuable. The purpose of this paper is to improve the efficiency and feasibility of planning by minimising the number of charges, minimising the total production costs and maximising the total throughput, considering the hard constraints and soft constraints. A multi-objective mathematical programming model for the problem is formulated, and it is shown that the problem is NP-hard. Two new meta-heuristics are designed, one is guided variable neighbourhood search (GVNS) combined with harmony search, and the other is GVNS combined with simulated annealing. Compared with enumeration algorithm, tabu search, variable neighbourhood search (VNS), harmony search, extend next fit decreasing (ENFD) and skewed VNS (SVNS), variable neighbourhood descent (VND), the numerical results by actual production data have shown that the proposed model and GVNHS are feasible and effective for ICP.

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The batch machine scheduling of continuous caster with flexible jobs is first proposed based on its character. The difference with classical problem is first summarized. The preprocess of the problem based on rule is proposed, and then the mathematical model with minimizing setup costs is proposed. To improve the efficiency of local search, the particle swarm optimization (PSO) is introduced, and then the PSO combined with heuristic is embedded into the iterated local search (ILS) to solve the problem. The solution space is divided into many subspaces based on the charge information, and then the subspaces are integrated after local search. The maximum number of iteration is introduced as stopping condition. Then, the proposed hybrid algorithm and ILS are compared, and the changing of number of generation, learning factors, and the maximum number of iteration are also tested, respectively. Finally, the simulation results show that the proposed algorithm can solve the problem efficiently.