844 research outputs found
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind
The exceptional benefits of wind power as an environmentally responsible
renewable energy resource have led to an increasing penetration of wind energy
in today's power systems. This trend has started to reshape the paradigms of
power system operations, as dealing with uncertainty caused by the highly
intermittent and uncertain wind power becomes a significant issue. Motivated by
this, we present a new framework using adaptive robust optimization for the
economic dispatch of power systems with high level of wind penetration. In
particular, we propose an adaptive robust optimization model for multi-period
economic dispatch, and introduce the concept of dynamic uncertainty sets and
methods to construct such sets to model temporal and spatial correlations of
uncertainty. We also develop a simulation platform which combines the proposed
robust economic dispatch model with statistical prediction tools in a rolling
horizon framework. We have conducted extensive computational experiments on
this platform using real wind data. The results are promising and demonstrate
the benefits of our approach in terms of cost and reliability over existing
robust optimization models as well as recent look-ahead dispatch models.Comment: Accepted for publication at IEEE Transactions on Power System
A Practical Guide to Robust Optimization
Robust optimization is a young and active research field that has been mainly
developed in the last 15 years. Robust optimization is very useful for
practice, since it is tailored to the information at hand, and it leads to
computationally tractable formulations. It is therefore remarkable that
real-life applications of robust optimization are still lagging behind; there
is much more potential for real-life applications than has been exploited
hitherto. The aim of this paper is to help practitioners to understand robust
optimization and to successfully apply it in practice. We provide a brief
introduction to robust optimization, and also describe important do's and
don'ts for using it in practice. We use many small examples to illustrate our
discussions
Hybrid Strategies using Linear and Piecewise-Linear Decision Rules for Multistage Adaptive Linear Optimization
Decision rules offer a rich and tractable framework for solving certain
classes of multistage adaptive optimization problems. Recent literature has
shown the promise of using linear and nonlinear decision rules in which
wait-and-see decisions are represented as functions, whose parameters are
decision variables to be optimized, of the underlying uncertain parameters.
Despite this growing success, solving real-world stochastic optimization
problems can become computationally prohibitive when using nonlinear decision
rules, and in some cases, linear ones. Consequently, decision rules that offer
a competitive trade-off between solution quality and computational time become
more attractive. Whereas the extant research has always used homogeneous
decision rules, the major contribution of this paper is a computational
exploration of hybrid decision rules. We first verify empirically that having
higher uncertainty resolution or more linear pieces in early stages is more
significant than having it in late stages in terms of solution quality. Then we
conduct a comprehensive computational study for non-increasing (i.e., higher
uncertainty resolution in early stages) and non-decreasing (i.e., higher
uncertainty resolution in late stages) hybrid decision rules to illustrate the
trade-off between solution quality and computational cost. We also demonstrate
a case where a linear decision rule is superior to a piecewise-linear decision
rule within a simulator environment, which supports the need to assess the
quality of decision rules obtained from a look-ahead model within a simulator
rather than just using the look-ahead model's objective function value
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