Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets

Published Online:https://doi.org/10.1287/ijoc.2020.1037

References

  • Achiam J, Held D, Tamar A, Abbeel P (2017) Constrained policy optimization. Proc. Internat. Conf. Machine Learn. “(PMLR)”, 22–31.Google Scholar
  • Alvarez AM, Louveaux Q, Wehenkel L (2017) A machine learning-based approximation of strong branching. INFORMS J. Comput. 29(1):185–195.LinkGoogle Scholar
  • Bayat F, Johansen TA, Jalali AA (2011) Using hash tables to manage the time-storage complexity in a point location problem: Application to explicit model predictive control. Automatica J. IFAC 47(3):571–577.CrossrefGoogle Scholar
  • Bayat F, Johansen TA, Jalali AA (2012) Flexible piecewise function evaluation methods based on truncated binary search trees and lattice representation in explicit mpc. IEEE Trans. Control Systems Tech. 20(3):632–640.CrossrefGoogle Scholar
  • Bemporad A, Borrelli F, Morari M (2002a) Model predictive control based on linear programming—The explicit solution. IEEE Trans. Automatic Control 47(12):1974–1985.CrossrefGoogle Scholar
  • Bemporad A, Morari M, Dua V, Pistikopoulos EN (2002b) The explicit linear quadratic regulator for constrained systems. Automatica J. IFAC 38(1):3–20.CrossrefGoogle Scholar
  • Bezanson J, Edelman A, Karpinski S, Shah VB (2017) Julia: A fresh approach to numerical computing. SIAM Rev. 59(1):65–98.CrossrefGoogle Scholar
  • Birchfield AB, Xu T, Gegner KM, Shetye KS, Overbye TJ (2017) Grid structural characteristics as validation criteria for synthetic networks. IEEE Trans. Power Systems 32(4):3258–3265.CrossrefGoogle Scholar
  • Bonami P, Lodi A, Zarpellon G (2018) Learning a classification of mixed-integer quadratic programming problems. Proc. Internat. Conf. Integration Constraint Programming Artificial Intelligence Oper. Res. (Springer, Berlin), 595–604.Google Scholar
  • Borrelli L, Baotic T, Bemporad A, Morari T (2001) Efficient on-line computation of constrained optimal control. Proc. 40th IEEE Conf. Decision Control, vol. 2 (IEEE, New York), 1187–1192.Google Scholar
  • Christie RD, Wollenberg BF, Wangensteen I (2000) Transmission management in the deregulated environment. Proc. IEEE 88(2):170–195.CrossrefGoogle Scholar
  • Coffrin C, Bent R, Sundar K, Ng Y, Lubin M (2018) Powermodels.jl: An open-source framework for exploring power flow formulations. Proc. Power Systems Comput. Conf. (IEEE, New York) 1–8.Google Scholar
  • Dunning I, Huchette J, Lubin M (2017) JuMP: A modeling language for mathematical optimization. SIAM Rev. 59(2):295–320.CrossrefGoogle Scholar
  • Fisac JF, Akametalu AK, Zeilinger MN, Kaynama S, Gillula J, Tomlin CJ (2018) A general safety framework for learning-based control in uncertain robotic systems. IEEE Trans. Automatic Control 64(7): 2737–2752.Google Scholar
  • Fuchs AN, Jones C, Morari M (2010) Optimized decision trees for point location in polytopic data sets-application to explicit mpc. Proc. Amer. Control Conf. (IEEE, New York), 5507–5512.Google Scholar
  • Garcia J, Fernández F (2015) A comprehensive survey on safe reinforcement learning. J. Machine Learn. Res. 16(1):1437–1480.Google Scholar
  • Geyer T, Torrisi FD, Morari M (2008) Optimal complexity reduction of polyhedral piecewise affine systems. Automatica J. IFAC 44(7):1728–1740.CrossrefGoogle Scholar
  • Good IJ (1953) The population frequencies of species and the estimation of population parameters. Biometrika 40(3-4):237–264.CrossrefGoogle Scholar
  • Grigg C, Wong P, Albrecht P, Allan R, Bhavaraju M, Billinton R, Chen Q, et al. (1999) The IEEE Reliability Test System-1996. A report prepared by the reliability test system task force of the application of probability methods subcommittee. IEEE Trans. Power Systems 14(3):1010–1020.CrossrefGoogle Scholar
  • Herceg M, Mariethoz S, Morari M (2013) Evaluation of piecewise affine control law via graph traversal. Proc. Eur. Control Conf. (IEEE, New York), 3083–3088.Google Scholar
  • Huang X, Kwiatkowska M, Wang S, Wu M (2017) Safety verification of deep neural networks. Proc. Internat. Conf. Computer Aided Verification (Springer, Berlin), 3–29.Google Scholar
  • IEEE PES Task Force (2017) PGLib optimal power flow benchmarks. Accessed October 4, 2017, https://github.com/power-grid-lib/pglib-opf.Google Scholar
  • Jafargholi M, Peyrl H, Zanarini A, Herceg M, Mariéthoz S (2014) Accelerating space traversal methods for explicit model predictive control via space partitioning trees. Proc. Eur. Control Conf. (IEEE, New York), 103–108.Google Scholar
  • Johansen TA, Grancharova A (2003) Approximate explicit constrained linear model predictive control via orthogonal search tree. IEEE Trans. Automated Control 48(5):810–815.CrossrefGoogle Scholar
  • Karg B, Lucia S (2020) Efficient representation and approximation of model predictive control laws via deep learning. IEEE Trans. Cybernetics 50(9):3866–3878.Google Scholar
  • Khalil EB, Dilkina B, Nemhauser GL, Ahmed S, Shao Y (2017) Learning to run heuristics in tree search. Proc. 26th Internat. Joint Conf. Artificial Intelligence (AAAI Press, Palo Alto, CA), 659–666.Google Scholar
  • Krarup J, Rørbech MN (2004) LP formulations of the shortest path tree problem. 4OR 2(4):259–274.CrossrefGoogle Scholar
  • Kruber M, Lübbecke ME, Parmentier A (2017) Learning when to use a decomposition. Proc. Internat. Conf. AI OR Techniques Constraint Programming Combin. Optim. Problems (Springer, Berlin), 202–210.Google Scholar
  • Lesieutre BC, Molzahn DK, Borden AR, DeMarco CL (2011) Examining the limits of the application of semidefinite programming to power flow problems. Proc. 49th Allerton Conf (IEEE, New York), 1492–1499.Google Scholar
  • Li F, Bo R (2010) Small test systems for power system economic studies. Proc. IEEE PES General Meeting (IEEE, New York), 1–4.Google Scholar
  • Lillicrap TP, Hunt JJ, Pritzel A, Heess N, Erez T, Tassa Y, Silver D, et al. (2019) Continuous control with deep reinforcement learning. Preprint, submitted July 5, https://arxiv.org/abs/1509.02971.Google Scholar
  • Lu T, Zinkevich M, Boutilier C, Roy B, Schuurmans D (2017) Safe exploration for identifying linear systems via robust optimization. Preprint, submitted November 30, https://arxiv.org/abs/1711.11165.Google Scholar
  • McAllester DA, Schapire RE (2000) On the convergence rate of Good-Turing estimators. Proc. 13th Annual Conf. Comput. Learn. Theory (Morgan Kaufmann Publishers Inc., San Francisco, CA), 1–6.Google Scholar
  • McDiarmid C (1989) On the method of bounded differences. Surveys in Combin., 1989: Invited Papers Twelfth British Combin. Conf. (Cambridge University Press, Cambridge, UK), 148–188.Google Scholar
  • Mnih V, Kavukcuoglu K, Silver D, Rusu AA, Veness J, Bellemare MG, Graves A, et al. (2015) Human-level control through deep reinforcement learning. Nature 518(7540):529.CrossrefGoogle Scholar
  • Moldovan TM, Abbeel P (2012) Safe exploration in markov decision processes. Proc. 29th Internat. Conf. Machine Learn. (Omnipress), 1451–1458.Google Scholar
  • Ng Y, Roald LA, Misra S (2020) Github repository for identifying optimal active constraints. Accessed August 5, 2020, https://github.com/yeesian/MLforOpt.Google Scholar
  • Ng Y, Misra S, Roald LA, Backhaus S (2018) Statistical learning for DC optimal power flow. Proc. Power Systems Comput. Conf. (IEEE, New York), 1–7.Google Scholar
  • Price JE, Goodin J (2011) Reduced network modeling of WECC as a market design prototype. Proc. IEEE PES General Meeting (IEEE, New York), 1–6.Google Scholar
  • Thomsen JR, Yiu ML, Jensen CS (2012) Effective caching of shortest paths for location-based services. Proc. ACM SIGMOD Internat. Conf. Management Data (ACM, New York), 313–324.Google Scholar
  • Tøndel P, Johansen TA, Bemporad A (2003) Evaluation of piecewise affine control via binary search tree. Automatica J. IFAC 39(5):945–950.CrossrefGoogle Scholar
  • Tsiakis P, Shah N, Pantelides CC (2001) Design of multi-echelon supply chain networks under demand uncertainty. Indust. Engrg. Chemistry Res. 40(16):3585–3604.CrossrefGoogle Scholar
  • Van Hasselt H, Guez A, Silver D (2016) Deep Reinforcement Learning with Double q-Learning, vol. 16 (AAAI, Palo Alto, CA).CrossrefGoogle Scholar
  • Zhang J, Xiu X (2018) Kd tree-based approach for point location problem in explicit model predictive control. J. Franklin Inst. 355(13):5431–5451.Google Scholar
  • Zhang J, Xiu X, Xie Z, Hu B (2016) Using a two-level structure to manage the point location problem in explicit model predictive control. Asian J. Control 18(3):1075–1086.CrossrefGoogle Scholar
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