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Journal ArticleDOI

Solving two-stage robust optimization problems using a column-and-constraint generation method

01 Sep 2013-Operations Research Letters (North-Holland)-Vol. 41, Iss: 5, pp 457-461
TL;DR: A computational study on a two-stage robust location-transportation problem shows that the column-and-constraint generation algorithm performs an order of magnitude faster than existing Benders-style cutting plane methods.
About: This article is published in Operations Research Letters.The article was published on 2013-09-01. It has received 1010 citations till now. The article focuses on the topics: Robust optimization & Cutting-plane method.
Citations
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Journal ArticleDOI
TL;DR: Computational studies on the IEEE distribution test systems validate the effectiveness of the RDNP and reveal that distributed generation is critical in increasing the resilience of a distribution system against natural disasters in the form of microgrids.
Abstract: Natural disasters such as Hurricane Sandy can seriously disrupt the power grids. To increase the resilience of an electric distribution system against natural disasters, this paper proposes a resilient distribution network planning problem (RDNP) to coordinate the hardening and distributed generation resource allocation with the objective of minimizing the system damage. The problem is formulated as a two-stage robust optimization model. Hardening and distributed generation resource placement are considered in the distribution network planning. A multi-stage and multi-zone based uncertainty set is designed to capture the spatial and temporal dynamics of an uncertain natural disaster as an extension to the traditional ${N}$ - ${K}$ contingency approach. The optimal solution of the RDNP yields a resilient distribution system against natural disasters. Our computational studies on the IEEE distribution test systems validate the effectiveness of the proposed model and reveal that distributed generation is critical in increasing the resilience of a distribution system against natural disasters in the form of microgrids.

414 citations

Journal ArticleDOI
TL;DR: In this article, an adaptive robust optimization model for multi-period economic dispatch, and methods to construct such sets to model temporal and spatial correlations of uncertainty, are presented to deal with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue.
Abstract: 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.

326 citations


Cites background or methods from "Solving two-stage robust optimizati..."

  • ...Previous work has dealt with this problem using outer-approximation techniques [4] and exact methods based on mixed-integer programming (MIP) reformulations [12], [36], [40]....

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  • ...Indeed, (13) can be efficiently solved by adding and the associated constraints iteratively [4], [36]....

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  • ...[12], [36], [40]....

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  • ...Efficient solution methods for the two-stage robust UC have been proposed [4], [12], [16], [36]....

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  • ...The exact MIP method proposed in [36] is based on the KKT conditions, which are applicable to general polyhedral uncertainty sets....

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Journal ArticleDOI
TL;DR: In this paper, a robust co-optimization scheduling model was proposed to study the coordinated optimal operation of the two energy systems, while considering power system key uncertainties and natural gas system dynamics.
Abstract: The significant growth of gas-fired power plants and emerging power-to-gas (PtG) technology has intensified the interdependency between electricity and natural gas systems. This paper proposes a robust co-optimization scheduling model to study the coordinated optimal operation of the two energy systems. The proposed model minimizes the total costs of the two systems, while considering power system key uncertainties and natural gas system dynamics. Because of the limitation on exchanging private data and the challenge in managing complex models, the proposed co-optimization model is tackled via alternating direction method of multipliers (ADMM) by iteratively solving a power system subproblem and a gas system subproblem. The power system subproblem is solved by column-and-constraint generation (C&CG) and outer approximation (OA), and the nonlinear gas system subproblem is solved by converting into a mixed-integer linear programming model. To overcome nonconvexity of the original problem with binary variables, a tailored ADMM with a relax-round-polish process is developed to obtain high-quality solutions. Numerical case studies illustrate the effectiveness of the proposed model for optimally coordinating electricity and natural gas systems with uncertainties.

323 citations


Cites methods from "Solving two-stage robust optimizati..."

  • ...The power system subproblem is solved by C&CG [18], and the nonlinear gas system subproblem is solved by converting into an MILP model....

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  • ...The C&CG is implemented via a master-subproblem framework....

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  • ...The power system subproblem is solved by C&CG, in which the identified worst case realizations are directly used in further iterations of ADMM to improve the computation speed....

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  • ...The power system subproblem is solved by C&CG in a master-subproblem framework....

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  • ...Solve power system subproblem: Solve (49) and (2)– (25) using the C&CG method in Section III-A.1, with given P̄ bit = P̂ g (r) it , P̄ b,ptg at = P̂ g ,ptg(r) at λp,it = λ (r) p,it , λp,at = λ (r) p,at , and the worst case natural gas usage cuts generated so far....

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Journal ArticleDOI
TL;DR: In this article, transmission-constrained unit commitment (UC) with combined electricity and district heating networks (UC-CEHN) is formulated with a linear DHN model to coordinate short-term operation of electric power and heating systems.
Abstract: Wind power integration could be restricted by inflexible operation of combined heat and power (CHP) units due to the strong linkage between power generation and heating supply in winter. Utilization of the heat storage capacity of existing district heating network (DHN) is a cost-effective measure to enhance power system operational flexibility to accommodate large amounts of variable wind power. In this paper, transmission-constrained unit commitment (UC) with combined electricity and district heating networks (UC-CEHN) is formulated with a linear DHN model to coordinate short-term operation of electric power and district heating systems. The heat storage capacity of the DHN is modeled by capturing the quasi-dynamics of pipeline temperature. Both deterministic and robust models are developed to incorporate UC with the linear DHN model. Case studies are carried out for two test systems to show the potential benefits of the proposed method in terms of wind power integration and efficient operation.

307 citations


Cites methods from "Solving two-stage robust optimizati..."

  • ...Details of this algorithm is reported in [36]....

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  • ...The RUC-CEHN model is a typical two-stage RO that can be solved to global optimality with the column-and-constraint generation (C&CG) method [36]....

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Journal ArticleDOI
Tao Ding, Shiyu Liu, Wei Yuan1, Zhaohong Bie1, Bo Zeng 
TL;DR: Wang et al. as discussed by the authors proposed a two-stage robust optimization model to coordinate the discrete and continuous reactive power compensators and find a robust optimal solution that can hedge against any possible realization within the uncertain wind power output.
Abstract: Traditional reactive power optimization aims to minimize the total transmission losses by control reactive power compensators and transformer tap ratios, while guaranteeing the physical and operating constraints, such as voltage magnitudes and branch currents to be within their reasonable range. However, large amounts of renewable resources coming into power systems bring about great challenges to traditional planning and operation due to the stochastic nature. In most of the practical cases from China, the wind farms are centrally integrated into active distribution networks. By the use of conic relaxation based branch flow formulation, the reactive optimization problem in active distribution networks can be formulated as a mixed integer convex programming model that can be tractably dealt with. Furthermore, to address the uncertainties of wind power output, a two-stage robust optimization model is proposed to coordinate the discrete and continuous reactive power compensators and find a robust optimal solution that can hedge against any possible realization within the uncertain wind power output. Moreover, the second order cone programming-based column-and-constraint generation algorithm is employed to solve the proposed two-stage robust reactive power optimization model. Numerical results on 33-, 69- and 123-bus systems and comparison with the deterministic approach demonstrate the effectiveness of the proposed method.

290 citations


Cites background or methods from "Solving two-stage robust optimizati..."

  • ...It was proven in [32] that given a finite binary set, the column-and-constraint generation method could converge in finite iterations to obtain a global optimal solution....

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  • ...But the convergence performance of this method outperforms Bender’s algorithm [32], [33]....

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  • ..., continuous reactive power compensators) are represented as the “wait-and-see” decisions that can be adjusted after the first stage decisions are determined and the wind power uncertainty is revealed, which essentially provides the decision maker a recourse opportunity [32], [33]....

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References
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Journal ArticleDOI
TL;DR: In this paper, the authors propose an approach that attempts to make this trade-off more attractive by flexibly adjusting the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations.
Abstract: A robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended. Under this approach, we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes. A concern with such an approach is that it might be too conservative. In this paper, we propose an approach that attempts to make this trade-off more attractive; that is, we investigate ways to decrease what we call the price of robustness. In particular, we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations. An attractive aspect of our method is that the new robust formulation is also a linear optimization problem. Thus we naturally extend our methods to discrete optimization problems in a tractable way. We report numerical results for a portfolio optimization problem, a knapsack problem, and a problem from the Net Lib library.

3,364 citations

01 Jan 2004
TL;DR: An approach is proposed that flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations, and an attractive aspect of this method is that the new robust formulation is also a linear optimization problem, so it naturally extend to discrete optimization problems in a tractable way.
Abstract: A robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended. Under this approach, we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes. A concern with such an approach is that it might be too conservative. In this paper, we propose an approach that attempts to make this trade-off more attractive; that is, we investigate ways to decrease what we call the price of robustness. In particular, we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations. An attractive aspect of our method is that the new robust formulation is also a linear optimization problem. Thus we naturally extend our methods to discrete optimization problems in a tractable way. We report numerical results for a portfolio optimization problem, a knapsack problem, and a problem from the Net Lib library.

3,359 citations


"Solving two-stage robust optimizati..." refers background in this paper

  • ...Robust optimization (RO) [2, 3, 4, 11, 7, 8] is a recent optimization approach to deal with data uncertainty....

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Journal ArticleDOI
TL;DR: If U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods.
Abstract: We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we lay the foundation of robust convex optimization. In the main part of the paper we show that if U is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods.

2,501 citations


"Solving two-stage robust optimizati..." refers background in this paper

  • ...Robust optimization (RO) [2, 3, 4, 11, 7, 8] is a recent optimization approach to deal with data uncertainty....

    [...]

BookDOI
01 Jan 1989

2,186 citations

Journal ArticleDOI
TL;DR: In this paper, the extremal value of the linear program as a function of the parameterizing vector and the set of values of the parametric vector for which the program is feasible were derived using linear programming duality theory.
Abstract: J. F. Benders devised a clever approach for exploiting the structure of mathematical programming problems withcomplicating variables (variables which, when temporarily fixed, render the remaining optimization problem considerably more tractable). For the class of problems specifically considered by Benders, fixing the values of the complicating variables reduces the given problem to an ordinary linear program, parameterized, of course, by the value of the complicating variables vector. The algorithm he proposed for finding the optimal value of this vector employs a cutting-plane approach for building up adequate representations of (i) the extremal value of the linear program as a function of the parameterizing vector and (ii) the set of values of the parameterizing vector for which the linear program is feasible. Linear programming duality theory was employed to derive the natural families ofcuts characterizing these representations, and the parameterized linear program itself is used to generate what are usuallydeepest cuts for building up the representations.

2,133 citations