An improved cross entropy algorithm for steelmaking-continuous casting production scheduling with complicated technological routes

Abstract

In order to increase productivity and reduce energy consumption of steelmaking-continuous casting (SCC) production process, especially with complicated technological routes, the cross entropy (CE) method was adopted to optimize the SCC production scheduling (SCCPS) problem. Based on the CE method, a matrix encoding scheme was proposed and a backward decoding method was used to generate a reasonable schedule. To describe the distribution of the solution space, a probability distribution model was built and used to generate individuals. In addition, the probability updating mechanism of the probability distribution model was proposed which helps to find the optimal individual gradually. Because of the poor stability and premature convergence of the standard cross entropy (SCE) algorithm, the improved cross entropy (ICE) algorithm was proposed with the following improvements: individual generation mechanism combined with heuristic rules, retention mechanism of the optimal individual, local search mechanism and dynamic parameters of the algorithm. Simulation experiments validate that the CE method is effective in solving the SCCPS problem with complicated technological routes and the ICE algorithm proposed has superior performance to the SCE algorithm and the genetic algorithm (GA).

Keywords

steelmaking continuous casting / production scheduling / complicated technological routes / cross entropy / power consumption

References

[1] AbdelazizE A, SaidurR, MekhilefS. A review on energy saving strategies in industrial sector [J]. Renewable and Sustainable Energy Reviews, 2011, 15(1): 150-168

[2] BilimN. Optimum cutting speed of block-cutting machines in natural stones for energy saving [J]. Journal of Central South University, 2012, 19(5): 1234-1239

[3] TangL-x, LiuJ-y, RongA-y, YangZ-hou. A review of planning and scheduling systems and methods for integrated steel production [J]. European Journal of Operational Research, 2001, 133(1): 1-20

[4] TangL-x, LuhP B, LiuJ-y, FangLei. Steel-making process scheduling using Lagrangian relaxation [J]. International Journal of Production Research, 2002, 40(1): 55-70

[5] XuanH, TangL-xin. Scheduling a hybrid flowshop with batch production at the last stage [J]. Computers & Operations Research, 2007, 34(9): 2718-2733

[6] AtighehchianA, BijariM, TarkeshH. A novel hybrid algorithm for scheduling steel-making continuous casting production [J]. Computers & Operations Research, 2009, 36(8): 2450-2461

[7] LiT-k, SuZ-xiong. Two-stage genetic algorithm for SMCC production scheduling [J]. Chinese Journal of Management Science, 2009, 17(5): 68-74

[8] SuZ-x, LiT-k, WangW-ling. Improved algorithm for SM-CC production scheduling problem [J]. Computer Engineering and Applications, 2011, 47(5): 242-245

[9] MaoK, PanQ-k, PangX-f, ChaiT-you. A novel Lagrangian relaxation approach for a hybrid flowshop scheduling problem in the steelmaking-continuous casting process [J]. European Journal of Operational Research, 2014, 236: 51-60

[10] PacciarelliD, PranzoM. Production scheduling in a steelmaking-continuous casting plant [J]. Computers & Chemical Engineering, 2004, 28(12): 2823-2835

[11] ZhuD-f, ZhengZ, GaoX-qiang. Intelligent optimization-based production planning and simulation analysis for steelmaking and continuous casting process [J]. Journal of Iron and Steel Research, International, 2010, 17(9): 19-30

[12] YuS-p, ChaiT-y, ZhengB-lin. Hybrid intelligent optimal scheduling method for steelmaking and continuous casting and its application [J]. Journal of Systems Engineering, 2010, 25(3): 380-386

[13] YuS-p, PangX-f, ChaiT-y, ZhengB-lin. Research on production scheduling for steelmaking and continuous casting with processing time uncertainty [J]. Control and Decision, 2009, 24(10): 1467-1472

[14] PangX-f, YuS-p, ZhangZ-y, ZhengB-l, ChaiT-you. Optimal rescheduling method for steelmakingcontinuous casting [J]. Journal of Systems Engineering, 2010, 25(1): 98-103

[15] FengZ-j, YangG-k, DuB, HuangK-wei. Two stage optimization algorithms based on heuristic and linear programming in continuous casting scheduling [J]. Metallurgical Industry Automation, 2005, 29(4): 18-22

[16] WangH-b, XuA-j, YaoL, TianN-y, DuXi. Appling an improved genetic algorithm for solving the production scheduling problem of steelmaking and continuous casting [J]. Journal of University Science and Technology Beijing, 2010, 32(09): 1232-1237

[17] BellabdaouiA, TeghemJ. A mixed-integer linear programming model for the continuous casting planning [J]. International Journal of Production Economics, 2006, 104(2): 260-270

[18] ZhouY-l, LiT-ke. Study on LD-CC production scheduling model and its solution aiming at energy saving [J]. Metallurgical Industry Automation, 2012, 36(5): 20-23

[19] FarzaneganA, ArdiE G, ValianA, HasanzadehV. Simulation of clinker grinding circuits of cement plant based on process models calibrated using GAsearch method [J]. Journal of Central South University, 2014, 21(2): 799-810

[20] HuangR-h, YangC-lin. Ant colony system for job shop scheduling with time windows [J]. The International Journal of Advanced Manufacturing Technology, 2008, 39: 151-157

[21] ToledoC F M, FrancaP M, MorabitoR, KimmsA. A multi population genetic algorithm to solve the synchronized and integrated two-level lot sizing and scheduling problem [J]. International Journal of Production Research, 2009, 47(11): 3097-3119

[22] BendavidI, GolanyB. Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology [J]. Annals of Operations Research, 2011, 189(1): 25-42

[23] MattrandC, BourinetJ M. The cross-entropy method for reliability assessment of cracked structures subjected to random Markovian loads [J]. Reliability Engineering & System Safety, 2014, 123: 171-182

[24] ChepuriK, Homem-De-MelloT. Solving the vehicle routing problem with stochastic demands using the cross entropy method [J]. Annals of Operations Research, 2005, 134(1): 153-181

[25] LouS-z, ShiZ-ke. Solving vehicle routing problem with stochastic demands based on cross-entropy method [J]. Computer Engineering and Applications, 2006, 42(29): 20-22

[26] CasertaM, RicoE Q. A cross entropy-Lagrangean hybrid algorithm for the multi-item capacitated lot-sizing problem with setup times [J]. Computers & Operations Research, 2009, 36(2): 530-548

[27] MaherM, LiuR, NgoduyD. Signal optimisation using the cross entropy method [J]. Transportation Research Part C: Emerging Technologies, 2013, 27: 76-88

[28] de BOERP T, KroeseD P, MannorS, RubinsteinR Y. A tutorial on the cross-entropy method [J]. Annals of Operations Research, 2005, 134(1): 19-67

[29] RubinsteinR. The cross-entropy method for combinatorial and continuous optimization [J]. Methodology and computing in applied probability, 1999, 1(2): 127-190

[30] RubinsteinR, KroeseD PThe cross-entropy method: A unified approach to combinatorial optimization, Monte-Carlo simulation and machine learning [M], 2004BerlinSpringer29-58

[31] PezzellaF, MorgantiG, CiaschettiG. A genetic algorithm for the flexible job-shop scheduling problem [J]. Computers & Operations Research, 2008, 35(10): 3202-3212

[32] LiuW-qingDesign of experiments [M], 2005BeijingTsinghua University Press64-75