551 research outputs found
Contingency-Constrained Unit Commitment With Intervening Time for System Adjustments
The N-1-1 contingency criterion considers the con- secutive loss of two
components in a power system, with intervening time for system adjustments. In
this paper, we consider the problem of optimizing generation unit commitment
(UC) while ensuring N-1-1 security. Due to the coupling of time periods
associated with consecutive component losses, the resulting problem is a very
large-scale mixed-integer linear optimization model. For efficient solution, we
introduce a novel branch-and-cut algorithm using a temporally decomposed
bilevel separation oracle. The model and algorithm are assessed using multiple
IEEE test systems, and a comprehensive analysis is performed to compare system
performances across different contingency criteria. Computational results
demonstrate the value of considering intervening time for system adjustments in
terms of total cost and system robustness.Comment: 8 pages, 5 figure
Modeling of Competition and Collaboration Networks under Uncertainty: Stochastic Programs with Resource and Bilevel
We analyze stochastic programming problems with recourse characterized by a bilevel structure. Part of the uncertainty in such problems is due to actions of other actors such that the considered decision maker needs to develop a model to estimate their response to his decisions. Often, the resulting model exhibits connecting constraints in the leaders (upper-level) subproblem. It is shown that this problem can be formulated as a new class of stochastic programming problems with equilibrium constraints (SMPEC). Sufficient optimality conditions are stated. A solution algorithm utilizing a stochastic quasi-gradient method is proposed, and its applicability extensively explained by practical numerical examples
Robust optimization methods for chance constrained, simulation-based, and bilevel problems
The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty set. The robust version of a mathematical optimization problem is generally referred to as the robust counterpart problem. Robust optimization is popular because of the computational tractability of the robust counterpart for many classes of uncertainty sets, and its applicability in wide range of topics in practice. In this thesis, we propose robust optimization methodologies for different classes of optimization problems. In Chapter 2, we give a practical guide on robust optimization. In Chapter 3, we propose a new way to construct uncertainty sets for robust optimization using the available historical data information. Chapter 4 proposes a robust optimization approach for simulation-based optimization problems. Finally, Chapter 5 proposes approximations of a specific class of robust and stochastic bilevel optimization problems by using modern robust optimization techniques
On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints
Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this setup, we develop a cutting-plane algorithm that computes approximate bilevel-feasible points. We apply this method to a bilevel model of the European gas market in which we use a joint chance constraint to model uncertain loads. Since the chance constraint is not available in closed form, this fits into the black-box setting studied before. For the applied model, we use further problem-specific insights to derive bounds on the objective value of the bilevel problem. By doing so, we are able to show that we solve the application problem to approximate global optimality. In our numerical case study we are thus able to evaluate the welfare sensitivity in dependence of the achieved safety level of uncertain load coverage
Integer Bilevel Linear Programming Problems: New Results and Applications
Integer Bilevel Linear Programming Problems: New Results and Application
Integer Bilevel Linear Programming Problems: New Results and Applications
Integer Bilevel Linear Programming Problems: New Results and Application
A Framework for Generalized Benders' Decomposition and Its Application to Multilevel Optimization
We describe a framework for reformulating and solving optimization problems
that generalizes the well-known framework originally introduced by Benders. We
discuss details of the application of the procedures to several classes of
optimization problems that fall under the umbrella of multilevel/multistage
mixed integer linear optimization problems. The application of this abstract
framework to this broad class of problems provides new insights and a broader
interpretation of the core ideas, especially as they relate to duality and the
value functions of optimization problems that arise in this context
A Survey of Contextual Optimization Methods for Decision Making under Uncertainty
Recently there has been a surge of interest in operations research (OR) and
the machine learning (ML) community in combining prediction algorithms and
optimization techniques to solve decision-making problems in the face of
uncertainty. This gave rise to the field of contextual optimization, under
which data-driven procedures are developed to prescribe actions to the
decision-maker that make the best use of the most recently updated information.
A large variety of models and methods have been presented in both OR and ML
literature under a variety of names, including data-driven optimization,
prescriptive optimization, predictive stochastic programming, policy
optimization, (smart) predict/estimate-then-optimize, decision-focused
learning, (task-based) end-to-end learning/forecasting/optimization, etc.
Focusing on single and two-stage stochastic programming problems, this review
article identifies three main frameworks for learning policies from data and
discusses their strengths and limitations. We present the existing models and
methods under a uniform notation and terminology and classify them according to
the three main frameworks identified. Our objective with this survey is to both
strengthen the general understanding of this active field of research and
stimulate further theoretical and algorithmic advancements in integrating ML
and stochastic programming
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more
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