Abstract and Applied Analysis

Improved Cross Entropy Algorithm for the Optimum of Charge Planning Problem

Fan Yang and Qiqiang Li

Full-text: Open access

Abstract

To solve the charge planning problem involving charges and the orders in each charge, a traveling salesman problem based charge planning model and the improved cross entropy algorithm are proposed. Firstly, the charge planning problem with unknown charge number is modeled as a traveling salesman problem. The objective of the model is to minimize the dissimilarity costs between each order and its charge center order, the open order costs, and the unselected order costs. Secondly, the improved cross entropy algorithm is proposed with the improved initial state transition probability matrix which is constructed according to the differences of steel grades and order widths between orders. Finally, an actual numerical example shows the effectiveness of the model and the algorithm.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 857521, 5 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425049084

Digital Object Identifier
doi:10.1155/2014/857521

Mathematical Reviews number (MathSciNet)
MR3230537

Citation

Yang, Fan; Li, Qiqiang. Improved Cross Entropy Algorithm for the Optimum of Charge Planning Problem. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 857521, 5 pages. doi:10.1155/2014/857521. https://projecteuclid.org/euclid.aaa/1425049084


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References

  • H. S. Lee, S. S. Murthy, S. W. Haider, and D. V. Morse, “Primary production scheduling at steelmaking industries,” IBM Journal of Research and Development, vol. 40, no. 2, pp. 231–252, 1996.
  • L. X. Tang, Z. H. Yang, and M. G. Wang, “Model and algorithm of furnace charge plan for steelmaking-continuous casting production scheduling,” Journal of Northeastern University (Natural Science), vol. 17, pp. 440–445, 1996.
  • L. Tang and S. Jiang, “The charge batching planning problem in steelmaking process using lagrangian relaxation algorithm,” Industrial & Engineering Chemistry Research, vol. 48, no. 16, pp. 7780–7787, 2009.
  • H. Dong, M. Huang, W. H. Ip, and X. Wang, “On the integrated charge planning with flexible jobs in primary steelmaking processes,” International Journal of Production Research, vol. 48, no. 21, pp. 6499–6535, 2010.
  • Y. Xue, D. Zheng, and Q. Yang, “Optimum charge plan of steelmaking continuous casting based on the modified discrete particle swarm optimization algorithm,” Computer Integrated Manufacturing Systems, vol. 17, no. 7, pp. 1509–1517, 2011.
  • C. Wang, Q. Liu, Q. Y. Li, B. Wang, F. M. Xie, and B. L. Wang, “Optimal charge plan model for steelmaking based on modified partheno-genetic algorithm,” Control Theory and Applications, vol. 30, no. 6, pp. 734–741, 2013.
  • R. Rubinstein, “The cross-entropy method for combinatorial and continuous optimization,” Methodology and Computing in Applied Probability, vol. 1, no. 2, pp. 127–190, 1999.
  • P. de Boer, D. P. Kroese, and S. Mannor, “A tutorial on the cross-entropy method,” Annals of Operations Research, vol. 134, pp. 19–67, 2005.
  • K. Chepuri and T. Homem-de-Mello, “Solving the vehicle routing problem with stochastic demands using the cross-entropy method,” Annals of Operations Research, vol. 134, pp. 153–181, 2005.
  • G. Alon, D. P. Kroese, T. Raviv, and R. Y. Rubinstein, “Application of the cross-entropy method to the buffer allocation problem in a simulation-based environment,” Annals of Operations Research, vol. 134, pp. 137–151, 2005.
  • R. Y. Rubinstein, “Cross-entropy and rare events for maximal cut and partition problems,” ACM Transactions on Modeling and Computer Simulation, vol. 12, no. 1, pp. 27–53, 2002. \endinput