Improving the computational efficiency of stochastic programs using automated algorithm configuration: an application to decentralized energy systems

  • Hannes SchwarzEmail author
  • Lars Kotthoff
  • Holger Hoos
  • Wolf Fichtner
  • Valentin Bertsch
S.I.: Stochastic Modeling and Optimization, in memory of András Prékopa


The optimization of decentralized energy systems is an important practical problem that can be modeled using stochastic programs and solved via their large-scale, deterministic-equivalent formulations. Unfortunately, using this approach, even when leveraging a high degree of parallelism on large high-performance computing systems, finding close-to-optimal solutions still requires substantial computational effort. In this work, we present a procedure to reduce this computational effort substantially, using a state-of-the-art automated algorithm configuration method. We apply this procedure to a well-known example of a residential quarter with photovoltaic systems and storage units, modeled as a two-stage stochastic mixed-integer linear program. We demonstrate that the computing time and costs can be substantially reduced by up to 50% by use of our procedure. Our methodology can be applied to other, similarly-modeled energy systems.


OR in energy Large-scale optimization Stochastic programming Uncertainty modeling Automated algorithm configuration Sequential model-based algorithm configuration 



The authors would like to gratefully acknowledge the funding provided by the Helmholtz Association of German Research Centers via the Research Programme “Storage and Cross-Linked Infrastructures”. In addition, the authors also acknowledge support by the state of Baden-Württemberg through bwHPC and the German Research Foundation (DFG) through Grant No. INST 35/1134-1 FUGG, as well as through an NSERC Discovery Grant. We also acknowledge the use of Compute Canada/Calcul Canada computing resources. Valentin Bertsch acknowledges funding from the ESRI’s Energy Policy Research Centre. All omissions and errors are our own.


  1. Altmann, M., Brenninkmeijer, A., Lanoix, J.-C., Ellison, D., Crisan, A., & Hugyecz, A., et al. (2010). Decentralized energy systems. Technical report European Parliament’s Committee (ITRE). Accessed 29 Sept 2016.
  2. Andriosopoulos, K., Zopounidis, C., & Doumpos, M. (2016). Editorial to the special issue “OR in energy modeling and management”. Computers & Operations Research, 66, 225–227. Scholar
  3. Ansótegui, C., Sellmann, M., & Tierney, K. (2009). A gender-based genetic algorithm for the automatic configuration of algorithms. In D. Hutchison, T. Kanade, J. Kittler, J. M. Kleinberg, F. Mattern, J. C. Mitchell, et al. (Eds.), Principles and practice of constraint programming—CP 2009 (Vol. 5732, pp. 142–157)., Lecture Notes in Computer Science Berlin: Springer.CrossRefGoogle Scholar
  4. Atamtürk, A., & Savelsbergh, M. W. P. (2005). Integer-programming software systems. Annals of Operations Research, 140, 67–124. Scholar
  5. Avdoulas, C., Bekiros, S., & Boubaker, S. (2018). Evolutionary-based return forecasting with nonlinear STAR models: Evidence from the Eurozone peripheral stock markets. Annals of Operations Research, 262, 307–333. Scholar
  6. Ben-Ayed, O., Blair, C. E., Boyce, D. E., & LeBlanc, L. J. (1992). Construction of a real-world bilevel linear programming model of the highway network design problem. Annals of Operations Research, 34, 219–254. Scholar
  7. Beraldi, P., Conforti, D., & Violi, A. (2008). A two-stage stochastic programming model for electric energy producers. Computers & Operations Research, 35, 3360–3370. Scholar
  8. Bergstra, J. S., Bardenet, R., Bengio, Y., & Kégl, B. (2011). Algorithms for hyper-parameter optimization. In J. Shawe-Taylor, R. S. Zemel, P. L. Bartlett, F. Pereira, & K. Q. Weinberger (Eds.), Advances in neural information processing systems (Vol. 24, pp. 2546–2554). Red Hook: Curran Associates Inc.Google Scholar
  9. Dantzig, G. B. (1955). Linear programming under uncertainty. Management Science, 1, 197–206.CrossRefGoogle Scholar
  10. Fawcett, C., & Hoos, H. H. (2016). Analysing differences between algorithm configurations through ablation. Journal of Heuristics, 22, 431–458. Scholar
  11. Fragnière, E., Gondzio, J., & Vial, J.-P. (2000). Building and solving large-scale stochastic programs on an affordable distributed computing system. Annals of Operations Research, 99, 167–187. Scholar
  12. Hutter, F., Babic, D., Hoos, H. H., & Hu, A. J. (2007). Boosting verification by automatic tuning of decision procedures. In Austin, TX, USA (pp. 27–34).
  13. Hutter, F., Hoos, H. H., & Leyton-Brown, K. (2010). Automated configuration of mixed integer programming solvers. In D. Hutchison, T. Kanade, J. Kittler, J. M. Kleinberg, F. Mattern, J. C. Mitchell, et al. (Eds.), Integration of AI and OR techniques in constraint programming for combinatorial optimization problems (Vol. 6140, pp. 186–202)., Lecture Notes in Computer Science Berlin: Springer.CrossRefGoogle Scholar
  14. Hutter, F., Hoos, H. H., & Leyton-Brown, K. (2011). Sequential model-based optimization for general algorithm configuration. In D. Hutchison, T. Kanade, J. Kittler, J. M. Kleinberg, F. Mattern, J. C. Mitchell, et al. (Eds.), Learning and intelligent optimization (Vol. 6683, pp. 507–523)., Lecture Notes in Computer Science Berlin: Springer.CrossRefGoogle Scholar
  15. Hutter, F., Hoos, H. H., Leyton-Brown, K., & Stützle, T. (2009). ParamILS: An automatic algorithm configuration framework. Journal of Artificial Intelligence Research, 36, 267–306. Scholar
  16. IBM. (2016). ILOG CPLEX optimization studio: CPLEX user’s manual, version 12 release 6. Accessed 3 June 2016.
  17. Jones, D. R., Schonlau, M., & Welch, W. J. (1998). Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13, 455–492. Scholar
  18. Khalilpourazari, S., & Arshadi Khamseh, A. (2017). Bi-objective emergency blood supply chain network design in earthquake considering earthquake magnitude: A comprehensive study with real world application. Annals of Operations Research, 52, 168. Scholar
  19. Kobayakawa, T., & Kandpal, T. C. (2016). Optimal resource integration in a decentralized renewable energy system: Assessment of the existing system and simulation for its expansion. Energy for Sustainable Development, 34, 20–29. Scholar
  20. Kuznia, L., Zeng, B., Centeno, G., & Miao, Z. (2013). Stochastic optimization for power system configuration with renewable energy in remote areas. Annals of Operations Research, 210, 411–432. Scholar
  21. Mascia, F., López-Ibáñez, M., Dubois-Lacoste, J., & Stützle, T. (2014). Grammar-based generation of stochastic local search heuristics through automatic algorithm configuration tools. Computers & Operations Research, 51, 190–199. Scholar
  22. Owens, B. (2014). The rise of distributed power. General electric (ecomagination). Accessed 30 Sept 2016.
  23. Pintér, J. D. (2017). How difficult is nonlinear optimization? A practical solver tuning approach, with illustrative results. Annals of Operations Research, 31, 635. Scholar
  24. Prékopa, A. (1995). Stochastic programming. Dordrecht: Springer.CrossRefGoogle Scholar
  25. Prékopa, A., Ganzer, S., Deák, I., & Patyi, K. (1980). The STABIL stochastic programming model and its experimental application to the electrical energy Sector of the Hungarian economy. In M. A. H. Dempster (Ed.), stochastic programming. London: Academic Press.Google Scholar
  26. Schwarz, H., Bertsch, V., & Fichtner, W. (2018a). Two-stage stochastic, large-scale optimization of a decentralized energy system: A case study focusing on solar PV, heat pumps and storage in a residential quarter. OR Spectrum, 40, 265–310. Scholar
  27. Schwarz, H., Schermeyer, H., Bertsch, V., & Fichtner, W. (2018b). Self-consumption through power-to-heat and storage for enhanced PV integration in decentralised energy systems. Solar Energy, 163, 150–161. Scholar
  28. Shapiro, A., Dentcheva, D., & Ruszczynski, A. P. (2009). Lectures on stochastic programming: modeling and theory (MPS-SIAM series on optimization) (Vol. 9). Philadelphia, PA: SIAM.CrossRefGoogle Scholar
  29. Snoek, J., Larochelle, H., & Adams, R. P. (2012). Practical Bayesian optimization of machine learning algorithms. In F. Pereira, C. J. C. Burges, L. Bottou, & K. Q. Weinberger (Eds.), Advances in neural information processing systems (Vol. 25, pp. 2951–2959). Red Hook: Curran Associates Inc.Google Scholar
  30. Taborda, D., & Zdravkovic, L. (2012). Application of a hill-climbing technique to the formulation of a new cyclic nonlinear elastic constitutive model. Computers and Geotechnics, 43, 80–91. Scholar
  31. Talbi, E.-G. (2016). Combining metaheuristics with mathematical programming, constraint programming and machine learning. Annals of Operations Research, 240, 171–215. Scholar
  32. Velik, R., & Nicolay, P. (2016). Energy management in storage-augmented, grid-connected prosumer buildings and neighborhoods using a modified simulated annealing optimization. Computers & Operations Research, 66, 248–257. Scholar
  33. Wallace, S. W., & Fleten, S.-E. (2003). Stochastic programming models in energy. In Stochastic programming (Vol. 10, pp. 637–677, Handbooks in Operations research and management science). Amsterdam: Elsevier.Google Scholar
  34. Wolfe, P. (2008). The implications of an increasingly decentralised energy system. Energy Policy, 36, 4509–4513. Scholar
  35. Yazdanie, M., Densing, M., & Wokaun, A. (2016). The role of decentralized generation and storage technologies in future energy systems planning for a rural agglomeration in Switzerland. Energy Policy, 96, 432–445. Scholar
  36. Zokaee, S., Jabbarzadeh, A., Fahimnia, B., & Sadjadi, S. J. (2017). Robust supply chain network design: An optimization model with real world application. Annals of Operations Research, 257, 15–44. Scholar

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Authors and Affiliations

  1. 1.Chair of Energy Economics, Institute for Industrial Production (IIP)Karlsruhe Institute of Technology (KIT)KarlsruheGermany
  2. 2.Department of Computer ScienceUniversity of WyomingLaramieUSA
  3. 3.Leiden Institute of Advanced Computer Science (LIACS)Universiteit LeidenLeidenThe Netherlands
  4. 4.Department of Computer ScienceUniversity of British Columbia (UBC)VancouverCanada
  5. 5.Economic and Social Research Institute (ESRI)DublinIreland
  6. 6.Department of Economics, Trinity College DublinDublinIreland
  7. 7.Department of Energy Systems Analysis, German Aerospace Center (DLR)StuttgartGermany
  8. 8.University of StuttgartStuttgartGermany

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