American Journal of Mathematical and Computer Modelling

| Peer-Reviewed |

Identifying a Satisfactory Operation Point for Fuzzy Multiobjective Environmental/Economic Dispatch Problem

Received: 07 October 2016    Accepted: 19 October 2016    Published: 09 November 2016
Views:       Downloads:

Share This Article

Abstract

In this paper, reference point based neural network (NN) algorithm is proposed for solving fuzzy multiobjective environmental/economic dispatch problem (FM-EEDP). There are instabilities in the global market, implications of global financial crisis and the rapid fluctuations of prices, for this reasons a fuzzy representation of environmental/economic dispatch problem (EEDP) has been investigated. Our approach has two characteristic features. Firstly, FM-EEDP has been defuzzified. Secondly reference point based NN algorithm is implemented in such a way that the decision-maker (DM) participate early in the optimization process instead of leaving him/her alone with the final choice. The target is to identify the Pareto-optimal region closest to the DM preference so as to achieve the pollution limitations which controlled using environmental protection rules and to carry out the maximum cost limitation. Moreover to help the DM to identify the best compromise solution from a finite set of alternatives, TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) method is implemented. On the basis of the application of the standard IEEE 30-bus 6-genrator test system, we can conclude that the proposed method can provide a sound optimal power flow by considering the multiobjective problem. Also, with a number of trade-off solutions in the region of interests, we proved that the DM able to make a better and more reliable decision.

DOI 10.11648/j.ajmcm.20160101.11
Published in American Journal of Mathematical and Computer Modelling (Volume 1, Issue 1, November 2016)
Page(s) 1-14
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Previous article
Keywords

Environmental/Economic Dispatch Problem, Neural Network, Reference Point, Fuzzy Numbers, TOPSIS Method

References
[1] L. Alcorta, F. Nixson, The Global Financial Crisis and the Developing World: Impact on and Implications for the Manufacturing Sector, United nations: Industrial development organization, Vienna (2011) 1-51.
[2] A. A. Mousa, I. M. El_Desoky, Stability of Pareto optimal allocation of land reclamation by multistage decision-based multipheromone ant colony optimization, Swarm and Evolutionary Computation 13 (2013) 13–21.
[3] R. Bellman, L. Zadeh, Decision Making in a fuzzy environment, Management Science 17 (1970) 141-164.
[4] M. Sakwa, Fuzzy sets and Interactive Multiobjective Optimization, Plenum Press, New York (1993).
[5] S. F. Brodesky, R. W. Hahn, Assessing the influence of power pools on emission constrained economic dispatch, IEEE Trans. Power Syst. 1 (1) (1986) 57–62.
[6] A. Farag, S. Al-Baiyat, T. C. Cheng, Economic load dispatch multiobjective opti¬mization procedures using linear programming techniques, IEEE Trans. Power Syst. 10 (2) (1995) 731–738.
[7] C. S. Chang, K. P. Wong, B. Fan, Security-constrained multiobjective generation dispatch using bicriterion global optimization, IEE Proc. Gen. Transm. Distrib. 142 (4) (1995) 406–414.
[8] J. X. Xu, C. S. Chang, X. W. Wang, Constrained multiobjective global optimization of longitudinal interconnected power system by genetic algorithm, IEE Proc. Gen. Transm. Distrib. 143 (5) (1996) 435–446.
[9] J. Zahavi, L. Eisenberg, Economic–environmental power dispatch, IEEE Trans. Syst. Man Cybern. SMC 5 (5) (1985) 485–489.
[10] Y. T. Hsiao, H. D. Chiang, C. C. Liu, Y. L. Chen, A computer package for optimal multiobjective VAR planning in large scale power systems, IEEE Trans. Power Syst. 9 (2) (1994) 668–676.
[11] B. S. Kermanshahi, Y. Wu, K. Yasuda, R. Yokoyama, Environmental marginal cost evaluation by non-inferiority surface, IEEE Trans. Power Syst. 5 (4) (1990) 1151–1159.
[12] M. A. Abido, A novel multiobjective evolutionary algorithm for environmental/economic power dispatch, Electr. Power Syst. Res. 65 (2003) 71–81.
[13] M. A. Abido, Environmental/economic power dispatch using multiobjective evo¬lutionary algorithms, IEEE Trans. Power Syst. 18 (4) (2003) 1529–1537.
[14] A. A. Galal, A. A. Mousa, B. N. Al-Matrafi, Ant Colony Optimization Approach Based Genetic Algorithms for Multiobjective Optimal Power Flow Problem under Fuzziness, Applied Mathematics 4 (2013) 595-603, doi: 10.4236/am.2013.44084.
[15] M. Azzam and A. A. Mousa, Using genetic algorithm and topsis technique for multiobjective reactive power compensation, Electric Power Systems Research 80 (2010) 675–681.
[16] M. S. Osman, M. A. Abo-Sinna, and A. A. Mousa, IT-CEMOP: An Iterative Co-evolutionary Algorithm for Multiobjective Optimization Problem with Nonlinear Constraints, Journal of Applied Mathematics & Computation (AMC) 183 (2006) 373-389.
[17] M. R. Gent, J. W. Lamont, Minimum-Emission Dispatch, IEEE Transactions on Power Apparatus and Systems PAS-90 (6) (1971) 2650-2660.
[18] J. Nanda, D. P. Kothari, K. S. Lingamurthy, Economic-Emission Load Dispatch through Goal Programming Techniques, IEEE Transactions on Energy Conversion 3 (1) (1988) 26-32.
[19] J. S. Dhillon, S. C. Parti, D. P. Kothari, Multiobjective Optimal Thermal Power Dispatch. Electrical Power and Energy Systems, 16 (6) (1994) 383-389.
[20] M. A. Abido, A Niched Pareto Genetic Algorithm for Multiobjective Environmental/Economic Dispatch, Electrical Power and Energy Systems 25 (2) (2003) 97-105.
[21] R. T. F. Ah King, H. C. S. Rughooputh, Elitist Multiobjective Evolutionary Algorithm for Environmental/Economic Dispatch, IEEE Congress on Evolutionary Computation, Canberra, Australia 2 (2003) 1108-1114.
[22] M. A. El-Shorbagy, A. A. Mousa, S. M. Nasr, A chaos-based evolutionary algorithm for general nonlinear programming problems, Chaos, Solitons and Fractals 85 (2016) 8-21.
[23] X.-S. Yang, S. S. S. Hosseini, A. H. Gandomi, Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect, Applied Soft Computing 12 (2012) 1180–1186.
[24] L. Xie, S. Wang, Z. Wu, Study on Economic, Rapid and Environmental Power Dispatch Based on Fuzzy Multi-objective Optimization, Modern Applied Science 3 (6) (2009) 38-44.
[25] K. K. Vishwakarma, H. M. Dubey, M. Pandit and B. K. Panigrahi, Simulated Annealing Approach For Solving Economic Load Dispatch Problems With Valve Point Loading Effects, International Journal of Engineering, Science and Technology 4 (4) (2012) 60-72.
[26] C. Yaser, A pseudo spot price of electricity algorithm applied to environmental economic active power dispatch problem, Turk J Elec Eng & Comp Sci 20 (6) (2012) 990-1005.
[27] E. D. Manteaw, N. A. Odero, Multi-objective environmental/economic dispatch solution using ABC_PSO hybrid algoithm, International Journal of Scientific and Research Publications 2 (12) (2012) 1-7.
[28] A. A. Mousa, M. A. El-Shorbagy, W. F. Abd El-Wahed, Local search based hybrid particle swarm optimization for multiobjective optimization, International journal of Swarm and evolutionary computation 3 (2012) 1-14.
[29] A. A. Mousa, K. A. Kotb, Hybrid multiobjective evolutionary algorithm based technique for economic emission load dispatch optimization problem, Scientific Research and Essays 7 (25) (2012) 2242-2250.
[30] M. A. Gargeya, S. P. Pabba, Economic Load Dispatch Using Genetic Algorithm And Pattern Search Methods International Journal Of Advanced Research In Electrical, Electronics And Instrumentation Engineering 2 (4) (2013) 1203-1212.
[31] Hardiansyah, A Modified Particle Swarm Optimization Technique for Economic Load Dispatch with Valve-Point Effect, I. J. Intelligent Systems and Applications 7 (2013) 32-41.
[32] A. A. El-Sawy, Z. M. Hendawy, M. A. El-Shorbagy, Reference Point Based TR-PSO for Multi-Objective Environmental/Economic Dispatch, Applied Mathematics 4 (2013) 803-813.
[33] M. Pradhan, P. K. Roy b, T. Pal, Grey wolf optimization applied to economic load dispatch problems, Electrical Power and Energy Systems 83 (2016) 325–334.
[34] A. Y. Abdelaziz, E. S. Ali, S. M. Abd Elazim, Implementation of flower pollination algorithm for solving economic load dispatch and combined economic emission dispatch problems in power systems, Energy 101 (2016) 506e518.
[35] M. Basu, Kinetic gas molecule optimization for nonconvex economic dispatch problem, Electrical Power and Energy Systems 80 (2016) 325–332.
[36] M. Ghasemi, M. Taghizadeh, S. Ghavidel, A. Abbasian, Colonial competitive differential evolution: An experimental study for optimal economic load dispatch, Applied Soft Computing 40 (2016) 342–363.
[37] X. He, Y. Rao, J. Huang, A novel algorithm for economic load dispatch of power systems, Neurocomputing 171 (2016) 1454–1461.
[38] T. T. Nguyen, D. N. Vo, The application of one rank cuckoo search algorithm for solving economic load dispatch problems, Applied Soft Computing 37 (2015) 763–773.
[39] T. Sen, H. D. Mathur, A new approach to solve Economic Dispatch problem using a Hybrid ACO–ABC–HS optimization algorithm, Electrical Power and Energy Systems 78 (2016) 735–744.
[40] M. Ghasemi, J. Aghaei, E. Akbari, S. Ghavidel, L. Li, A differential evolution particle swarm optimizer for various types of multi-area economic dispatch problems, Energy 107 (2016) 182-195.
[41] Q. Liu, J. Wang, A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming, IEEE Transactions on Neural Networks 19 (2008) 558–570.
[42] Q. Liu, J. Wang, Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise linear objective functions, IEEE Transactions on Neural Networks 22 (2011) 601–613
[43] Y. Yang, J. Cao, X. Xu, J. Liu, A generalized neural network for solving a class of minimax optimization problems with linear constraints, Applied Mathematics and Computation 218 (2012) 7528–7537.
[44] R. Furtuna, S. Curteanu, and F. Leon, An elitist non-dominated sorting genetic algorithm enhanced with a neural network applied to the multi-objective optimization of a polysiloxane synthesis process, Engineering Applications of Artificial Intelligence 24 (2011) 772–785.
[45] E. N. Dragoi, S. Curteanu, A. Galaction, D. Cascaval, Optimization methodology based on neural networks and self-adaptive differential evolution algorithm applied to an aerobic fermentation process, Appl. Soft Comput. J. 13 (1) (2013) 222–238.
[46] X. Hu, Applications of the general projection neural network in solving extended linear-quadratic programming problems with linear constraints, Neuro computing 72 (2009) 1131–1137.
[47] B. S. Kermanshahi, Y. Wu, K. Yasuda, R. Yokoyama, Environmental marginal cost evaluation by non-inferiority surface, IEEE Trans. Power Syst. 5 (4) (1990) 1151-1159.
[48] A. P. Wierzbicki, The use of reference objectives in multiobjective optimization, Multiple Criteria Decision Making Theory and Applications, Berlin: Springer-Verlag 177 (1980) 468-486.
[49] K.-z. Chen, Y. Leung, K. S. Leung, X.-b. Gao, A Neural Network for Solving Nonlinear Programming Problem, Neural Computing & Applications 11 (2) (2002) 103-111.
[50] O. L. Mangasarian, nonlinear programming, McGraw-Hill Book Company, New York (1994).
[51] C. L. Hwang, K. Yoon, Multiple Attribute Decision Making: Methods and Applications, Springer-Verlag, New York, 1981.
[52] D. L. Olson, Comparison of weights in TOPSIS models, Math. Comput. Model. 40 (2004) 721–727.
[53] J. Carpentier, Contribution to the economic dispatch problem. Bulletin Society Francaise Electriciens 3 (8) (1962) 431–447.
[54] A. J. Wood, F. Bruce, Power generation operation and control. Wollenberg: John Wiley & Sons, Inc, 1984.
[55] R. Zimmerman, D. Gan, MATPOWER: A Matlab power system simulation package, Available: http://www.pserc.cornell.edu/matpower/.
Author Information
  • Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Koum, Egypt

  • Department of Mathematics and Statistics, Faculty of Sciences, Taif University, Taif, Saudi Arabia

Cite This Article
  • APA Style

    A. A. Mousa, M. A. El-Shorbagy. (2016). Identifying a Satisfactory Operation Point for Fuzzy Multiobjective Environmental/Economic Dispatch Problem. American Journal of Mathematical and Computer Modelling, 1(1), 1-14. https://doi.org/10.11648/j.ajmcm.20160101.11

    Copy | Download

    ACS Style

    A. A. Mousa; M. A. El-Shorbagy. Identifying a Satisfactory Operation Point for Fuzzy Multiobjective Environmental/Economic Dispatch Problem. Am. J. Math. Comput. Model. 2016, 1(1), 1-14. doi: 10.11648/j.ajmcm.20160101.11

    Copy | Download

    AMA Style

    A. A. Mousa, M. A. El-Shorbagy. Identifying a Satisfactory Operation Point for Fuzzy Multiobjective Environmental/Economic Dispatch Problem. Am J Math Comput Model. 2016;1(1):1-14. doi: 10.11648/j.ajmcm.20160101.11

    Copy | Download

  • @article{10.11648/j.ajmcm.20160101.11,
      author = {A. A. Mousa and M. A. El-Shorbagy},
      title = {Identifying a Satisfactory Operation Point for Fuzzy Multiobjective Environmental/Economic Dispatch Problem},
      journal = {American Journal of Mathematical and Computer Modelling},
      volume = {1},
      number = {1},
      pages = {1-14},
      doi = {10.11648/j.ajmcm.20160101.11},
      url = {https://doi.org/10.11648/j.ajmcm.20160101.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajmcm.20160101.11},
      abstract = {In this paper, reference point based neural network (NN) algorithm is proposed for solving fuzzy multiobjective environmental/economic dispatch problem (FM-EEDP). There are instabilities in the global market, implications of global financial crisis and the rapid fluctuations of prices, for this reasons a fuzzy representation of environmental/economic dispatch problem (EEDP) has been investigated. Our approach has two characteristic features. Firstly, FM-EEDP has been defuzzified. Secondly reference point based NN algorithm is implemented in such a way that the decision-maker (DM) participate early in the optimization process instead of leaving him/her alone with the final choice. The target is to identify the Pareto-optimal region closest to the DM preference so as to achieve the pollution limitations which controlled using environmental protection rules and to carry out the maximum cost limitation. Moreover to help the DM to identify the best compromise solution from a finite set of alternatives, TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) method is implemented. On the basis of the application of the standard IEEE 30-bus 6-genrator test system, we can conclude that the proposed method can provide a sound optimal power flow by considering the multiobjective problem. Also, with a number of trade-off solutions in the region of interests, we proved that the DM able to make a better and more reliable decision.},
     year = {2016}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Identifying a Satisfactory Operation Point for Fuzzy Multiobjective Environmental/Economic Dispatch Problem
    AU  - A. A. Mousa
    AU  - M. A. El-Shorbagy
    Y1  - 2016/11/09
    PY  - 2016
    N1  - https://doi.org/10.11648/j.ajmcm.20160101.11
    DO  - 10.11648/j.ajmcm.20160101.11
    T2  - American Journal of Mathematical and Computer Modelling
    JF  - American Journal of Mathematical and Computer Modelling
    JO  - American Journal of Mathematical and Computer Modelling
    SP  - 1
    EP  - 14
    PB  - Science Publishing Group
    SN  - 2578-8280
    UR  - https://doi.org/10.11648/j.ajmcm.20160101.11
    AB  - In this paper, reference point based neural network (NN) algorithm is proposed for solving fuzzy multiobjective environmental/economic dispatch problem (FM-EEDP). There are instabilities in the global market, implications of global financial crisis and the rapid fluctuations of prices, for this reasons a fuzzy representation of environmental/economic dispatch problem (EEDP) has been investigated. Our approach has two characteristic features. Firstly, FM-EEDP has been defuzzified. Secondly reference point based NN algorithm is implemented in such a way that the decision-maker (DM) participate early in the optimization process instead of leaving him/her alone with the final choice. The target is to identify the Pareto-optimal region closest to the DM preference so as to achieve the pollution limitations which controlled using environmental protection rules and to carry out the maximum cost limitation. Moreover to help the DM to identify the best compromise solution from a finite set of alternatives, TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) method is implemented. On the basis of the application of the standard IEEE 30-bus 6-genrator test system, we can conclude that the proposed method can provide a sound optimal power flow by considering the multiobjective problem. Also, with a number of trade-off solutions in the region of interests, we proved that the DM able to make a better and more reliable decision.
    VL  - 1
    IS  - 1
    ER  - 

    Copy | Download

  • Sections