Robust SCUC considering continuous/discrete uncertainties and quick-start units: A two-stage robust optimization with mixed-integer recourse

2016 ◽  
Author(s):  
Lei Wu
Keyword(s):  
Robust Optimization ◽  
Mixed Integer ◽  
Two Stage ◽  
Integer Recourse

scholarly journals Convex approximations for two-stage mixed-integer mean-risk recourse models with conditional value-at-risk

2019 ◽  
Vol 181 (2) ◽  
pp. 473-507 ◽  
Author(s):  
E. Ruben van Beesten ◽  
Ward Romeijnders
Keyword(s):  
At Risk ◽  
Error Bounds ◽  
Value At Risk ◽  
Risk Measure ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Two Stage ◽  
Special Cases ◽  
Integer Recourse ◽  
Mean Risk

Abstract In traditional two-stage mixed-integer recourse models, the expected value of the total costs is minimized. In order to address risk-averse attitudes of decision makers, we consider a weighted mean-risk objective instead. Conditional value-at-risk is used as our risk measure. Integrality conditions on decision variables make the model non-convex and hence, hard to solve. To tackle this problem, we derive convex approximation models and corresponding error bounds, that depend on the total variations of the density functions of the random right-hand side variables in the model. We show that the error bounds converge to zero if these total variations go to zero. In addition, for the special cases of totally unimodular and simple integer recourse models we derive sharper error bounds.

scholarly journals Two-Stage Robust Optimization Model for Uncertainty Investment Portfolio Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Dongqing Luan ◽  
Chuming Wang ◽  
Zhong Wu ◽  
Zhijie Xia
Keyword(s):  
Robust Optimization ◽  
Financial Management ◽  
Value At Risk ◽  
Optimization Theory ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Equal Weight ◽  
Investment Portfolio ◽  
Two Stage ◽  
Mip Model

Investment portfolio can provide investors with a more robust financial management plan, but the uncertainty of its parameters is a key factor affecting performance. This paper conducts research on investment portfolios and constructs a two-stage mixed integer programming (TS-MIP) model, which comprehensively considers the five dimensions of profit, diversity, skewness, information entropy, and conditional value at risk. But the deterministic TS-MIP model cannot cope with the uncertainty. Therefore, this paper constructs a two-stage robust optimization (TS-RO) model by introducing robust optimization theory. In case experiments, data crawler technology is used to obtain actual data from real websites, and a variety of methods are used to verify the effectiveness of the proposed model in dealing with uncertainty. The comparison of models found that, compared with the traditional equal weight model, the investment benefits of the TS-MIP model and the TS-RO model proposed have been improved. Among them, the Sharpe ratio, Sortino ratio, and Treynor ratio have the largest increase of 19.30%, 8.25%, and 7.34%, respectively.

scholarly journals Exploiting the Structure of Two-Stage Robust Optimization Models with Exponential Scenarios

2020 ◽  
Author(s):  
Hossein Hashemi Doulabi ◽  
Patrick Jaillet ◽  
Gilles Pesant ◽  
Louis-Martin Rousseau
Keyword(s):  
Robust Optimization ◽  
Single Stage ◽  
Mixed Integer ◽  
Optimization Models ◽  
Master Problem ◽  
Maximization Problem ◽  
Planning Problem ◽  
Two Stage ◽  
Integer Programs ◽  
Mixed Integer Programs

This paper addresses a class of two-stage robust optimization models with an exponential number of scenarios given implicitly. We apply Dantzig–Wolfe decomposition to exploit the structure of these models and show that the original problem reduces to a single-stage robust problem. We propose a Benders algorithm for the reformulated single-stage problem. We also develop a heuristic algorithm that dualizes the linear programming relaxation of the inner maximization problem in the reformulated model and iteratively generates cuts to shape the convex hull of the uncertainty set. We combine this heuristic with the Benders algorithm to create a more effective hybrid Benders algorithm. Because the master problem and subproblem in the Benders algorithm are mixed-integer programs, it is computationally demanding to solve them optimally at each iteration of the algorithm. Therefore, we develop novel stopping conditions for these mixed-integer programs and provide the relevant convergence proofs. Extensive computational experiments on a nurse planning problem and a two-echelon supply chain problem are performed to evaluate the efficiency of the proposed algorithms.

scholarly journals K-adaptability in two-stage mixed-integer robust optimization

2019 ◽  
Vol 12 (2) ◽  
pp. 193-224 ◽  
Author(s):  
Anirudh Subramanyam ◽  
Chrysanthos E. Gounaris ◽  
Wolfram Wiesemann
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Mixed Integer ◽  
Finite Convergence ◽  
Two Stage ◽  
Infinite Dimensional ◽  
Benchmark Data ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation

Abstract We study two-stage robust optimization problems with mixed discrete-continuous decisions in both stages. Despite their broad range of applications, these problems pose two fundamental challenges: (i) they constitute infinite-dimensional problems that require a finite-dimensional approximation, and (ii) the presence of discrete recourse decisions typically prohibits duality-based solution schemes. We address the first challenge by studying a K-adaptability formulation that selects K candidate recourse policies before observing the realization of the uncertain parameters and that implements the best of these policies after the realization is known. We address the second challenge through a branch-and-bound scheme that enjoys asymptotic convergence in general and finite convergence under specific conditions. We illustrate the performance of our algorithm in numerical experiments involving benchmark data from several application domains.

scholarly journals Evaluation of Wind Energy Accommodation Based on Two-Stage Robust Optimization

2020 ◽  
Vol 26 (3) ◽  
pp. 61-68
Author(s):  
Kunpeng Tian ◽  
Weiqing Sun ◽  
Dong Han ◽  
Ce Yang
Keyword(s):  
Renewable Energy ◽  
Power System ◽  
Wind Energy ◽  
Robust Optimization ◽  
Optimization Problem ◽  
Mixed Integer ◽  
Master Problem ◽  
Two Stage ◽  
Energy Accommodation ◽  
Robust Optimization Problem

Large-scale renewable energy integration brings unprecedented challenges to electric power system planning and operation. The paper aims at economic dispatch and the safe operation of high penetration renewable energy power systems. According to the principle of power system dispatchability, the assessment of wind energy accommodation is formulated into a two-stage robust optimization problem with a min-max-min structure. Based on the benders algorithm, the intractable robust optimization problem is transformed into the form of sub-problem and master problem. Strong duality theory and big-M method are used to recast the sub problem into a mixed integer linear programming. The envelope of wind energy accommodation can be obtained by using commercial software to solve the master problem and sub problem alternately. For the realization of arbitrary wind power within the envelope, the amount of wind energy leakage and load shedding in power system operation are acceptable. An example of modified IEEE 39-bus test systems is used to verify the effectiveness and practicability of the evaluation method.

scholarly journals A loose Benders decomposition algorithm for approximating two-stage mixed-integer recourse models

2020 ◽  
Author(s):  
Niels van der Laan ◽  
Ward Romeijnders
Keyword(s):  
Error Bounds ◽  
Benders Decomposition ◽  
Decomposition Algorithm ◽  
Mixed Integer ◽  
Large Problem ◽  
Two Stage ◽  
Convex Approximations ◽  
Integer Recourse ◽  
Benders Decomposition Algorithm ◽  
Problem Instances

Abstract We propose a new class of convex approximations for two-stage mixed-integer recourse models, the so-called generalized alpha-approximations. The advantage of these convex approximations over existing ones is that they are more suitable for efficient computations. Indeed, we construct a loose Benders decomposition algorithm that solves large problem instances in reasonable time. To guarantee the performance of the resulting solution, we derive corresponding error bounds that depend on the total variations of the probability density functions of the random variables in the model. The error bounds converge to zero if these total variations converge to zero. We empirically assess our solution method on several test instances, including the SIZES and SSLP instances from SIPLIB. We show that our method finds near-optimal solutions if the variability of the random parameters in the model is large. Moreover, our method outperforms existing methods in terms of computation time, especially for large problem instances.

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