Improved genetic algorithm for magnetic material two-stage multi-product production scheduling: a case study * Yefeng Liu, Tianyou Chai, S. Joe Qin, Quanke Pan, Shengxiang Yang Abstract—In this paper an improved genetic algorithm (GA) was present for magnetic material two-stage, multi-product, production scheduling problem (TMPS) with parallel machines. TMPS was changed into molding-stage’s multi-product production scheduling problem (MMPS) and the scheduling model was set up for the first time. A set of random solutions were explored first, better feasible solutions were obtained by GA. To shorten the solving time and improve solution accuracy, an improved GA was proposed. We improved GA’s crossover operator, adopted heuristic greedy 3PM crossover operator (HG3PMCO) to reduce GA’s computational time. Through contrast of computational results of MILP, general GA and improved GA, the improved GA has demonstrated its effectiveness and reliability in solving the molding sintering production scheduling problems and the MILP model set up for the first time is reasonable. At last, the improved genetic algorithm was used in molding stage and sintering stage TMPS of magnetic material. I. INTRODUCTION In the situation of production equipment and technology have reached a certain level. Optimized short-term planning and scheduling is the key to corporate profits. There are large bodies of literatures on process scheduling. Pinto and Grossmann proposed a mixed-integer linear programming (MILP) model aimed to multi-stage short-term scheduling of batch production [1]. Cerda et al. presented an MILP model to solve the problem of single-stage multi-product scheduling problem (SMSP) with parallel lines [2]. A general description for SMSP was proposed by Hui et al. [ 3 ]. A formulation for scheduling of a multi-purpose enterprise was proposed by Ierapetritou et al. The major limitation of the method is requiring all the orders’ pre-ordering in advance [ 4 ], [ 5 ]. A new framework for optimal cyclic schedule based on the idea of operating periodicity was presented by Wu and Ierapetritou [6]. A new MILP for a pipeline transporting scheduling was proposed by Cafaro and Cerda [ 7 ]. Timed place petri-net (TPPN) can search the reachability tree to get the optimization set. A novel approach based on the TPPN was proposed by Ghaeli et al. In the method, heuristic algorithm was applied for decreasing the search times [ * This work was supported by National Basic Research Program of China (2009CB320601), Natural Science Foundation of China (61020106003), and the 111 Project of Ministry of Education of China ( B08015). Y.F. Liu, T.Y. Chai and Q.K. Pan are with the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang,110004, China (phone: +86-138-9798-6776; e-mail: lyf-327@163.com). S. Joe Qin is with the School of Engineering, University of Southern California, USA (e-mail: sqin@usc.edu). S.X. Yang is with the Department of Computer Science, University of Leicester, University Road, Leicester LE1 7RH, UK(e-mail: s.yang@mcs.le.ac.uk). 8]. For decreasing the size of an MILP model, many authors adopted heuristic rule in the method. Above heuristic rules, such as imposing the pre-ordering constraints and pruning the feasible predecessors were also used by [ 9 ], [ 10 ], [ 11 ]. However, it is difficult to obtain the optimal solutions when in the method the heuristic rules are used and the makespan is minimizing [12]. Meta-heuristic methods are effective in getting the near-optimal solutions for large-size problems. Till now, meta-heuristic methods have solved many production scheduling problem, but among the methods only some problems on genetic algorithms (GA)[13], [14], [15], [16], [17]; the methods on list-based threshold-accepting algorithm (LBTA) is [18], the methods for multi-stage multi-product scheduling problems based on simulated annealing (SA) are[ 19 ], [ 20 ]. Due to the characteristics of multi-stage multi-product scheduling problem, some authors believe that it is difficult to solving the process scheduling problems by genetic algorithm, simulated annealing and tabu search and other meta-heuristic methods. The reason is that it is difficult to get the original feasible solution(s). In this paper, production process description of magnetic material was presented first. Then MMPS MILP model was set up for the first time. The third, introduce to the improve GA The fourth, through comparison of MILP, general GA and improved GA, the improved GA has demonstrated its effectiveness and reliability in solving the scheduling problems of magnetic material and the model is proved to be reasonable. Conclusions to this paper are given. II. PROBLEM DEFINITION A. Description of production process of magnetic material Magnetic material (especially rare earth permanent magnet) becomes the focus of international competition because of its wide range of applications and non-renewable. China is not only the world's largest rare earth occupy country, but also magnetic material produce country. In recent years, rare earth prices have raised perpendicularly because of China restrict to its mining and export which leads to high production costs and fund operation difficulty. The feature of magnetic material production process is long and complex. The flow chart from ingredients to 51st IEEE Conference on Decision and Control December 10-13, 2012. Maui, Hawaii, USA 978-1-4673-2064-1/12/$31.00 ©2012 IEEE 2521 978-1-4673-2066-5/12/$31.00 ©2012 IEEE