國立虎尾科技大學 |

Optimization under Variable Uncertainty.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Optimization under Variable Uncertainty./
作者:	Sharma, Kartikey.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
面頁冊數:	171 p.
附註:	Source: Dissertations Abstracts International, Volume: 81-10, Section: B.
Contained By:	Dissertations Abstracts International81-10B.
標題:	Operations research. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27740891
ISBN:	9781658485241

Optimization under Variable Uncertainty.
Sharma, Kartikey.

Optimization under Variable Uncertainty. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 171 p.

Source: Dissertations Abstracts International, Volume: 81-10, Section: B.

Thesis (Ph.D.)--Northwestern University, 2020.

This item must not be sold to any third party vendors.

In this dissertation, we study models and methods to address uncertainties that can varyin optimization problems. Robust optimization is a popular approach for optimizationunder uncertainty, especially if limited information is available about the distribution ofthe uncertainty. It models the uncertainty through sets and finds a robust optimal solu-tion that is feasible for all realizations of the uncertainty within the set and is optimalfor the worst-case realization. The structure of these sets determines the complexity ofthe resulting optimization problem. In most models, the uncertainty set is assumed to beexogenous i.e., pre-determined and is unaffected by decisions or other uncertainty realiza-tions in the problem. This thesis introduces endogenous uncertainty models, which maybe affected by decisions that are made in the problem or by other uncertainty realizationswithin the problem.In the first chapter, we take a step towards generalizing robust linear optimizationto problems with decision dependent uncertainties. We show these problems to be NP-complete in general settings. To alleviate these computational inefficiencies, we introducea class of uncertainty sets whose sizes depend on binary decisions. We propose reformu-lations that improve upon alternative standard linearization techniques. To illustrate theadvantages of this framework, a shortest path problem is discussed, where the uncertainarc lengths are affected by decisions. The proposed notion of proactive uncertainty con-trol provides modeling and performance advantages, and mitigates over conservatism ofcommon robust optimization approaches.While the impact of the decisions on the uncertainty set was fixed in the first chap-ter, we extend the decision-dependent models to allow for uncertainty in the influence ofdecisions on the sets in the second chapter. Here, the exact impact of the decision on theuncertainty set itself may be uncertain. This situation arises in many practical settingswhere the decision’s impact may not be known a priori. It is especially relevant for prob-lems in which the decision is on the gathering of information. We leverage robust andstochastic optimization to incorporate uncertain influence into the optimization problem.We then evaluate the performance of these models on a power systems unit commitmentproblem.The third chapter discusses the topic of Connected Uncertainties, i.e., uncertainty mod-els in which past realizations influence future uncertainties. For this class of problems,we develop a novel modeling framework that naturally incorporates this dependence viaconnected uncertainty sets, whose parameters at each period depend on previous uncer-tainty realizations. To find optimal here-and-now solutions, we reformulate robust anddistributionally robust constraints for popular set structures and demonstrate this mod-eling framework numerically on broadly applicable knapsack and portfolio optimizationproblems.In the fourth chapter of the thesis, we leverage the idea of connected uncertainty to de-velop robust adaptive classifiers for streaming data. Classification algorithms are effective,when data can be modeled by time-invariant distributions. In streaming settings, a classi-fier needs to be updated continuously, and hence static classifiers lose their reliability overtime. We consider streaming data sets in which the behavior of each class can be mod-eled by a time series. For classification of such streaming data, we extend the MinimaxProbability Machine to incorporate a time series model using the principles of connecteduncertainty sets. We illustrate the new methods by numerical experiments on syntheticdata.Overall, this thesis led to insights in two directions. First, we introduced uncertaintysets which depended on decisions. This enabled us to model reducing the uncertaintyat a price, which is common in practical applications. This approach also allowed usto capture many problems in which the uncertainty naturally depends on decisions. Inthe second direction, we studied multi-period problems where today’s uncertainty canaffect the uncertainty tomorrow. This led us to capture correlations over time, which arecommon in many applications. Our future goal is to further extend this work in bothdirections. Specifically, we want to solve larger unit commitment problems, solve theproblem of continuous variables affecting uncertainty sets and merge decision dependentand connected uncertainties.

ISBN: 9781658485241Subjects--Topical Terms:

573517
Operations research.
Subjects--Index Terms:

Decision dependent uncertainty

Optimization under Variable Uncertainty.
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020 $a 9781658485241
035 $a (MiAaPQ)AAI27740891
035 $a AAI27740891
040 $a MiAaPQ $c MiAaPQ
100 1 $a Sharma, Kartikey. $3 1241396
245 1 0 $a Optimization under Variable Uncertainty.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 171 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-10, Section: B.
500 $a Advisor: Nohadani, Omid.
502 $a Thesis (Ph.D.)--Northwestern University, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a In this dissertation, we study models and methods to address uncertainties that can varyin optimization problems. Robust optimization is a popular approach for optimizationunder uncertainty, especially if limited information is available about the distribution ofthe uncertainty. It models the uncertainty through sets and finds a robust optimal solu-tion that is feasible for all realizations of the uncertainty within the set and is optimalfor the worst-case realization. The structure of these sets determines the complexity ofthe resulting optimization problem. In most models, the uncertainty set is assumed to beexogenous i.e., pre-determined and is unaffected by decisions or other uncertainty realiza-tions in the problem. This thesis introduces endogenous uncertainty models, which maybe affected by decisions that are made in the problem or by other uncertainty realizationswithin the problem.In the first chapter, we take a step towards generalizing robust linear optimizationto problems with decision dependent uncertainties. We show these problems to be NP-complete in general settings. To alleviate these computational inefficiencies, we introducea class of uncertainty sets whose sizes depend on binary decisions. We propose reformu-lations that improve upon alternative standard linearization techniques. To illustrate theadvantages of this framework, a shortest path problem is discussed, where the uncertainarc lengths are affected by decisions. The proposed notion of proactive uncertainty con-trol provides modeling and performance advantages, and mitigates over conservatism ofcommon robust optimization approaches.While the impact of the decisions on the uncertainty set was fixed in the first chap-ter, we extend the decision-dependent models to allow for uncertainty in the influence ofdecisions on the sets in the second chapter. Here, the exact impact of the decision on theuncertainty set itself may be uncertain. This situation arises in many practical settingswhere the decision’s impact may not be known a priori. It is especially relevant for prob-lems in which the decision is on the gathering of information. We leverage robust andstochastic optimization to incorporate uncertain influence into the optimization problem.We then evaluate the performance of these models on a power systems unit commitmentproblem.The third chapter discusses the topic of Connected Uncertainties, i.e., uncertainty mod-els in which past realizations influence future uncertainties. For this class of problems,we develop a novel modeling framework that naturally incorporates this dependence viaconnected uncertainty sets, whose parameters at each period depend on previous uncer-tainty realizations. To find optimal here-and-now solutions, we reformulate robust anddistributionally robust constraints for popular set structures and demonstrate this mod-eling framework numerically on broadly applicable knapsack and portfolio optimizationproblems.In the fourth chapter of the thesis, we leverage the idea of connected uncertainty to de-velop robust adaptive classifiers for streaming data. Classification algorithms are effective,when data can be modeled by time-invariant distributions. In streaming settings, a classi-fier needs to be updated continuously, and hence static classifiers lose their reliability overtime. We consider streaming data sets in which the behavior of each class can be mod-eled by a time series. For classification of such streaming data, we extend the MinimaxProbability Machine to incorporate a time series model using the principles of connecteduncertainty sets. We illustrate the new methods by numerical experiments on syntheticdata.Overall, this thesis led to insights in two directions. First, we introduced uncertaintysets which depended on decisions. This enabled us to model reducing the uncertaintyat a price, which is common in practical applications. This approach also allowed usto capture many problems in which the uncertainty naturally depends on decisions. Inthe second direction, we studied multi-period problems where today’s uncertainty canaffect the uncertainty tomorrow. This led us to capture correlations over time, which arecommon in many applications. Our future goal is to further extend this work in bothdirections. Specifically, we want to solve larger unit commitment problems, solve theproblem of continuous variables affecting uncertainty sets and merge decision dependentand connected uncertainties.
590 $a School code: 0163.
650 4 $a Operations research. $3 573517
650 4 $a Industrial engineering. $3 679492
653 $a Decision dependent uncertainty
653 $a Optimization
653 $a Robust optimization
653 $a Variable uncertainty
690 $a 0796
690 $a 0546
710 2 $a Northwestern University. $b Industrial Engineering and Management Sciences. $3 1180832
773 0 $t Dissertations Abstracts International $g 81-10B.
790 $a 0163
791 $a Ph.D.
792 $a 2020
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27740891