Journal of Intelligent Manufacturing

, Volume 30, Issue 3, pp 1335–1350 | Cite as

An improved backtracking search algorithm for casting heat treatment charge plan problem

  • Jianxin Zhou
  • Hu Ye
  • Xiaoyuan JiEmail author
  • Weilin Deng


This study investigates the optimization of the charge plan in casting heat treatment. The optimization problem is formulated as a 0–1 integer programming model aiming at maximizing the utilization of the furnaces, minimizing the holding temperature differences and the overall delivery deadline of castings in a furnace. To approach the mathematical model, a two-steps solution methodology is designed. First, the feasible casting candidate sets are generated in consideration of the holding temperature and cooling mode constraints. Then, an improved backtracking search algorithm (IBSA) is proposed to obtain optimal charge plan for each feasible candidate set. The best one among the optimal charge plans obtained by IBSA is selected as the final charge plan. In IBSA, a mapping mechanism is applied to make original backtracking search algorithm (BSA) suitable to discrete problems. Improvements that consist of the modification of historical population updating mechanism, the hybrid of mutation and crossover strategy of difference evaluation algorithm, a greedy local search algorithm and the re-initialization operator are also made to enhance the exploitation and exploration ability of IBSA. The comparisons of simulation experiments demonstrate the effectiveness of the proposed model and the performance of the proposed algorithm.


Charge plan Heat treatment Backtracking search algorithm Difference evaluation Greedy local search 



This work is supported by the National Science and Technology Key Projects of Numerical Control under Grant No. 2012ZX04012-011.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Material Processing and Die & Mould TechnologyHuazhong University of Science and TechnologyWuhanChina

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