Tight and Compact Sample Average Approximation for Joint Chance-Constrained Problems with Applications to Optimal Power Flow

References

• Abdi A, Fukasawa R (2016) On the mixing set with a knapsack constraint. Math. Programming 157(1):191–217.Crossref, Google Scholar
• Ahmed S, Xie W (2018) Relaxations and approximations of chance constraints under finite distributions. Math. Programming 170(1):43–65.Crossref, Google Scholar
• Ahmed S, Luedtke J, Song Y, Xie W (2017) Nonanticipative duality, relaxations, and formulations for chance-constrained stochastic programs. Math. Programming 162(1):51–81.Crossref, Google Scholar
• Atamtürk A, Nemhauser GL, Savelsbergh MWP (2000) Conflict graphs in solving integer programming problems. Eur. J. Oper. Res. 121(1):40–55.Crossref, Google Scholar
• Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math. Programming 88(3):411–424.Crossref, Google Scholar
• Bienstock D, Chertkov M, Harnett S (2014) Chance-constrained optimal power flow: Risk-aware network control under uncertainty. SIAM Rev. 56(3):461–495.Crossref, Google Scholar
• Cheema MA, Shen Z, Lin X, Zhang W (2014) A unified framework for efficiently processing ranking related queries. Amer-Yahia S, Christophides V, Kementsietsidis A, Garofalakis M, Idreos S, Leroy V, eds. Advances in Database Technology - EDBT 2014: 17th Internat. Conf. Extending Database Technology (OpenProceedings.org, Konstanz, Germany), 427–438.Google Scholar
• Chen G, Zhang H, Hui H, Song Y (2021) Scheduling HVAC loads to promote renewable generation integration with a learning-based joint chance-constrained approach. Preprint, submitted December 18, https://arxiv.org/abs/2112.09827.Google Scholar
• Conforti M, Cornuéjols G, Zambelli G (2014) Integer Programming, vol. 271 (Springer, Cham, Switzerland).Crossref, Google Scholar
• Daníelsson J, Jorgensen BN, de Vries CG, Yang X (2008) Optimal portfolio allocation under the probabilistic VaR constraint and incentives for financial innovation. Ann. Finance 4(3):345–367.Crossref, Google Scholar
• Dentcheva D, Prékopa A, Ruszczynski A (2000) Concavity and efficient points of discrete distributions in probabilistic programming. Math. Programming 89(1):55–77.Crossref, Google Scholar
• Dey TK (1998) Improved bounds for planar k-sets and related problems. Discrete Comput. Geometry 19(3):373–382.Crossref, Google Scholar
• Edelsbrunner H, Welzl E (1985) On the number of line separations of a finite set in the plane. J. Combin. Theory Ser. A 38(1):15–29.Crossref, Google Scholar
• Edelsbrunner H, Welzl E (1986) Constructing belts in two-dimensional arrangements with applications. SIAM J. Comput. 15(1).Crossref, Google Scholar
• Elçi Ö, Noyan N, Bülbül K (2018) Chance-constrained stochastic programming under variable reliability levels with an application to humanitarian relief network design. Comput. Oper. Res. 96:91–107.Crossref, Google Scholar
• Esteban-Pérez A, Morales JM (2023) Distributionally robust optimal power flow with contextual information. Eur. J. Oper. Res. 306(3):1047–1058.Crossref, Google Scholar
• Frank S, Steponavice I, Rebennack S (2012) Optimal power flow: A bibliographic survey I. Energy Systems 3(3):221–258.Crossref, Google Scholar
• Günlük O, Pochet Y (2001) Mixing mixed-integer inequalities. Math. Programming 90(3):429–457.Crossref, Google Scholar
• Gurobi Optimization, LLC (2022) Gurobi optimizer reference manual. Accessed July, 2023, https://www.gurobi.com.Google Scholar
• Henrion R (2007) Structural properties of linear probabilistic constraints. Optim. 56(4):425–440.Crossref, Google Scholar
• Henrion R, Strugarek C (2011) Convexity of chance constraints with dependent random variables: The use of copulae. Stochastic Optimization Methods in Finance and Energy (Springer, New York), 427–439.Crossref, Google Scholar
• Hong LJ, Yang Y, Zhang L (2011) Sequential convex approximations to joint chance constrained programs: A Monte Carlo approach. Oper. Res. 59(3):617–630.Link, Google Scholar
• Hou AM, Roald LA (2020) Chance constraint tuning for optimal power flow. Internat. Conf. Probab. Methods Appl. Power Systems, 1–6.Google Scholar
• Jiang N, Xie W (2022) ALSO-X and ALSO-X+: Better convex approximations for chance constrained programs. Oper. Res. 70(6):3581–3600.Link, Google Scholar
• Küçükyavuz S, Jiang R (2022) Chance-constrained optimization under limited distributional information: A review of reformulations based on sampling and distributional robustness. EURO J. Comput. Optim. 10:100030.Crossref, Google Scholar
• Lagoa CM, Li X, Sznaier M (2005) Probabilistically constrained linear programs and risk-adjusted controller design. SIAM J. Optim. 15(3):938–951.Crossref, Google Scholar
• Lejeune MA, Dehghanian P (2020) Optimal power flow models with probabilistic guarantees: A Boolean approach. IEEE Trans. Power Systems 35(6):4932–4935.Crossref, Google Scholar
• Luedtke J (2014) A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support. Math. Programming 146(1–2):219–244.Crossref, Google Scholar
• Luedtke J, Ahmed S (2008) A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19(2):674–699.Crossref, Google Scholar
• Luedtke J, Ahmed S, Nemhauser GL (2010) An integer programming approach for linear programs with probabilistic constraints. Math. Programming 122(2):247–272.Crossref, Google Scholar
• Miller BL, Wagner HM (1965) Chance constrained programming with joint constraints. Oper. Res. 13(6):930–945.Link, Google Scholar
• Nair R, Miller-Hooks E (2011) Fleet management for vehicle sharing operations. Transportation Sci. 45(4):524–540.Link, Google Scholar
• Najjarbashi A, Lim GJ (2020) A decomposition algorithm for the two-stage chance-constrained operating room scheduling problem. IEEE Access 8:80160–80172.Crossref, Google Scholar
• Natarajan K, Pachamanova D, Sim M (2008) Incorporating asymmetric distributional information in robust value-at-risk optimization. Management Sci. 54(3):573–585.Link, Google Scholar
• Nemirovski A, Shapiro A (2006) Scenario approximations of chance constraints. Probabilistic and Randomized Methods for Design Under Uncertainty (Springer, London), 3–47.Google Scholar
• Nemirovski A, Shapiro A (2007) Convex approximations of chance constrained programs. SIAM J. Optim. 17(4):969–996.Crossref, Google Scholar
• Nivasch G (2008) An improved, simple construction of many halving edges. Contemporary Math. 453:299–306.Crossref, Google Scholar
• OASYS (2023) Data and code for a tight and compact model of the SAA-based joint chance-constrained OPF. https://github.com/groupoasys/TC_SAA_JCC-OPF.Google Scholar
• Peña-Ordieres A, Luedtke JR, Wächter A (2020) Solving chance-constrained problems via a smooth sample-based nonlinear approximation. SIAM J. Optim. 30(3):2221–2250.Crossref, Google Scholar
• Peña-Ordieres A, Molzahn DK, Roald LA, Wächter A (2021) DC optimal power flow with joint chance constraints. IEEE Trans. Power Systems 36(1):147–158.Crossref, Google Scholar
• Power Grid Lib (2022) https://github.com/power-grid-lib/pglib-opf.Google Scholar
• Prékopa A (2003) Probabilistic programming. Ruszczynski A, Shapiro A, eds. Stochastic Programming, Handbooks in Operations Research and Management Science, vol. 10 (Elsevier, Amsterdam), 267–351.Google Scholar
• Qiu F, Ahmed S, Dey SS, Wolsey LA (2014) Covering linear programming with violations. INFORMS J. Comput. 26(3):531–546.Link, Google Scholar
• Roald L, Andersson G (2018) Chance-constrained AC optimal power flow: Reformulations and efficient algorithms. IEEE Trans. Power Systems 33(3):2906–2918.Crossref, Google Scholar
• Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J. Risk 2(3):21–41.Crossref, Google Scholar
• Roos T, Widmayer P (1994) K-violation linear programming. Inform. Processing Lett. 52(2):109–114.Crossref, Google Scholar
• Shapiro A (2003) Monte Carlo sampling methods. Ruszczynski A, Shapiro A, eds. Stochastic Programming, Handbooks in Operations Research and Management Science, vol. 10 (Elsevier, Amsterdam), 353–425.Google Scholar
• Shaw K, Irfan M, Shankar R, Yadav SS (2016) Low carbon chance constrained supply chain network design problem: A Benders decomposition based approach. Comput. Indust. Engrg. 98:483–497.Crossref, Google Scholar
• Song Y, Luedtke JR, Küçükyavuz S (2014) Chance-constrained binary packing problems. INFORMS J. Comput. 26(4):735–747.Link, Google Scholar
• Sun H, Xu H, Wang Y (2014) Asymptotic analysis of sample average approximation for stochastic optimization problems with joint chance constraints via conditional value at risk and difference of convex functions. J. Optim. Theory Appl. 161(1):257–284.Crossref, Google Scholar
• Taleizadeh AA, Niaki STA, Makui A (2012) Multiproduct multiple-buyer single-vendor supply chain problem with stochastic demand, variable lead-time, and multi-chance constraint. Expert Systems Appl. 39(5):5338–5348.Crossref, Google Scholar
• Tanner MW, Sattenspiel L, Ntaimo L (2008) Finding optimal vaccination strategies under parameter uncertainty using stochastic programming. Math. Biosciences 215(2):144–151.Crossref, Google Scholar
• Tayur SR, Thomas RR, Natraj NR (1995) An algebraic geometry algorithm for scheduling in presence of setups and correlated demands. Math. Programming 69(1):369–401.Crossref, Google Scholar
• Tóth CD, O’Rourke J, Goodman JE (2017) Handbook of Discrete and Computational Geometry (CRC Press, Boca Raton, FL).Google Scholar
• Tóth G (2000) Point sets with many k-sets. Proc. 16th Annual Sympos. Comput. Geometry, 37–42.Google Scholar
• Van Ackooij W, Zorgati R, Henrion R, Möller A (2011) Chance constrained programming and its applications to energy management. Stochastic Optimization—Seeing the Optimal for the Uncertain, 291–320.Google Scholar
• Vrakopoulou M, Margellos K, Lygeros J, Andersson G (2013) Probabilistic guarantees for the N-1 security of systems with wind power generation. Reliability and Risk Evaluation of Wind Integrated Power Systems (Springer, New Delhi), 59–73.Crossref, Google Scholar
• Xie W, Ahmed S (2016) On the quantile cut closure of chance-constrained problems. Internat. Conf. Integer Programming Combin. Optim. (Springer, Cham, Switzerland), 398–409.Google Scholar
• Xie W, Ahmed S (2018) On quantile cuts and their closure for chance constrained optimization problems. Math. Programming 172(1):621–646.Crossref, Google Scholar
• Zhang Y, Shen S, Mathieu JL (2015) Data-driven optimization approaches for optimal power flow with uncertain reserves from load control. Amer. Control Conf. (IEEE, Piscataway, NJ), 3013–3018.Google Scholar