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Decision Rules for Optimization under Uncertainty: Algorithms, Advances, and Applications
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- Author / Creator
- Rahal, Said Salim
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This thesis aims to investigate, develop and advance solution techniques for optimization under uncertainty in process control, scheduling and operations research applications. Decision rule methods offer a rich and flexible framework for solving these classes of problems. Recent literature has shown the promise of decision rules in which uncertainty-dependent decisions are represented as functions, whose parameters are decision variables to be optimized, of the underlying uncertain parameters.
First, we investigate hybrid strategies using linear and piecewise linear decision rule and we empirically illustrate that it is more favorable to have higher uncertainty refinement, equivalently better approximation quality of decisions, at the start of the decision-making process. We also demonstrate a case where, unexpectedly, a linear decision rule is superior to a more complex piecewise-linear decision rule within a simulator. This bolsters the need to assess the quality of decision rule in a simulator to obtain an impartial assessment of its solution quality.
Second, we develop a systematic approach to devise a linear decision rule for unit-specific event-based continuous-time formulation via steel-making and continuous casting problem. We illustrate the solution quality of reactive, proactive and hybrid scheduling strategies and we emphasize the added value of the latter strategy as an attractive trade-off between solution conservatism and excessive scheduling modifications.
Third, we utilize the concept of performing simple successive operations to extract complex features, borrowed from the deep learning community, in the context of optimization under uncertainty. It led to the development of deep lifted decision rules which are shown to offer attractive approximation quality. In this regard, we craft solution heuristics to optimize the aforementioned decision rule inspired by the stochastic gradient descent method.
Fourth, we propose an approach to construct polyhedral norm uncertainty sets, in particular, we characterize asymmetry in data-drive uncertain parameters using distribution information. We show the added value of capturing the asymmetry and the benefits of modelling the data-driven uncertain parameters as an intersection of two polyhedral norm sets. This work addresses the assumptions often made in optimization under uncertainty regarding a predefined polytopic uncertainty set.
Fifth, we draw a connection between linear parametric programming and decision rules. We suggest using decision rules to approximate parametric solutions for optimization problems with a large number of uncertain parameters and variables. Parametric programming is limited by the latter class of problems due to exacerbating complexity and memory storage requirements. We develop a rectilinear activation unit decision rule approximate algorithm which incorporates a branching scheme to refine the approximate solution. The concept of rectilinear activation unit decision rule is based on augmenting new flexible uncertain parameters (i.e., features) obtained from a 1-layer network to a linear decision rule. We demonstrate the benefits of the algorithm in terms of solution quality and computational cost.
In terms of its overall impact, this thesis makes several important contributions. From a methodological perspective, it introduces and advances the use of novel decision rules as promising solution techniques for optimization under uncertainty. From an application perspective, it develops and promotes the less-known decision rule methods in process scheduling and control.
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- Graduation date
- Fall 2021
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- Type of Item
- Thesis
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- Degree
- Doctor of Philosophy
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- License
- This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.