Binary-Real Coded Genetic Algorithm Based *k*-Means Clustering for Unit Commitment Problem

Author(s)
Mai A. Farag^{1},
M. A. El-Shorbagy^{1},
I. M. El-Desoky^{1},
A. A. El-Sawy^{1,2},
A. A. Mousa^{1,3}

Affiliation(s)

^{1}
Department of Basic Engineering Science, Faculty of Engineering, Menoufiya University, Al Minufya, Egypt.

^{2}
Department of Mathematics, Faculty of Science, Qassim University, Qassim, Saudi Arabia.

^{3}
Department of Mathematics, Faculty of Sciences, Taif University, Taif, Saudi Arabia.

ABSTRACT

This paper presents a new algorithm for solving unit commitment (UC) problems using a binary-real coded genetic algorithm based on*k*-means clustering technique. UC is a NP-hard nonlinear mixed-integer optimization problem, encountered as one of the toughest problems in power systems, in which some power generating units are to be scheduled in such a way that the forecasted demand is met at minimum production cost over a time horizon. In the proposed algorithm, the algorithm integrates the main features of a binary-real coded genetic algorithm (GA) and *k*-means clustering technique. The binary coded GA is used to obtain a feasible commitment schedule for each generating unit; while the power amounts generated by committed units are determined by using real coded GA for the feasible commitment obtained in each interval. *k*-means clustering algorithm divides population into a specific number of subpopulations with dynamic size. In this way, using *k*-means clustering algorithm allows the use of different GA operators with the whole population and avoids the local problem minima. The effectiveness of the proposed technique is validated on a test power system available in the literature. The proposed algorithm performance is found quite satisfactory in comparison with the previously reported results.

This paper presents a new algorithm for solving unit commitment (UC) problems using a binary-real coded genetic algorithm based on

Cite this paper

Farag, M. , El-Shorbagy, M. , El-Desoky, I. , El-Sawy, A. and Mousa, A. (2015) Binary-Real Coded Genetic Algorithm Based*k*-Means Clustering for Unit Commitment Problem. *Applied Mathematics*, **6**, 1873-1890. doi: 10.4236/am.2015.611165.

Farag, M. , El-Shorbagy, M. , El-Desoky, I. , El-Sawy, A. and Mousa, A. (2015) Binary-Real Coded Genetic Algorithm Based

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http://dx.doi.org/10.1080/15325000902762331

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http://dx.doi.org/10.1109/TPWRS.2003.821611

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http://dx.doi.org/10.1016/j.epsr.2005.07.002

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http://dx.doi.org/10.1016/j.enconman.2008.12.003

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[1] Wood, A.J. and Wollenberg, B.F. (1996) Power Generation, Operation and Control. John Wiley & Sons, New York.

[2] Guan, X.H., Luh, P.B., Yan, H. and Amalfi, J.A. (1992) An Optimization-Based Method for Unit Commitment. International Journal of Electrical Power & Energy Systems, 14, 9-17.

http://dx.doi.org/10.1016/0142-0615(92)90003-R

[3] Jeong, Y.W., Park, J.B., Shin, J.R. and Lee, K.Y. (2009) A Thermal Unit Commitment Approach Using an Improved Quantum Evolutionary Algorithm. Electric Power Components and Systems, 37, 770-786.

http://dx.doi.org/10.1080/15325000902762331

[4] Padhy, N.P. (2004) Unit Commitment—A Bibliographical Survey. IEEE Transactions on Power Systems, 19, 1196-1205.

http://dx.doi.org/10.1109/TPWRS.2003.821611

[5] Senjyu, T., Miyagi, T., Saber, A.Y., Urasaki, N. and Funabashi, T. (2006) Emerging Solution of Large-Scale Unitcommitment Problem by Stochastic Priority List. Electrical Power and Energy Systems, 76, 283-292.

http://dx.doi.org/10.1016/j.epsr.2005.07.002

[6] Rong, A., Hakonen, H. and Lahdelma, R. (2009) A Dynamic Regrouping Based Sequential Dynamic Programming Algorithm for Unit Commitment of Combined Heat and Power Systems. Energy Conversion and Management, 50, 1108-1115.

http://dx.doi.org/10.1016/j.enconman.2008.12.003

[7] Chen, C.L. and Wang, S.C. (1993) Branch-and-Bound Scheduling for Thermal Generating Units. IEEE Transactions on Energy Conversion, 8, 184-189.

[8] Singhal, P.K. (2011) Generation Scheduling Methodology for Thermal Units Using Lagrangian Relaxation. Proceedings of the 2nd IEEE International Conference on Current Trends in Technology, 1-6.

[9] Frangioni, A., Gentile, C. and Lacalandra, F. (2009) Tighter Approximated MILP Formulations for Unit Commitment Problems. IEEE Transactions on Power Systems, 24, 105-113.

http://dx.doi.org/10.1109/TPWRS.2008.2004744

[10] Sheble, G.B. and Fahd, G.N. (1993) Unit Commitment Literature Synopsis. IEEE Transactions on Power Systems, 9, 128-135.

http://dx.doi.org/10.1109/59.317549

[11] Swarup, K. and Simi, P. (2006) Neural Computation Using Discrete and Continuous Hopfield Networks for Power System Economic Dispatch and Unit Commitment. Neurocomputing, 70, 119-129.

http://dx.doi.org/10.1016/j.neucom.2006.05.002

[12] Kazarlis, S.A., Bakirtzis, A.G. and Petridis, V. (1996) A Genetic Algorithm Solution to the Unit Commitment Problem. IEEE Transactions on Power Systems, 11, 1129-1136.

[13] Arroyo, J.M. and Conejo, A.J. (2002) A Parallel Repair Genetic Algorithm to Solve the Unit Commitment Problem. IEEE Electrical Power Energy Systems, 17, 1216-1224.

http://dx.doi.org/10.1109/tpwrs.2002.804953

[14] Dang, C. and Li, M. (2007) A Floating-Point Genetic Algorithm for Solving the Unit Commitment Problem. European Journal of Operational Research, 181, 1370-1395.

http://dx.doi.org/10.1016/j.ejor.2005.10.071

[15] Sundararajan, D., Subramanian, B., Subramanian, K. and Krishnan, M. (2013) Generation Scheduling Problem by Intelligent Genetic Algorithm. Computers and Electrical Engineering, 39, 79-88.

[16] Datta, D. (2013) Unit Commitment Problem with Ramp Rate Constraint Using a Binary-Real-Coded Genetic Algorithm. Applied Soft Computing, 13, 3873-3883.

[17] Juste, K.A., Kita, H., Tanaka, E. and Hasegawa, J. (1999) An Evolutionary Programming Solution to the Unit Commitment Problem. IEEE Transactions on Power Systems, 14, 1452-1459.

http://dx.doi.org/10.1109/59.801925

[18] Simopoulos, N., Kavatza, S. and Vournas, C. (2006) Unit Commitment by an Enhanced Simulated Annealing Algorithm. IEEE Transactions on Power Systems, 21, 68-76.

http://dx.doi.org/10.1109/TPWRS.2005.860922

[19] Mantawy, A.H., Abdel-Magid, Y.L. and Selim, S.Z. (1999) Integrating Genetic Algorithms, Tabu Search, and Simulated Annealing for the Unit Commitment Problem. IEEE Transactions on Power Systems, 14, 829-836.

http://dx.doi.org/10.1109/59.780892

[20] Ebrahimi, J., Hosseinian, S.H. and Gharehpetian, G.B. (2011) Unit Commitment Problem Solution Using Shuffled Frog Leaping Algorithm. IEEE Transactions on Power Systems, 26, 573-581.

[21] Logenthiran, T. and Srinivasan, D. (2010) Particle Swarm Optimization for Unit Commitment Problem. Proceedings of the IEEE International Conference on Probabilistic Methods Applied to Power Systems, Singapore, 14-17 June 2010, 642-647.

http://dx.doi.org/10.1109/PMAPS.2010.5528899

[22] Mantawy, A.H., Abdel-Magid, Y.L. and Selim, S.Z. (1998) Unit Commitment by Tabu Search. IEE Proceedings— Generation, Transmission and Distribution, 145, 56-64.

http://dx.doi.org/10.1049/ip-gtd:19981681

[23] El-Saadawi, M.M., Tantawi, M.A. and Tawfik, E. (2004) A Fuzzy Optimization-Based Approach to Large Scale Thermal Unit Commitment. Electric Power Systems Research, 72, 245-252.

http://dx.doi.org/10.1016/j.epsr.2004.04.009

[24] Pourjamal, Y. and Ravadanegh, S.N. (2013) HSA Based Solution to the UC Problem. International Journal of Electrical Power & Energy Systems, 46, 211-220.

http://dx.doi.org/10.1016/j.ijepes.2012.10.042

[25] Chandrasekaran, K., Hemamalini, S., Simon, S.P. and Padhy, N.P. (2012) Thermal Unit Commitment Using Binary/ Real Coded Artificial Bee Colony Algorithm. Electric Power Systems Research, 84, 109-119.

[26] Mousa, A.A., El-Shorbagy, M.A. and Abd El-Wahed, W.F. (2012) Local Search Based Hybrid Particle Swarm Optimization for Multiobjective Optimization. International Journal of Swarm and Evolutionary Computation, 3, 1-14.

[27] Farag, M.A., El-Shorbagy, M.A., El-Desoky, I.M., El-Sawy, A.A. and Mousa, A.A. (2015) Genetic Algorithm Based on K-Means-Clustering Technique for Multi-Objective Resource Allocation Problems. British Journal of Applied Science & Technology, 8, 80-96.

http://dx.doi.org/10.9734/BJAST/2015/16570

[28] El-Shorbagy, M.A., Mousa, A.A. and Abd-El-Wahed, W.F. (2011) Hybrid Particle Swarm Optimization Algorithm for Multi-Objective Optimization. Lambert Academic Publishing GmbH & Co. KG, Berlin.

[29] El-Shorbagy, M.A., El-Sawy, A.A. and Hendawy, Z.M. (2013) Numerical Optimization & Swarm Intelligence for Optimization: Trust Region Algorithm & Particle Swarm Optimization. Lambert Academic Publishing GmbH & Co. KG, Berlin.

[30] Mousa, A.A. and El-Desoky, I.M. (2008) GENLS: Co-Evolutionary Algorithm for Nonlinear System of Equations. Applied Mathematics and Computation, 197, 633-642.

[31] Mousa, A.A. and El-Desoky, I.M. (2013) Stability of Pareto Optimal Allocation of Land Reclamation by Multistage Decision-Based Multipheromone Ant Colony Optimization. Swarm and Evolutionary Computation, 13, 13-21

[32] Abd El-Wahed, W.F., Mousa, A.A. and El-Shorbagy, M.A. (2011) Integrating Particle Swarm Optimization with Genetic Algorithms for Solving Nonlinear Optimization Problems. Journal of Computational and Applied Mathematics, 235, 1446-1453.

[33] Mousa, A.A. and El-Shorbagy, M.A. (2012) Enhanced Particle Swarm Optimization Based Local Search for Reactive Power Compensation Problem. Applied Mathematics, 3, 1276-1284.

http://dx.doi.org/10.4236/am.2012.330184

[34] Michalewiz, Z. (1996) Genetic Algorithms + Data Structures = Evolution Programs. Third Edition, Springer-Verlag, New York.

[35] Verma, M., Srivastava, M., Chack, N., Diswar, A.K. and Gupta, N. (2012) A Comparative Study of Various Clustering Algorithms in Data Mining. International Journal of Engineering Research and Applications (IJERA), 2, 1379-1384.

[36] Levine, S., Pilowski, I. and Boulton, D.M. (1969) The Classification of Depression by Numerical Taxonomy. The British Journal of Psychiatry, 115, 937-945.

http://dx.doi.org/10.1192/bjp.115.525.937

[37] Dolnicar, S. (2003) Using Cluster Analysis for Market Segmentation-Typical Misconceptions, Established Methodological Weaknesses and Some Recommendations for Improvement. Australasian Journal of Market Research, 11, 5-12.

[38] Hodson, F.R. (1971) Numerical Typology and Prehistoric Archaeology. In: Hodson, F.R., Kendall, D.G. and Tautu, P.A., Eds., Mathematics in the Archaeological and Historical Sciences, University Press, Edinburgh.

[39] Pratima, D., Nimmakanti, N. and Recognition, P. (2011) Algorithms for Cluster Identification Problem. Special Issue of International Journal of Computer Science & Informatics (IJCSI), 2, 2231-5292.

[40] Doreswamy and Hemanth, K.S. (2012) Similarity Based Cluster Analysis on Engineering Materials Data Sets. Advances in Intelligent Systems and Computing, 167, 161-168.

[41] Dilts, D., Khamalah, J. and Plotkin, A. (1995) Using Cluster Analysis for Medical Resource Decision Making. Cluster Analysis for Resource Decisions, 15, 333-347.

[42] Aggarwal, C.C. and Reddy, C.K. (2014) Data Clustering Algorithms and Applications. CRC Press, New York.

[43] MacQueen, J.B. (1967) Some Methods for Classification and Analysis of Multivariate Observation. In: Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, 281-297.

[44] Priya, R.P., Sivaraj, N. and Muruganandam, M. (2015) A Solution to Unit Commitment Problem with V2G Using Harmony Search Algorithm. International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, 4, 1208-1214.

[45] Goldberg, D.E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning. Addison Wesley, Reading.

[46] Grefenstette, J.J. (1986) Optimization of Control Parameters for Genetic Algorithms. IEEE Transactions on Systems, Man and Cybernetics, 16, 122-128.

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