用Lagrangian松弛法解化工批处理调度问题
Scheduling for Batch Chemical Processes Using Lagrangian Relaxation-Based Approach
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摘要: 研究基于Lagrangian松弛法的化工批处理过程的调度方法.建立了化工批处理过 程调度问题的一种混合整数规划(MILP)模型,并通过松弛离散变量和连续变量共存的约束, 将问题分解为一个两层次的优化问题,其中上层是原问题的对偶问题,下层由两个子问题构 成:一个与产品批量有关,另一个确定操作时间表,分别用线性规划和动态规划方法解这两个 子问题.然后从对偶问题的解构作原问题的可行解.数值试验结果证明了该方法的有效性.
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关键词:
- Lagrangian松弛法 /
- 化工批处理过程 /
- 调度 /
- 动态规划
Abstract: In this paper, an approach based on Lagrangian Relaxation to schedule batch chemical processes is presented. The scheduling problem is modeled as a compact MILP formulation. The constraints including both discrete and continuous variables are relaxed and the problem is turned into a two-level optimization problem. The high level is the dual of the original problem, and the low level consists of two subproblems ,one for batch-sizing, the other for deciding the time table. Linear programming and dynamic programming methods are used to solve the subproblems. A feasible solution is then constructed based on the solution of the dual problem. Computational results are given to demonstrate the effectiveness of the approach.-
Key words:
- Lagrangian relaxation /
- batch chemical processes /
- scheduling /
- dynamic programming
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