Modeling And Algorithm Of Production Scheduling In Tandem Cold Rolling

Cold rolling is an important production procedure after the hot rolling in the steel industry. The product of the cold rolling is the raw material for the production of automobiles, household appliance and so on. The cold rolling scheduling problem is a very complex problem which has coupling between coil parameters and machine performance, and there is rare research about it. This paper presents an effective decomposition-combination mechanism and a hybrid evolutionary algorithm with marriage of genetic algorithm and extremal optimization for solving this problem.This paper first defines constrains and object for the cold rolling scheduling, which is the foundation for building the mathematic model, after introducing the producing process. Considering the speciality of the cold rolling scheduling problem, this paper presents a model depriving from the standard PCTSP (prize collecting travelling salesman problem).This paper presents a decomposition-combination mechanism based on dynamic programming to divide the complex problem into several tractable sub-problems. Through the linearization of the mathematic model of the roll wear in cold strip rolling, we get the relation of the roughness of the strip and the weight. Based on that relationship, all the strips could be assigned to different groups. Then the solving procedure can be divided in to several stages, which is the first step for dynamic programming. We define the sub-schedule with a fixed first strip and a fixed terminal strip as the sub-path value for the dynamic programming, and define the state transition formula to get the shortest global path. And this paper presents a hybrid evolutionary algorithm based on extremal optimization for the sub-schedule problem.Extremal Optimization (EO) was recently proposed, which is inspired by self-organized critical models of co-evolution abstracted from the fundamental of ecosystem. The search process of EO eliminates those components having worst performance in sub-optimal solution, and replaces them with randomly selected new components iteratively, in order to get high-quality solutions. This paper proposed an extremal optimization algorithm designing for cold rolling scheduling.GA makes a population-based evolutionary search on entire space. It can explore the entire gene pool of solution configurations in which the crossover operation performs global exchanges and the mutation operation enhances the diversity of the population. Contrarily, EO exploits a single solution, with improvements achieved by repeatedly eliminating those components producing the worst fitness. It performs a local search that does not get stuck in the local minima. By combining the population- based search capacity of GA and the fine-grained local search efficacy of EO, we developed a hybrid evolutionary algorithm in this paper.Extensive experiment tests have been performed with production scale data, by using the VC++ platform. The result demonstrates that the proposed extremal optimization algorithm and the hybrid algorithm can extensively improve the local fitness for the scheduling solution. After analyzing the convergent curve of those algorithms, I found the hybrid algorithm is the best, and extremal optimization algorithm is better than the traditional genetic algorithm. What's more, the proposed decomposition-combination mechanism for solving the cold rolling scheduling problem is proved to be effective in optimizing the scheduling solution.