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H. Milton Stewart School of Industrial and Systems Engineering

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https://hdl.handle.net/1853/70758

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College of Engineering

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Organizational Unit

William M. Keck Virtual Factory Lab (VFL)

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https://finding-aids.library.gatech.edu/agents/corporate_entities/1032

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Publication Search Results

Now showing 1 - 10 of 25

Data-driven stochastic optimization approaches with applications in power systems

(Georgia Institute of Technology, 2019-07-26) Basciftci, Beste

In this thesis, we focus on data-driven stochastic optimization problems with an emphasis in power systems applications. On the one hand, we address the inefficiencies in maintenance and operations scheduling problems which emerge due to disregarding the uncertainties, and not utilizing statistical analysis methods. On the other hand, we develop a partially adaptive general purpose stochastic programming approach for effectively modeling and solving a class of problems in sequential decision-making.
Distributed integer programming

(Georgia Institute of Technology, 2017-08-15) Karabulut, Ezgi

In this thesis, we study distributed integer programming problems that involve multiple players with integer programming problems linked together with a common resource constraint. Our goal is to design decentralized algorithms that do not require a central processor to allocate the resource across the players to solve the overall problem. The algorithms that we design have optimality guarantees when applied to problems for which the marginal value of each additional resource is non-increasing. For problems that do not have this step-wise concave structure, we propose approximation algorithms and provide error bounds. We also perform experiments to evaluate the algorithms' average performance on problems without the desired structure. Finally, we consider the same problem in an online setting. We show that there exists no deterministic online algorithms for our problem that has the state of the art error bound. Therefore we propose a randomized decentralized online algorithm for our problem whose error bound matches the results in the literature.
Relaxations and approximations of chance constrained stochastic programs

(Georgia Institute of Technology, 2017-06-21) Xie, Weijun

A chance constrained stochastic programming (CCSP) problem involves constraints with random parameters that are required to be satisfied with a prespecified probability threshold. Such constraints are used to model reliability requirements in a variety of application areas such as finance, energy, service and manufacturing. Except under very special conditions, chance constraints impart severe nonconvexities making the optimization problem extremely difficult. Moreover, in many cases, the probability distribution of the random parameters is not fully specified giving rise to additional difficulties. This thesis makes several contributions towards alleviating these two difficulties in CCSP. In the first part of this thesis we consider CCSP problems with finitely supported probability distributions. Such problems can be reformulated as mixed integer programming (MIP) problems. We propose two new efficiently solvable Lagrangian dual problems for these problems, and show that their corresponding primal formulations lead to MIP formulations that can be stronger than traditional formulations. We next study a well-known family of cuts for these problems known as quantile cuts. We show that the closure of the infinite family of all quantile cuts has a finite description, and a recursive application of quantile closure operations recovers the convex hull of the nonconvex chance constrained set in the limit. Furthermore, we show that in the pure integer setting, the convergence is finite. Our final result in this part concerns with approximation algorithms for CCSP. We first prove that CCSP is constant factor inapproximable in general. On the other hand, for CCSP problems involving covering type constraints, we prove a bicriteria approximation result where, by relaxing the required probability threshold by a constant factor, we can provide a constant factor approximation algorithm. In the second part of the thesis we consider distributionally robust chance constrained problems (DRCCPs) where the chance constraint is required to hold for all probability distributions of the random constraint parameters from a given ambiguity set. First, we study DRCCPs involving convex nonlinear uncertain constraints and ambiguity sets specified by convex moment constraints. We develop deterministic reformulations of such DRCCPs and identify conditions under which such reformulations are convex. Our results generalize and extend several existing results on convex reformulations of DRCCPs. Next, we apply the proposed reformulation scheme to an optimal power flow problem involving uncertainty stemming from renewable power generation. In particular, we develop a convex programming approach for a distributionally robust chance constrained optimal power flow model that ensures low probability of violating upper and lower limits of a line/bus capacity under a wide family of distributions of uncertain renewable generation. Finally, we study a conservative approximation - referred to as a Bonferroni approximation - of a joint chance constraint, i.e.~a chance constraint involving a system of multiple uncertain constraints. The Bonferroni approximation scheme uses the union bound to approximate the joint chance constraint by a system of {\em single} chance constraints, one for each original uncertain constraint and each of whose probability thresholds needs to be appropriately set. We show that such a Bonferroni approximation is exact when the uncertainties are separable across the individual constraints, i.e., each uncertain constraint involves a different set of uncertain parameters and corresponding distribution families. We show that, while in general the optimization over the Bonferroni approximation is NP-hard, there are various sufficient conditions under which it is convex and tractable.
Large scale multistage stochastic integer programming with applications in electric power systems

(Georgia Institute of Technology, 2017-05-10) Zou, Jikai

Multistage stochastic integer programming (MSIP) is a framework for sequential decision making under uncertainty, where the uncertainty is modeled by a general stochastic process, and the decision space involves integer variables and complicated constraints. Many power system applications, such as generation capacity planning and scheduling under uncertainty stemming from renewable generation, demand variability and price volatility, can be naturally formulated as MSIP problems. In this thesis, we develop general purpose solution methods for large-scale MSIP problems and demonstrate their effectiveness on various power systems applications. In the first part of this thesis, we consider an MSIP approach for electrical power generation capacity expansion problems under demand and fuel price uncertainty. We propose a partially adaptive stochastic mixed integer optimization model in which the capacity expansion plan is fully adaptive to the uncertainty evolution up to a certain period, and is static thereafter. Any solution to the partially adaptive model is feasible to the multistage model and we provide analytical bounds on the quality of such a solution. We propose an algorithm that solves a sequence of partially adaptive models, to recursively construct an approximate solution to the multistage problem. We apply the proposed approach to a realistic generation expansion case study. In the second part of this thesis, we develop decomposition algorithms for general MSIP problems with binary state variables. By exploiting the binary nature of the state variables, we extend the nested Benders decomposition algorithm to this problem class. Key to our developments are new families of cuts that guarantee finite convergence of the proposed algorithm. We also propose a stochastic variant of the nested Benders decomposition algorithm, called Stochastic Dual Dynamic integer Programming (SDDiP), and give a rigorous proof of its finite convergence with probability one to an optimal policy. We provide extensive computational results using the SDDiP approach for generation capacity planning, portfolio optimization, and airline revenue management problems. The final part of this thesis focuses on adapting the SDDiP approach to solve the multistage stochastic unit commitment (MSUC) problem. Unit commitment is a key operational problem in power systems used to determine the optimal generation schedule over the next day or week. Incorporating uncertainty in this already difficult optimization problem imparts severe challenges. We reformulate the MSUC problem such that each stage problem only depends on information from the previous stage and the uncertainty realization. This new formulation is amenable to our SDDiP approach. We propose a variety of computational enhancements to adapt the method to MSUC. Through extensive computational results, we demonstrate the effectiveness of our approach in solving realistic scale MSUC problems.
Robust optimization for renewable energy integration in power system operations

(Georgia Institute of Technology, 2016-07-20) Lorca Galvez, Alvaro Hugo

Optimization provides critical support for the operation of electric power systems. As power systems evolve, enhanced operational methodologies are required, and innovative optimization models have the potential to support them. The need for sustainability has led to many transformations, including the deep adoption of wind and solar energy in many power systems. These renewable energy sources have tremendous environmental benefits and can be very convenient economically, however, the power supply they provide is highly uncertain and difficult to predict accurately. This Thesis proposes Robust Optimization models and algorithms for improving the management of uncertainty in electric power system operations. The main goal is to devise new operational methodologies to support the integration of variable renewable energy sources. The first part of this Thesis presents the development of an adaptive robust optimization model for the economic dispatch problem under uncertainty in wind power. The goal of this problem is to determine the power output levels of generating units in order to minimize costs while satisfying several technical constraints. The concept of dynamic uncertainty set is developed to account for temporal and spatial correlations in wind speeds. Further, a simulation platform is implemented to combine the dispatch model with statistical prediction tools in a rolling-horizon framework. Extensive numerical experiments are carried out on this platform using real wind data, showing the potential benefits of the proposed approach in terms of cost and reliability improvements over deterministic models and simpler robust optimization models that ignore temporal and spatial correlations. The second part proposes a multistage adaptive robust optimization model for the unit commitment problem, under uncertainty in nodal net loads. The purpose of this problem is to schedule available generating capacities in each hour of the next day, including on/off generator decisions. The proposed model takes into account the time causality of the hourly unfolding of uncertainty in the power system operation process, which is shown to be relevant when ramping capacities are limited and net loads present significant variability. To deal with large-scale systems, the idea of simplified affine policies is explored and a solution method based on constraint generation is developed. Extensive computational experiments on a 118-bus test case and a real-world power system with 2736 buses demonstrate that the proposed algorithm is effective in handling large-scale power systems and that the proposed multistage robust model can significantly outperform a traditional deterministic model and an existing two-stage robust model in both operational cost and system reliability. The third part develops a more sophisticated multistage robust unit commitment model, where the temporal and spatial correlations of wind and solar power are considered, as well as energy storage devices. A new specialized simplified affine policy is proposed for dispatch decisions, and an efficient algorithmic framework using a combination of constraint generation and duality based reformulation with various improvements is developed. Extensive computational experiments show that the proposed method can efficiently solve the problem on a 2736-bus system under high dimensional uncertainty of 60 wind farms and 30 solar farms. The computational results also suggest that the proposed model leads to significant benefits in both costs and reliability over robust models with traditional uncertainty sets as well as deterministic models with reserve rules. Finally, the fourth part explores how to jointly consider the non-convexity of the power flow equations and the uncertainty in renewable outputs in power dispatch problems. Here, a two-stage adaptive robust optimization model is developed for the alternating current optimal power flow problem, considering multiple time periods and including technical details such as transmission line capacities and the reactive capability curves of conventional generators and renewable units. To solve this challenging problem, it is proposed to use convex relaxations and an alternating direction method to identify worst-case uncertainty realizations. Further, a speed-up technique based on screening transmission line constraints is explored. Extensive computational experiments show that the solution method is efficient and that there are significant advantages both from the economic and reliability standpoints as compared to a deterministic model for this problem.
Track layout accommodating dynamic routing in automated material handling systems

(Georgia Institute of Technology, 2016-05-10) Lee, Junho

Modern semiconductor fabrication facilities depend on automated material handling systems (AMHSs) to manage the processes and variations in time required to produce advanced semiconductor products. Unified AMHSs, which operate overhead hoist transport vehicles, support direct tool-to-tool transfers between different bays. AMHSs continue to use static routing, but dynamic routing schemes have been studied to improve traffic conditions. In this dissertation, we propose an approach integrating optimization and simulation to design a track layout of an AMHS employing dynamic routing. We present a network design problem accommodating alternative paths. Our formulation is based on a multi-commodity network design problem, and we add secondary flow variables to represent rerouted vehicles. The problem requires input data, especially a base graph and commodities, reflecting realistic traffic conditions. We use simulation to validate the design from the optimization problem and provide its input data. We obtain a solution design using a heuristic that combines optimization and simulation. Our computational results illustrate that the parameter that controls the uniqueness of alternative paths has a significant impact on the routing performance of vehicles.
Large-scale unit commitment: Decentralized mixed integer programming approaches

(Georgia Institute of Technology, 2015-08-19) Feizollahi, Mohammadjavad

We investigate theory and application of decentralized optimization for mixed integer programming (MIP) problems. Our focus is on loosely coupled MIPs where different blocks of the problem have mixed integer linear feasible sets and a small number of linear constraints couple these blocks together. We develop decentralized optimization approaches based on Lagrangian and augmented Lagrangian duals for such MIPs. The contributions of this dissertation are a) proof of exactness of augmented Lagrangian dual (ALD) for MIPs, b) decentralized exact and heuristic algorithms for MIPs, and c) application to decentralized unit commitment (UC). We demonstrate remarkable performance of parallel implementation of the heuristic decentralized algorithm to solve large-scale UC instances. Solving ALD for MIPs in parallel , investigating ALD for (convex) mixed integer nonlinear programs, decentralized approaches for stochastic and robust MIPs and applications to other variants of UC are discussed as future research directions.
Congestion-aware dynamic routing in automated material handling systems

(Georgia Institute of Technology, 2014-08-20) Bartlett, Kelly K.

In semiconductor manufacturing, automated material handling systems (AMHSs) transport wafers through a complex re-entrant manufacturing process. In some systems, Overhead Hoist Transport (OHT) vehicles move throughout the facility on a ceiling-mounted track system, delivering wafers to machines and storage locations. To improve efficiency in such systems, this thesis proposes an adaptive dynamic routing approach that allows the system to self-regulate, reducing steady-state travel times by 4-6% and avoiding excessive congestion and deadlock. Our approach allows vehicles to be rerouted while in progress in response to changes in the location and severity of congestion as measured by edge traversal time estimates updated via exponential smoothing. Our proposed method is efficient enough to be used in a large system where several routing decisions are made each second. We also consider how the effectiveness of a AMHS layout differs between static and dynamic routing. We demonstrate that dynamic routing significantly reduces sensitivity to shortcut placement and allows an eight-fold increase in the number of shortcuts along the center loop. This reduces travel times by an additional 24%. To demonstrate the effectiveness of our proposed routing approach, we use a high-fidelity simulation of vehicle movement. To test the impact of routing methods on layout effectiveness, we developed an associated Excel-based automated layout generation tool that allows the efficient generation of thousands of candidate layouts. The user selects from among a set of modular templates to create a design and all simulation files are generated with the click of a button.
Integer programming approaches for semicontinuous and stochastic optimization

(Georgia Institute of Technology, 2014-04-07) Angulo Olivares, Gustavo, I

This thesis concerns the application of mixed-integer programming techniques to solve special classes of network flow problems and stochastic integer programs. We draw tools from complexity and polyhedral theory to analyze these problems and propose improved solution methods. In the first part, we consider semi-continuous network flow problems, that is, a class of network flow problems where some of the variables are required to take values above a prespecified minimum threshold whenever they are not zero. These problems find applications in management and supply chain models where orders in small quantities are undesirable. We introduce the semi-continuous inflow set with variable upper bounds as a relaxation of general semi-continuous network flow problems. Two particular cases of this set are considered, for which we present complete descriptions of the convex hull in terms of linear inequalities and extended formulations. We also consider a class of semi-continuous transportation problems where inflow systems arise as substructures, for which we investigate complexity questions. Finally, we study the computational efficacy of the developed polyhedral results in solving randomly generated instances of semi-continuous transportation problems. In the second part, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of optimizing a linear function on the subset of vertices of P that are not contained in X. This problem is closely related to finding the k-best basic solutions to a linear problem and finds applications in stochastic integer programming. We observe that the complexity of the problem depends on how P and X are specified. For instance, P can be explicitly given by its linear description, or implicitly by an oracle. Similarly, X can be explicitly given as a list of vectors, or implicitly as a face of P. While removing vertices turns to be hard in general, it is tractable for tractable 0-1 polytopes, and compact extended formulations can be obtained. Some extensions to integral polytopes are also presented. The third part is devoted to the integer L-shaped method for two-stage stochastic integer programs. A widely used model assumes that decisions are made in a two-step fashion, where first-stage decisions are followed by second-stage recourse actions after the uncertain parameters are observed, and we seek to minimize the expected overall cost. In the case of finitely many possible outcomes or scenarios, the integer L-shaped method proposes a decomposition scheme akin to Benders' decomposition for linear problems, but where a series of mixed-integer subproblems have to be solved at each iteration. To improve the performance of the method, we devise a simple modification that alternates between linear and mixed-integer subproblems, yielding significant time savings in instances from the literature. We also present a general framework to generate optimality cuts via a cut-generating problem. Using an extended formulation of the forbidden-vertices problem, we recast our cut-generating problem as a linear problem and embed it within the integer L-shaped method. Our numerical experiments suggest that this approach can prove beneficial when the first-stage set is relatively complicated.
Topics in discrete optimization: models, complexity and algorithms

(Georgia Institute of Technology, 2013-08-12) He, Qie

In this dissertation we examine several discrete optimization problems through the perspectives of modeling, complexity and algorithms. We first provide a probabilistic comparison of split and type 1 triangle cuts for mixed-integer programs with two rows and two integer variables in terms of cut coefficients and volume cutoff. Under a specific probabilistic model of the problem parameters, we show that for the above measure, the probability that a split cut is better than a type 1 triangle cut is higher than the probability that a type 1 triangle cut is better than a split cut. The analysis also suggests some guidelines on when type 1 triangle cuts are likely to be more effective than split cuts and vice versa. We next study a minimum concave cost network flow problem over a grid network. We give a polytime algorithm to solve this problem when the number of echelons is fixed. We show that the problem is NP-hard when the number of echelons is an input parameter. We also extend our result to grid networks with backward and upward arcs. Our result unifies the complexity results for several models in production planning and green recycling including the lot-sizing model, and gives the first polytime algorithm for some problems whose complexities were not known before. Finally, we examine how much complexity randomness will bring to a simple combinatorial optimization problem. We study a problem called the sell or hold problem (SHP). SHP is to sell k out of n indivisible assets over two stages, with known first-stage prices and random second-stage prices, to maximize the total expected revenue. Although the deterministic version of SHP is trivial to solve, we show that SHP is NP-hard when the second-stage prices are realized as a finite set of scenarios. We show that SHP is polynomially solvable when the number of scenarios in the second stage is constant. A max{1/2,k/n}-approximation algorithm is presented for the scenario-based SHP.