A new robust optimization approach for scheduling under uncertainty: I. Bounded uncertainty
A new robust optimization approach for scheduling under uncertainty: I. Bounded uncertainty
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DOI：
10.1016/j.compchemeng.2003.09.020
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发表时间：
2004-06-15
影响因子：
4.3
通讯作者：
Floudas, CA
中科院分区：
文献类型：
--
作者：
Lin, XX;Janak, SL;Floudas, CA
研究了有界不确定性条件下的排序问题。我们提出了一种新的鲁棒优化方法，当应用到混合整数线性规划（MILP）问题产生的“鲁棒”的解决方案，在某种意义上免疫有界不确定性。同时考虑了目标函数中的系数、不等式的左、右侧参数。鲁棒优化技术被开发用于两种类型的不确定性数据：有界不确定性和有界对称不确定性。通过引入少量的辅助变量和约束条件，确定性的鲁棒对应的问题，制定确定最优解的（相对）大小的不确定数据，可行性公差，和“可靠性水平”时，应用概率测量。然后将鲁棒优化方法应用于不确定性调度问题。基于Floudas及其同事提出的一种新颖有效的连续时间短期调度模型[Ind. Eng. Chem. Res. 37（1998 a）4341; Ind. Eng. Chem. Res. 37（1998 b）4360; Ind. Eng. Chem. Res. 38（1999）3446; Comp. Chem. Engng. 25（2001）665; Ind.Eng.Chem.Res.41（2002）3884; Ind. Eng. Chem. Res.（2003）]，解决了调度问题中有界不确定性的三个最常见的来源，即任务的处理时间、产品的市场需求以及产品和原材料的价格。几个小的例子和工业案例研究的计算结果表明，所提出的方法的有效性。(C)2003 Elsevier Ltd.保留所有权利。
The problem of scheduling under bounded uncertainty is addressed. We propose a novel robust optimization methodology, which when applied to mixed-integer linear programming (MILP) problems produces "robust" solutions which are in a sense immune against bounded uncertainty. Both the coefficients in the objective function, the left-hand-side parameters and the right-hand-side parameters of the inequalities are considered. Robust optimization techniques are developed for two types of uncertain data: bounded uncertainty and bounded and symmetric uncertainty. By introducing a small number of auxiliary variables and constraints, a deterministic robust counterpart problem is formulated to determine the optimal solution given the (relative) magnitude of uncertain data, feasibility tolerance, and "reliability level" when a probabilistic measurement is applied. The robust optimization approach is then applied to the scheduling under uncertainty problem. Based on a novel and effective continuous-time short-term scheduling model proposed by Floudas and coworkers [Ind. Eng. Chem. Res. 37 (1998a) 4341; Ind. Eng. Chem. Res. 37 (1998b) 4360; Ind. Eng. Chem. Res. 38 (1999) 3446; Comp. Chem. Engng. 25 (2001) 665; Ind. Eng. Chem. Res. 41 (2002) 3884; Ind. Eng. Chem. Res. (2003)], three of the most common sources of bounded uncertainty in scheduling problems are addressed, namely processing times of tasks, market demands for products, and prices of products and raw materials. Computational results on several small examples and an industrial case study are presented to demonstrate the effectiveness of the proposed approach. (C) 2003 Elsevier Ltd. All rights reserved.