Partitioning the Data Domain of Combinatorial Problems for Sequential Optimization
Christian Hinrichs, Joerg Bremer, Sönke Martens, Michael Sonnenschein
Citation: Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 8, pages 551–559 (2016)
Abstract. Following the long-term goal of substituting conventional power generation with cleaner energy will lead to an integration of a large share of small energy generation units imposing large problem sizes for coordination. The expected huge number of entities leads to a need for new techniques reducing the computational effort for coordination. Predictive scheduling is a frequent task in energy grid control. For a number of energy resources, schedules have to be found that fulfill several objectives at the same time. Considering day-ahead scenarios with 96-dimensional schedules imposes additional challenges to this already hard combinatorial problem. We explore the effects of reducing complexity by partitioning the data domain of the optimization problem for a sequential approach that integrates energy models for constraint handling directly into the optimization process. We explore the effects of different partitioning schemes and evaluate the trade-off between accuracy and effort with several simulation studies.
- P. Palensky and D. Dietrich, “Demand side management: Demand response, intelligent energy systems, and smart loads,” Industrial Informatics, IEEE Transactions on, vol. 7, no. 3, pp. 381–388, Aug 2011. http://dx.doi.org/10.1109/TII.2011.2158841.
- N. . P. F. Arteconi, A. ; Hewitt, “Domestic demand-side management (dsm): Role of heat pumps and thermal energy storage (tes) systems,” Applied Thermal Engineering, 2013, Vol.51(1-2), pp.155-165, vol. 51, no. 1-2, p. 155. http://dx.doi.org/10.1016/j.applthermaleng.2012.09.023.
- J. Bremer and M. Sonnenschein, “Model-based integration of constrained search spaces into distributed planning of active power provision,” Comput. Sci. Inf. Syst., vol. 10, no. 4, pp. 1823–1854, 2013. http://dx.doi.org/10.2298/CSIS130304073B.
- J. Bremer and M. Sonnenschein, “Constraint-handling for optimization with support vector surrogate models – A novel decoder approach,” in ICAART 2013 – Proceedings of the 5th International Conference on Agents and Artificial Intelligence, J. Filipe and A. Fred, Eds., vol. 2. Barcelona, Spain: SciTePress, 2013. http://dx.doi.org/10.5220/0004241100910100. ISBN 978-989-8565-38-9 pp. 91–100.
- J. Bremer, B. Rapp, and M. Sonnenschein, “Encoding distributed search spaces for virtual power plants,” in IEEE Symposium Series on Computational Intelligence 2011 (SSCI 2011), Paris, France, 4 2011. http://dx.doi.org/10.1109/CIASG.2011.5953329.
- S. McArthur, E. Davidson, V. Catterson, A. Dimeas, N. Hatziargyriou, F. Ponci, and T. Funabashi, “Multi-agent systems for power engineering applications—Part I: Concepts, approaches, and technical challenges,” IEEE Transactions on Power Systems, vol. 22, no. 4, pp. 1743–1752, 2007. http://dx.doi.org/10.1109/TPWRS.2007.908471.
- M. Sonnenschein, C. Hinrichs, A. Nieße, and U. Vogel, “Supporting renewable power supply through distributed coordination of energy resources,” in ICT Innovations for Sustainability, ser. Advances in Intelligent Systems and Computing, L. M. Hilty and B. Aebischer, Eds. Springer International Publishing, 2015, vol. 310, pp. 387–404. ISBN 978-3-319-09227-0. http://dx.doi.org/10.1007/978-3-319-09228-7_23
- A. Nieße, S. Beer, J. Bremer, C. Hinrichs, O. Lünsdorf, and M. Sonnenschein, “Conjoint dynamic aggregation and scheduling for dynamic virtual power plants,” in Federated Conference on Computer Science and Information Systems - FedCSIS 2014, Warsaw, Poland, M. Ganzha, L. A. Maciaszek, and M. Paprzycki, Eds., 9 2014. http://dx.doi.org/10.15439/2014F76.
- J. Bremer and M. Sonnenschein, “A distributed greedy algorithm for constraint-based scheduling of energy resources,” in FedCSIS, M. Ganzha, L. A. Maciaszek, and M. Paprzycki, Eds., 2012. ISBN 978-83-60810-51-4 pp. 1285–1292.
- C. A. Coello Coello, “Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 11-12, pp. 1245–1287, Jan. 2002. doi: 10.1016/S0045-7825(01)00323-1.
- S. Koziel and Z. Michalewicz, “Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization,” Evol. Comput., vol. 7, pp. 19–44, 03 1999. http://dx.doi.org/10.1162/evco.19184.108.40.206.
- J. Bremer and M. Sonnenschein, “Sampling the search space of energy resources for self-organized, agent-based planning of active power pro- vision,” in EnviroInfo, ser. Berichte aus der Umweltinformatik. Shaker, 2013, pp. 214–222.
- D. M. J. Tax and R. P. W. Duin, “Support vector data description,” Mach. Learn., vol. 54, no. 1, pp. 45–66, 2004. http://dx.doi.org/10.1023/B:MACH.0000008084.60811.49.
- V. K. Vassilev, T. C. Fogarty, and J. F. Miller, “Information characteristics and the structure of landscapes,” Evol. Comput., vol. 8, no. 1, pp. 31–60, Mar. 2000. http://dx.doi.org/10.1162/106365600568095.
- J. Bremer and M. Sonnenschein, “Parallel tempering for constrained many criteria optimization in dynamic virtual power plants,” in 2014 IEEE Symposium on Computational Intelligence Applications in Smart Grid, CIASG 2014, Orlando, FL, USA, December 9-12, 2014. IEEE, 2014. http://dx.doi.org/10.1109/CIASG.2014.7011551 pp. 51–58.
- S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, no. 4598, pp. 671–680, 1983. http://dx.doi.org/10.1126/science.220.4598.671.
- Y. Li, V. A. Protopopescu, N. Arnold, X. Zhang, and A. Gorin, “Hybrid parallel tempering and simulated annealing method,” Applied Mathematics and Computation, vol. 212, no. 1, pp. 216–228, 2009. http://dx.doi.org/10.1016/j.amc.2009.02.023.
- A. Müller, J. J. Schneider, and E. Schömer, “Packing a multidisperse system of hard disks in a circular environment,” Phys. Rev. E, vol. 79, p. 021102, Feb 2009. http://dx.doi.org/10.1103/PhysRevE.79.021102.
- N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” The Journal of Chemical Physics, vol. 21, no. 6, pp. 1087–1092, 1953. http://dx.doi.org/10.1063/1.1699114.
- W. K. Hastings, “Monte carlo sampling methods using markov chains and their applications,” Biometrika, vol. 57, no. 1, pp. 97–109, 1970. http://dx.doi.org/10.1093/biomet/57.1.97.
- W. H. Wong and F. Liang, “Dynamic weighting in Monte Carlo and optimization,” Applied Mathematics. Proceedings of the National Academic of Science, vol. 94, pp. 14 220–14 224, Dec. 1997.
- E. Marinari and G. Parisi, “Simulated tempering: a new Monte Carlo scheme,” Europhys. Lett., vol. 19, no. 6, 1992.
- S. Brown and T. Head-Gordon, “Cool walking: A new markov chain monte carlo sampling method.” Journal of Computational Chemistry, vol. 24, no. 1, pp. 68–76, 2003. http://dx.doi.org/10.1002/jcc.10181.
- D. L. Donoho, “High-dimensional data analysis: The curses and bless- ings of dimensionality. aide-memoire of a lecture at,” in AMS Conference on Math Challenges of the 21st Century, 2000.
- M. Verleysen and D. François, “The curse of dimensionality in data mining and time series prediction,” in Computational Intelligence and Bioinspired Systems, Lecture Notes in Computer Science 3512. Springer, 2005. http://dx.doi.org/10.1007/11494669_93 pp. 758–770.
- S. Shan and G. G. Wang, “Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions,” Structural and Multidisciplinary Optimization, vol. 41, no. 2, pp. 219–241, 2010. http://dx.doi.org/10.1007/s00158-009-0420-2.