Abstract
While measuring forecasting accuracy has been intensively studied by researchers, the consideration of sets of non-dominated solutions has not yet been explored in the literature. Even when considering measures that are in harmony, small changes in model parameters can result in a trained system capable of forecasting different time series characteristics. In this regard, this study shows how a set of non-dominated forecasting models can assist decision makers to pick the most suitable model for operations on dynamic environments. In particular, the system presents an interesting trade-off provided with assistance of a new strategic measure, which forces the forecasting model to learn the highest values of the time series. An automatic self-adaptive forecasting framework, calibrated with Multi-Objective VND inspired techniques, and able to perform k-steps-ahead forecasting, is considered. There is a growing demand for learning big-data time series, such as those derived from sensors in energy mini/microgrid systems, in which real-time decisions should be made quickly and can vary according to the available energy resources. Thus, a case of study is considered using data from disaggregated power readings of a typical microgrid due to the fact that load demand forecasting, with different components of a house, is of crucial importance for management and operation of new emerging decentralized systems.
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Notes
A search was conducted on different global reference databases such as Web of Science, SCOPUS and IEEEXplore looking up for publications until October, 2020.
Creating Pareto Fronts is a straightforward way to store models that present non-dominated characteristics [29].
HFM code is currently available at https://github.com/vncoelho/HFM.
OptFrame [9, 10] code is currently available at https://github.com/optframe/optframe.
The code can be currently accessed at https://github.com/vncoelho/HFM, commit version with hash fbc2cd3657ad0519235280cd511f582914d8557b.
References
Adhikari, R.: A neural network based linear ensemble framework for time series forecasting. Neurocomputing 157, 231–242 (2015). https://doi.org/10.1016/j.neucom.2015.01.012
Armel, K.C., Gupta, A., Shrimali, G., Albert, A.: Is disaggregation the holy grail of energy efficiency? the case of electricity. Energy policy 52, 213–234 (2013). https://doi.org/10.1016/j.enpol.2012.08.062. Special section: transition pathways to a low carbon economy
Aslam, S., Khalid, A., Javaid, N.: Towards efficient energy management in smart grids considering microgrids with day-ahead energy forecasting. Electr. Power Syst. Res. 182, 106232 (2020)
Bukhari, A.H., Raja, M.A.Z., Sulaiman, M., Islam, S., Shoaib, M., Kumam, P.: Fractional neuro-sequential arfima-lstm for financial market forecasting. IEEE Access 8, 71326–71338 (2020)
Cagnano, A., De Tuglie, E., Mancarella, P.: Microgrids: overview and guidelines for practical implementations and operation. Appl. Energy 258, 114039 (2020)
Cascio, M.L.L., Pesamosca, G.: Learning with zero error in feedforward neural networks. In: Marinaro, M., Morasso, P.G. (eds.) ICANN ’94, pp. 619–622. Springer, London, London (1994)
Coelho, B.N., Coelho, V.N., Coelho, I.M., Ochi, L.S., Haghnazar, R., Zuidema, D., da Costa, A.R.: A multi-objective green UAV routing problem. Comput. Oper. Res. 88, 306–315 (2017)
Coelho, I.M., Coelho, V.N., Luz, E.J.D.S., Ochi, L.S., Guimaraes, F.G., Rios, E.: A GPU deep learning metaheuristic based model for time series forecasting. Appl. Energy 201, 412–418 (2017)
Coelho, I.M., Coelho, V.N., Zudio, A., Araújo, R., Haddad, M.N., Munhoz, P.L.A., Maia, B.S.M., Ochi, L.S., Souza, M.J.F.: Microbenchmark studies in optframe: a 10-year anniversary. In: LII Simpósio Brasileiro de Pesquisa Operacional, pp. 1 – 12. João Pessoa, PB (2020)
Coelho, I.M., Ribas, S., Perche, M.H.P., Munhoz, P.L.A., Souza, M.F., Ochi, L.S.: Optframe: a computational framework for combinatorial optimization problems. In: XLII Simpósio Brasileiro de Pesquisa Operacional, pp. 1887 – 1898. Bento Gonçalves, RS (2010)
Coelho, V., Coelho, I., Coelho, B., Souza, M., Guimarães, F., da S. Luz, E., Barbosa, A., Coelho, M., Netto, G., Costa, R., Pinto, A., de P. Figueiredo, A., Elias, M., Filho, D., Oliveira, T.: EEG time series learning and classification using a hybrid forecasting model calibrated with GVNS. Electronic notes in discrete mathematics 58, 79 – 86 (2017). https://doi.org/10.1016/j.endm.2017.03.011. 4th International conference on variable neighborhood search
Coelho, V.N., Coelho, I.M., Coelho, B.N., Reis, A.J.R., Enayatifar, R., Souza, M.J.F., Guimarães, F.G.: A self-adaptive evolutionary fuzzy model for load forecasting problems on smart grid environment. Appl. Energy 169, 567–584 (2016). https://doi.org/10.1016/j.apenergy.2016.02.045
Coelho, V.N., Coelho, I.M., Meneghini, I.R., Souza, M.J.F., Guimaraes, F.G.: An automatic calibration framework applied on a metaheuristic fuzzy model for the cif competition. In: 2016 International joint conference on neural networks (IJCNN), pp. 1507–1514 (2016). https://doi.org/10.1109/IJCNN.2016.7727377
Coelho, V.N., Coelho, I.M., Souza, M.J.F., Oliveira, T.A., Cota, L.P., Haddad, M.N., Mladenovic, N., Silva, R.C.P., Guimarães, F.G.: Hybrid self-adaptive evolution strategies guided by neighborhood structures for combinatorial optimization problems. Evol. Comput. 24(4), 637–666 (2016). https://doi.org/10.1162/EVCO_a_00187
Coelho, V.N., Oliveira, T.A., Coelho, I.M., Coelho, B.N., Fleming, P.J., Guimarães, F.G., Ramalhinho, H., Souza, M.J., Talbi, E.G., Lust, T.: Generic pareto local search metaheuristic for optimization of targeted offers in a bi-objective direct marketing campaign. Comput. Oper. Res. 78, 578–587 (2017). https://doi.org/10.1016/j.cor.2016.09.008
Dai, Z., Dong, X., & Kang, J., Lianying, H.: Forecasting stock market returns: new technical indicators and two-step economic constraint method. North Am J Econ Financ 53, 101216. https://doi.org/10.1016/j.najef.2020.101216
Derbentsev, V., Matviychuk, A., Soloviev, V.N.: Forecasting of cryptocurrency prices using machine learning. In: Advanced Studies of Financial Technologies and Cryptocurrency Markets, pp. 211–231. Springer (2020)
Dubois, D., Prade, H.: A review of fuzzy set aggregation connectives. Inf. Sci. 36(1–2), 85–121 (1985)
Faloutsos, C., Flunkert, V., Gasthaus, J., Januschowski, T., Wang, Y.: Forecasting big time series: Theory and practice. In: Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 3209–3210 (2019)
Glover, F.W., Kochenberger, G.A.: Handbook of Metaheuristics, vol. 57. Springer, Berlin (2006)
Hamilton, J.D.: Time series analysis, vol. 2. Princeton University Press, Princeton (1994)
Hansen, P., Mladenovic, N., Pérez, J.A.M.: Variable neighborhood search: methods and applications. 4OR Quart J. Belg. Fr. Ital. Oper. Res. Soc. 6, 319–360 (2008)
Hong, T., Wilson, J., Xie, J.: Long term probabilistic load forecasting and normalization with hourly information. Smart Grid IEEE Trans. 5(1), 456–462 (2014)
Hyndman, R.J., Koehler, A.B.: Another look at measures of forecast accuracy. Int. J. Forecast. 22(4), 679–688 (2006). https://doi.org/10.1016/j.ijforecast.2006.03.001
Jeong, G., Park, S., Hwang, G.: Time series forecasting based day-ahead energy trading in microgrids: mathematical analysis and simulation. IEEE Access 8, 63885–63900 (2020)
Kolter, J.Z., Johnson, M.J.: Redd: A public data set for energy disaggregation research. In: Workshop on Data Mining Applications in Sustainability (SIGKDD), San Diego, CA (2011)
Koochaksaraei, R.H., Meneghini, I.R., Coelho, V.N., Guimarães, F.G.: A new visualization method in many-objective optimization with chord diagram and angular mapping. Knowledge-Based Syst. 138(Supplement C), 134–154 (2017). https://doi.org/10.1016/j.knosys.2017.09.035
Livieris, I.E., Pintelas, E., Stavroyiannis, S., Pintelas, P.: Ensemble deep learning models for forecasting cryptocurrency time-series. Algorithms 13(5), 121 (2020)
Lust, T., Teghem, J.: Two-phase pareto local search for the biobjective traveling salesman problem. J. Heuristics 16, 475–510 (2010)
Meneghini, I.R., Koochaksaraei, R.H., Guimarães, F.G., Gaspar-Cunha, A.: Information to the eye of the beholder: Data visualization for many-objective optimization. In: 2018 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8 (2018). https://doi.org/10.1109/CEC.2018.8477889
Mladenovic, N., Hansen, P.: A variable neighborhood search. Comput. Oper. Res. 24, 1097–1100 (1997)
Nethercote, N., Seward, J.: Valgrind: a program supervision framework. Elect. Notes Theor. Comput. Sci. 89(2), 44–66 (2003)
Oliveira, T.A., Gabrich, Y.B., Ramalhinho, H., Oliver, M., W Cohen, M., S Ochi, L., Gueye, S., Protti, F., A Pinto, A., VM Ferreira, D., et al.: Mobility, citizens, innovation and technology in digital and smart cities. Future Internet 12(2), 22 (2020)
Oliveira, T.A., Oliver, M., Ramalhinho, H.: Challenges for connecting citizens and smart cities: Ict, e-governance and blockchain. Sustainability 12(7), 2926 (2020)
Qiu, X., Suganthan, P.N., Amaratunga, G.A.: Ensemble incremental learning random vector functional link network for short-term electric load forecasting. Knowledge-Based Syst. 145, 182–196 (2018)
Refaeilzadeh, P., Tang, L., Liu, H.: Cross-validation. In: Encyclopedia of database systems, pp. 532–538. Springer (2009)
Rios, E., Ochi, L.S., Boeres, C., Coelho, V.N., Coelho, I.M., Farias, R.: Exploring parallel multi-gpu local search strategies in a metaheuristic framework. J. Parallel Distrib. Comput. 111, 39–55 (2018)
Rodríguez, F., Florez-Tapia, A.M., Fontán, L., Galarza, A.: Very short-term wind power density forecasting through artificial neural networks for microgrid control. Renew. Energy 145, 1517–1527 (2020)
Schürholz, D., Kubler, S., Zaslavsky, A.: Artificial intelligence-enabled context-aware air quality prediction for smart cities. J. Cleaner Prod. p. 121941 (2020)
Stanojević, B., Glover, F.: A new approach to generate pattern-efficient sets of non-dominated vectors for multi-objective optimization. Inf. Sci. (2020)
Sun, M., Feng, C., Zhang, J.: Multi-distribution ensemble probabilistic wind power forecasting. Renew. Energy 148, 135–149 (2020)
Veit, A., Goebel, C., Tidke, R., Doblander, C., Jacobsen, H.A.: Household electricity demand forecasting: benchmarking state-of-the-art methods. In: Proceedings of the 5th International Conference on Future Energy Systems, e-Energy ’14, pp. 233–234. ACM, New York, NY, USA (2014). https://doi.org/10.1145/2602044.2602082
Villalón, A., Rivera, M., Salgueiro, Y., Muñoz, J., Dragičević, T., Blaabjerg, F.: Predictive control for microgrid applications: a review study. Energies 13(10), 2454 (2020)
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Coelho, V.N., Koochaksaraei, R.H. Non-dominated solutions for time series learning and forecasting. Optim Lett 16, 395–408 (2022). https://doi.org/10.1007/s11590-021-01720-5
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DOI: https://doi.org/10.1007/s11590-021-01720-5