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Deep lifted decision rules for two-stage adaptive optimization problems
Computers & Chemical Engineering ( IF 4.3 ) Pub Date : 2022-01-11 , DOI: 10.1016/j.compchemeng.2022.107661
Said Rahal 1 , Zukui Li 1 , Dimitri J. Papageorgiou 2
Affiliation  

This paper presents a novel method to generate flexible piecewise linear decision rules for two-stage adaptive optimization problems. Borrowing the idea of a neural network, the lifting network consists of multiple processing layers that enable the construction of more flexible piecewise linear functions used in decision rules whose quality and flexibility is superior to linear decision rules and axially-lifted ones. Two solution methods are proposed to optimize the weights and the decision rule approximation quality: a derivative-free method via an evolutionary algorithm and a derivative-based method using approximate derivative information. For the latter method, we suggest local-search heuristics that scale well and reduce the computational time by several folds while offering similar solution quality. We illustrate the flexibility of the proposed method in comparison to linear and axial piecewise linear decision rules via a transportation and an airlift operations scheduling problem.



中文翻译:

两阶段自适应优化问题的深度提升决策规则

本文提出了一种为两阶段自适应优化问题生成灵活分段线性决策规则的新方法。借用神经网络的思想,提升网络由多个处理层组成,可以构建更灵活的分段线性函数,用于决策规则,其质量和灵活性优于线性决策规则和轴向提升的决策规则。提出了两种解决方法来优化权重和决策规则逼近质量:通过进化算法的无导数方法和使用近似导数信息的基于导数的方法。对于后一种方法,我们建议采用局部搜索启发式方法,该方法可以很好地扩展并将计算时间减少几倍,同时提供类似的解决方案质量。

更新日期:2022-01-24
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