A new robust optimization approach for scheduling under uncertainty - II. Uncertainty with known probability distribution
A new robust optimization approach for scheduling under uncertainty - II. Uncertainty with known probability distribution
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DOI：
10.1016/j.compchemeng.2006.05.035
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发表时间：
2007-01-19
影响因子：
4.3
通讯作者：
Floudas, Christodoulos A.
中科院分区：
文献类型：
--
作者：
Janak, Stacy L.;Lin, Xiaoxia;Floudas, Christodoulos A.
在这项工作中，我们考虑不确定性下的调度问题，其中不确定的问题参数可以描述一个已知的概率分布函数。一种新的鲁棒优化方法，最初由Lin，Janak和Floudas [Lin，X.，Janak，S. L.，& Floudas。C. A.（2004年）。一种新的不确定性调度鲁棒优化方法：I.有限的不确定性。Computers and Chemical Engineering，28，1069-1085]，为了考虑由已知的概率分布描述的不确定性而进行了扩展。这种鲁棒的优化公式是基于最小-最大框架，当应用到混合整数线性规划（MILP）问题，产生“鲁棒”的解决方案，对数据的不确定性免疫。在MILP问题中，目标函数的系数以及不等式约束的系数和右端参数都考虑了不确定性。鲁棒优化技术被开发用于由几种已知分布描述的不确定数据，包括均匀分布、正态分布、两个正态分布之差、一般离散分布、二项分布和泊松分布。鲁棒优化配方引入了少量的辅助变量和额外的约束到原来的MILP问题，生成一个确定性的鲁棒对应问题，提供了最佳/可行的解决方案的（相对）幅度的不确定数据，可行性公差，和可靠性水平。然后将鲁棒优化方法应用于不确定条件下的短期调度问题。使用Houdas及其同事开发的短期调度的连续时间模型[lerapetritou，M。G. & Floudas，C. A.（1998年a）。短期调度的有效连续时间公式：1。多用途批处理。工业工程化学研究，37，4341-4359; Lin，X. & Floudas，C. A. (200 1）。通过有效的连续时间公式设计、综合和调度多用途批处理厂。化学工程，25，665-674]，探讨了调度问题中最常见的三种不确定性来源，包括任务的处理时间、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)2006年由Elsevier Ltd.出版
In this work, we consider the problem of scheduling under uncertainty where the uncertain problem parameters can be described by a known probability distribution function. A novel robust optimization methodology, originally proposed by Lin, Janak, and Floudas [Lin, X., Janak, S. L., & Floudas. C. A. (2004). A new robust optimization approach for scheduling under uncertainty: I. Bounded uncertainty. Computers and Chemical Engineering, 28, 1069-1085], is extended in order to consider uncertainty described by a known probability distribution. This robust optimization formulation is based on a min-max framework and when applied to mixed-integer linear programming (MILP) problems, produces "robust" solutions that are immune against data uncertainty. Uncertainty is considered in the coefficients of the objective function, as well as the coefficients and right-hand-side parameters of the inequality constraints in MILP problems. Robust optimization techniques are developed for uncertain data described by several known distributions including a uniform distribution, a normal distribution, the difference of two normal distributions, a general discrete distribution, a binomial distribution, and a poisson distribution. The robust optimization formulation introduces a small number of auxiliary variables and additional constraints into the original MILP problem, generating a deterministic robust counterpart problem which provides the optimal/feasible solution given the (relative) magnitude of the uncertain data, a feasibility tolerance, and a reliability level. The robust optimization approach is then applied to the problem of short-term scheduling under uncertainty. Using the continuous-time model for short-term scheduling developed by Houdas and co-workers [lerapetritou, M. G. & Floudas, C. A. (1998a). Effective continuous-time formulation for short-term scheduling: 1. Multipurpose batch processes. Ind. Eng. Chem. Res., 37, 4341-4359; Lin, X. & Floudas, C. A. (200 1). Design, synthesis and scheduling of multipurpose batch plants via an effective continuous-time formulation. Comp. Chem. Engng., 25, 665-674], three of the most common sources of uncertainty in scheduling problems are explored including processing times of tasks, market demands for products, and prices of products and raw materials. Computational results on several examples and an industrial case study are presented to demonstrate the effectiveness of the proposed approach. (c) 2006 Published by Elsevier Ltd.