A Hybrid Optimization Technique Coupling an Evolutionary and a Local Search Algorithm for Economic Emission Load Dispatch Problem
ABSTRACT
This paper presents an optimization technique coupling two optimization techniques for solving Economic Emission Load Dispatch Optimization Problem EELD. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS), where it maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ε-dominance. To improve the solution quality, local search technique was applied as neighborhood search engine, where it intends to explore the less-crowded area in the current archive to possibly obtain more non-dominated solutions. TOPSIS technique can incorporate relative weights of criterion importance, which has been implemented to identify best compromise solution, which will satisfy the different goals to some extent. Several optimization runs of the proposed approach are carried out on the standard IEEE 30-bus 6-genrator test system. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.
This paper presents an optimization technique coupling two optimization techniques for solving Economic Emission Load Dispatch Optimization Problem EELD. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS), where it maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ε-dominance. To improve the solution quality, local search technique was applied as neighborhood search engine, where it intends to explore the less-crowded area in the current archive to possibly obtain more non-dominated solutions. TOPSIS technique can incorporate relative weights of criterion importance, which has been implemented to identify best compromise solution, which will satisfy the different goals to some extent. Several optimization runs of the proposed approach are carried out on the standard IEEE 30-bus 6-genrator test system. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.
KEYWORDS
Economic Emission Load Dispatch, Evolutionary Algorithms, Multiobjective Optimization, Local Search
Economic Emission Load Dispatch, Evolutionary Algorithms, Multiobjective Optimization, Local Search
Cite this paper
nullA. Mousa and K. Kotb, "A Hybrid Optimization Technique Coupling an Evolutionary and a Local Search Algorithm for Economic Emission Load Dispatch Problem," Applied Mathematics, Vol. 2 No. 7, 2011, pp. 890-898. doi: 10.4236/am.2011.27119.
nullA. Mousa and K. Kotb, "A Hybrid Optimization Technique Coupling an Evolutionary and a Local Search Algorithm for Economic Emission Load Dispatch Problem," Applied Mathematics, Vol. 2 No. 7, 2011, pp. 890-898. doi: 10.4236/am.2011.27119.
References
[1] S. F. Brodesky and R. W. Hahn, “Assessing the Influence of Power Pools on Emission Constrained Economic Dispatch,” IEEE Transactions on Power Systems, Vol. 1, No. 1, 1986, pp. 57-62. doi:10.1109/TPWRS.1986.4334844 [2] G. P. Granelli, M. Montagna, G. L. Pasini and P. Marannino, “Emission Constrained Dynamic Dispatch,” Electric Power Systems Research, Vol. 24, 1992, pp. 56-64. doi:10.1016/0378-7796(92)90045-3 [3] A. Farag, S. Al-Baiyat and T. C. Cheng, “Economic Load Dispatch Multiobjective Optimization Procedures Using Linear Programming Techniques,” IEEE Transactions on Power Systems, Vol. 10, No. 2, 1995, pp. 731-738. doi:10.1109/59.387910 [4] C. S. Chang, K. P. Wong and B. Fan, “Security-Cons-trained Multiobjective Generation Dispatch Using Bicriterion Global Optimization,” IEE Proceedings Generation, Transmission & Distribution, Vol. 142, No. 4, 1995, pp. 406-414. doi:10.1049/ip-gtd:19951806 [5] J. S. Dhillon, S. C. Parti and D. P. Kothari, “Stochastic Economic Emission Load Dispatch,” Electric Power System Research, Vol. 26, 1993, pp. 179-186. doi:10.1016/0378-7796(93)90011-3 [6] J. X. Xu, C. S. Chang and X. W. Wang, “Constrained Multiobjective Global Optimization of Longitudinal Interconnected Power System by Genetic Algorithm,” IEE Proceedings Generation, Transmission & Distribution, Vol. 143, No. 5, 1996, pp. 435-446. doi:10.1049/ip-gtd:19960418 [7] J. Zahavi and L. Eisenberg, “Economic-Environmental Power Dispatch,” IEEE Transactions on Systems, Man, and Cybernetics, Vol. 5, No. 5, 1985, pp. 485-489. doi:10.1109/TSMC.1975.5408370 [8] Y. T. Hsiao, H. D. Chiang, C. C. Liu and Y. L. Chen, “A Computer Package for Optimal Multi-Objective VAR Planning in Large Scale Power Systems,” IEEE Transactions on Power Systems, Vol. 9, No. 2, 1994, pp. 668-676. doi:10.1109/59.317676 [9] R. Yokoyama, S. H. Bae, T. Morita and H. Sasaki, “Multiobjective Generation Dispatch Based on Probability Security Criteria,” IEEE Transactions on Power Systems, Vol. 3, No. 1, 1988, pp. 317-324. doi:10.1109/59.43217 [10] B. S. Kermanshahi, Y. Wu, K. Yasuda and R. Yokoyama, “Environmental Marginal Cost Evaluation by Non-Inferiority Surface,” IEEE Transactions on Power Systems, Vol. 5, No. 4, 1990, pp. 1151-1159. doi:10.1109/59.99365 [11] M. Azzam and A. A. Mousa, “Using Genetic Algorithm and Topsis Technique for Multiobjective Reactive Power Compensation,” Electric Power Systems Research, Vol. 80, No. 6, 2010, pp. 675-681. doi:10.1016/j.epsr.2009.10.033 [12] M. S. Osman, M. A. Abo-Sinna and A. A. Mousa, “A Solution to the Optimal Power Flow Using Genetic Algorithm,” Mathematics & Computation, Vol. 155, No. 2, 2004, pp. 391-405. [13] M. S. Osman, M. A. Abo-Sinna and A. A. Mousa, “Epsilon-Dominance Based Multiobjective Genetic Algorithm for Economic Emission Load Dispatch Optimization Problem,” Electric Power Systems Research, Vol. 79, No. 11, 2009, pp. 1561-1567. doi:10.1016/j.epsr.2009.06.003 [14] M. A. Abido, “A Novel Multiobjective Evolutionary Algorithm for Environmental/Economic Power Dispatch,” Electric Power Systems Research, Vol. 65, No. 1, 2003, pp. 71-81. doi:10.1016/S0378-7796(02)00221-3 [15] M. A. Abido, “A Niched Pareto Genetic Algorithm for Multiobjective Environmental/Economic Dispatch,” Electrical Power and Energy Systems, Vol. 25, No. 2, 2003, pp. 97-105. doi:10.1016/S0142-0615(02)00027-3 [16] M. A. Abido, “Environmental/Economic Power Dispatch using Multiobjective Evolutionary Algorithms,” IEEE Transactions on Power Systems, Vol. 18, No. 4, 2003, pp. 1529-1537. doi:10.1109/TPWRS.2003.818693 [17] K. Deb, “Multi-Objective Optimization Using Evolutionary Algorithms,” Wiley, New York, 2001. [18] C. M .Fonseca and P. J. Fleming, “An Overview of Evolutionary Algorithms in Multiobjective Optimization,” Evolutionary Computation, Vol. 3, No. 1, 1995, pp. 1-16. doi:10.1162/evco.1995.3.1.1 [19] D. L. Olson, “Comparison of Weights in TOPSIS Models,” Mathematical and Computer Modelling, Vol. 40, No. 7-8, 2004, pp. 721-727. doi:10.1016/j.mcm.2004.10.003 [20] M. Laumanns, L. Thiele, K. Deb and E. Zitzler, “Archiving with Guaranteed Convergence and Diversity in Multi-Objective Optimization,” GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, Morgan Kaufmann Publishers, New York, July 2002, pp. 439-447. [21] D. Hazarika and P. K. Bordoloi, “Modified Loss Coefficients in the Determination of Optimum Generation Scheduling,” IEE Proceedings, Vol. 138, No. 2, 1991, pp. 166-172 [22] W. Y. Ng, “Generalized Generation Distribution Factors for Power System Security Evaluations,” IEEE Transactions on Power Apparatus and Systems, Vol. 100, 1981, pp. 1001-1005. doi:10.1109/TPAS.1981.316635 [23] A. A. Mousa, R. M. Rizk-Allah and W. F. A. El-Wahed, “A Hybrid Ant Colony Optimization Approach Based Local Search Scheme Formultiobjective Design Optimizations,” Electric Power Systems Research, Vol. 81, No. 4, 2011, pp. 1014-1023. doi:10.1016/j.epsr.2010.12.005 [24] R. Hooke and T. A. Jeeves, “Direct Search Solution of Numerical and Statistical Problems,” Journal of the ACM, Vol. 8, No. 2, 1961, pp. 212-229. doi:10.1145/321062.321069
[1] S. F. Brodesky and R. W. Hahn, “Assessing the Influence of Power Pools on Emission Constrained Economic Dispatch,” IEEE Transactions on Power Systems, Vol. 1, No. 1, 1986, pp. 57-62. doi:10.1109/TPWRS.1986.4334844 [2] G. P. Granelli, M. Montagna, G. L. Pasini and P. Marannino, “Emission Constrained Dynamic Dispatch,” Electric Power Systems Research, Vol. 24, 1992, pp. 56-64. doi:10.1016/0378-7796(92)90045-3 [3] A. Farag, S. Al-Baiyat and T. C. Cheng, “Economic Load Dispatch Multiobjective Optimization Procedures Using Linear Programming Techniques,” IEEE Transactions on Power Systems, Vol. 10, No. 2, 1995, pp. 731-738. doi:10.1109/59.387910 [4] C. S. Chang, K. P. Wong and B. Fan, “Security-Cons-trained Multiobjective Generation Dispatch Using Bicriterion Global Optimization,” IEE Proceedings Generation, Transmission & Distribution, Vol. 142, No. 4, 1995, pp. 406-414. doi:10.1049/ip-gtd:19951806 [5] J. S. Dhillon, S. C. Parti and D. P. Kothari, “Stochastic Economic Emission Load Dispatch,” Electric Power System Research, Vol. 26, 1993, pp. 179-186. doi:10.1016/0378-7796(93)90011-3 [6] J. X. Xu, C. S. Chang and X. W. Wang, “Constrained Multiobjective Global Optimization of Longitudinal Interconnected Power System by Genetic Algorithm,” IEE Proceedings Generation, Transmission & Distribution, Vol. 143, No. 5, 1996, pp. 435-446. doi:10.1049/ip-gtd:19960418 [7] J. Zahavi and L. Eisenberg, “Economic-Environmental Power Dispatch,” IEEE Transactions on Systems, Man, and Cybernetics, Vol. 5, No. 5, 1985, pp. 485-489. doi:10.1109/TSMC.1975.5408370 [8] Y. T. Hsiao, H. D. Chiang, C. C. Liu and Y. L. Chen, “A Computer Package for Optimal Multi-Objective VAR Planning in Large Scale Power Systems,” IEEE Transactions on Power Systems, Vol. 9, No. 2, 1994, pp. 668-676. doi:10.1109/59.317676 [9] R. Yokoyama, S. H. Bae, T. Morita and H. Sasaki, “Multiobjective Generation Dispatch Based on Probability Security Criteria,” IEEE Transactions on Power Systems, Vol. 3, No. 1, 1988, pp. 317-324. doi:10.1109/59.43217 [10] B. S. Kermanshahi, Y. Wu, K. Yasuda and R. Yokoyama, “Environmental Marginal Cost Evaluation by Non-Inferiority Surface,” IEEE Transactions on Power Systems, Vol. 5, No. 4, 1990, pp. 1151-1159. doi:10.1109/59.99365 [11] M. Azzam and A. A. Mousa, “Using Genetic Algorithm and Topsis Technique for Multiobjective Reactive Power Compensation,” Electric Power Systems Research, Vol. 80, No. 6, 2010, pp. 675-681. doi:10.1016/j.epsr.2009.10.033 [12] M. S. Osman, M. A. Abo-Sinna and A. A. Mousa, “A Solution to the Optimal Power Flow Using Genetic Algorithm,” Mathematics & Computation, Vol. 155, No. 2, 2004, pp. 391-405. [13] M. S. Osman, M. A. Abo-Sinna and A. A. Mousa, “Epsilon-Dominance Based Multiobjective Genetic Algorithm for Economic Emission Load Dispatch Optimization Problem,” Electric Power Systems Research, Vol. 79, No. 11, 2009, pp. 1561-1567. doi:10.1016/j.epsr.2009.06.003 [14] M. A. Abido, “A Novel Multiobjective Evolutionary Algorithm for Environmental/Economic Power Dispatch,” Electric Power Systems Research, Vol. 65, No. 1, 2003, pp. 71-81. doi:10.1016/S0378-7796(02)00221-3 [15] M. A. Abido, “A Niched Pareto Genetic Algorithm for Multiobjective Environmental/Economic Dispatch,” Electrical Power and Energy Systems, Vol. 25, No. 2, 2003, pp. 97-105. doi:10.1016/S0142-0615(02)00027-3 [16] M. A. Abido, “Environmental/Economic Power Dispatch using Multiobjective Evolutionary Algorithms,” IEEE Transactions on Power Systems, Vol. 18, No. 4, 2003, pp. 1529-1537. doi:10.1109/TPWRS.2003.818693 [17] K. Deb, “Multi-Objective Optimization Using Evolutionary Algorithms,” Wiley, New York, 2001. [18] C. M .Fonseca and P. J. Fleming, “An Overview of Evolutionary Algorithms in Multiobjective Optimization,” Evolutionary Computation, Vol. 3, No. 1, 1995, pp. 1-16. doi:10.1162/evco.1995.3.1.1 [19] D. L. Olson, “Comparison of Weights in TOPSIS Models,” Mathematical and Computer Modelling, Vol. 40, No. 7-8, 2004, pp. 721-727. doi:10.1016/j.mcm.2004.10.003 [20] M. Laumanns, L. Thiele, K. Deb and E. Zitzler, “Archiving with Guaranteed Convergence and Diversity in Multi-Objective Optimization,” GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, Morgan Kaufmann Publishers, New York, July 2002, pp. 439-447. [21] D. Hazarika and P. K. Bordoloi, “Modified Loss Coefficients in the Determination of Optimum Generation Scheduling,” IEE Proceedings, Vol. 138, No. 2, 1991, pp. 166-172 [22] W. Y. Ng, “Generalized Generation Distribution Factors for Power System Security Evaluations,” IEEE Transactions on Power Apparatus and Systems, Vol. 100, 1981, pp. 1001-1005. doi:10.1109/TPAS.1981.316635 [23] A. A. Mousa, R. M. Rizk-Allah and W. F. A. El-Wahed, “A Hybrid Ant Colony Optimization Approach Based Local Search Scheme Formultiobjective Design Optimizations,” Electric Power Systems Research, Vol. 81, No. 4, 2011, pp. 1014-1023. doi:10.1016/j.epsr.2010.12.005 [24] R. Hooke and T. A. Jeeves, “Direct Search Solution of Numerical and Statistical Problems,” Journal of the ACM, Vol. 8, No. 2, 1961, pp. 212-229. doi:10.1145/321062.321069