Ant Colony Optimization Approach Based Genetic Algorithms for Multiobjective Optimal Power Flow Problem under Fuzziness

Affiliation(s)

Department of Mathematics and Statistics, Faculty of Sciences, Taif University, Taif, KSA.

Department of Mathematics and Statistics, Faculty of Sciences, Taif University, Taif, KSA.

ABSTRACT

In this paper, a new optimization system based genetic algorithm is presented. Our approach integrates the merits of both ant colony optimization and genetic algorithm and it has two characteristic features. Firstly, since there is instabilities in the global market, implications of global financial crisis and the rapid fluctuations of prices, a fuzzy representation of the optimal power flow problem has been defined, where the input data involve many parameters whose possible values may be assigned by the expert. Secondly, by enhancing ant colony optimization through genetic algorithm, a strong robustness and more effectively algorithm was created. Also, stable Pareto set of solutions has been detected, where in a practical sense only Pareto optimal solutions that are stable are of interest since there are always uncertainties associated with efficiency data. The results on the standard IEEE systems demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal nondominated solutions of the multiobjective OPF.

Cite this paper

A. Galal, A. Mousa and B. Al-Matrafi, "Ant Colony Optimization Approach Based Genetic Algorithms for Multiobjective Optimal Power Flow Problem under Fuzziness,"*Applied Mathematics*, Vol. 4 No. 4, 2013, pp. 595-603. doi: 10.4236/am.2013.44084.

A. Galal, A. Mousa and B. Al-Matrafi, "Ant Colony Optimization Approach Based Genetic Algorithms for Multiobjective Optimal Power Flow Problem under Fuzziness,"

References

[1] 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

[2] 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

[3] 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

[4] Y. J. Feng, L. Yu and G. L. Zhang, “Ant Colony Pattern Search Algorithms for Unconstrained and Bound Constrained Optimization,” Applied Mathematics and Computation, Vol. 191, No. 1, 2007, pp. 42-56. doi:10.1016/j.amc.2006.09.142

[5] B. Baran and M. Schaerer, “A Multiobjective Ant Colony System for Vehicle Routing Problem with Time Windows,” Proceedings of 21st IASTED International Conference on Applied Informatics, Innsbruck, 10-13 February 2003, pp. 97-102.

[6] 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

[7] A. A. Mousa, R. M. Rizk-Allah and W. F. Abd El-Wahed, “A Hybrid Ant Colony Optimization Approach Based Local Search Scheme for Multiobjective Design Optimizations,” Electric Power Systems Research, Vol. 81, No. 4, 2011, pp. 1014-1023. doi:10.1016/j.epsr.2010.12.005

[8] A. A. Mousa and K. A. Kotb, “Hybrid Multiobjective Evolutionary Algorithm Based Technique for Economic Emission Load Dispatch Optimization Problem,” Scientific Research and Essays, Vol. 7, No. 25, 2012, pp. 2242-2250. doi:10.5897/SRE11.197

[9] E. Zitzler and L. Thiele, “Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach,” IEEE Transactions on Evolutionary Computation, Vol. 3, No. 4, 1999, pp. 257-271.

[10] S. Goss, S. Aron, J. L. Deneubourg and J. M. Pasteels, “The Self-Organizing Exploratory Pattern of the Argentine Ant,” Journal of Insect Behavior, Vol. 3, No. 2, 1990, pp. 159-168. doi:10.1007/BF01417909

[11] B. Baran and M. Schaerer, “A Multiobjective Ant Colony System for Vehicle Routing Problem with Time Windows,” Proceedings of 21st IASTED International Conference on Applied Informatics, Innsbruck, 10-13 February 2003, pp. 97-102.

[12] G. Fuellerer, K. F. Doerner, R. F. Hartl and M. Iorib, “Ant Colony Optimization for the Two-Dimensional Loading Vehicle Routing Problem,” Computers & Operations Research, Vol. 36, No. 3, 2009, pp. 655-673. doi:10.1016/j.cor.2007.10.021

[13] M. Dorigo and T. Stützle, “Ant Colony Optimization,” MIT Press, Cambridge, 2004. doi:10.1007/b99492

[14] 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, Vol. 183, No. 1, 2006, pp. 373-389. doi:10.1016/j.amc.2006.05.095

[15] B. S. Kermanshahi, Y. Wu, K. Yasuda and R. Yokoyama, “Environmental Marginal Cost Evaluation by Non-Inferiority Surface,” IEEE Transaction on Power Systems, Vol. 5, No. 4, 1990, pp. 1151-1159. doi:10.1109/59.99365

[1] 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

[2] 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

[3] 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

[4] Y. J. Feng, L. Yu and G. L. Zhang, “Ant Colony Pattern Search Algorithms for Unconstrained and Bound Constrained Optimization,” Applied Mathematics and Computation, Vol. 191, No. 1, 2007, pp. 42-56. doi:10.1016/j.amc.2006.09.142

[5] B. Baran and M. Schaerer, “A Multiobjective Ant Colony System for Vehicle Routing Problem with Time Windows,” Proceedings of 21st IASTED International Conference on Applied Informatics, Innsbruck, 10-13 February 2003, pp. 97-102.

[6] 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

[7] A. A. Mousa, R. M. Rizk-Allah and W. F. Abd El-Wahed, “A Hybrid Ant Colony Optimization Approach Based Local Search Scheme for Multiobjective Design Optimizations,” Electric Power Systems Research, Vol. 81, No. 4, 2011, pp. 1014-1023. doi:10.1016/j.epsr.2010.12.005

[8] A. A. Mousa and K. A. Kotb, “Hybrid Multiobjective Evolutionary Algorithm Based Technique for Economic Emission Load Dispatch Optimization Problem,” Scientific Research and Essays, Vol. 7, No. 25, 2012, pp. 2242-2250. doi:10.5897/SRE11.197

[9] E. Zitzler and L. Thiele, “Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach,” IEEE Transactions on Evolutionary Computation, Vol. 3, No. 4, 1999, pp. 257-271.

[10] S. Goss, S. Aron, J. L. Deneubourg and J. M. Pasteels, “The Self-Organizing Exploratory Pattern of the Argentine Ant,” Journal of Insect Behavior, Vol. 3, No. 2, 1990, pp. 159-168. doi:10.1007/BF01417909

[11] B. Baran and M. Schaerer, “A Multiobjective Ant Colony System for Vehicle Routing Problem with Time Windows,” Proceedings of 21st IASTED International Conference on Applied Informatics, Innsbruck, 10-13 February 2003, pp. 97-102.

[12] G. Fuellerer, K. F. Doerner, R. F. Hartl and M. Iorib, “Ant Colony Optimization for the Two-Dimensional Loading Vehicle Routing Problem,” Computers & Operations Research, Vol. 36, No. 3, 2009, pp. 655-673. doi:10.1016/j.cor.2007.10.021

[13] M. Dorigo and T. Stützle, “Ant Colony Optimization,” MIT Press, Cambridge, 2004. doi:10.1007/b99492

[14] 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, Vol. 183, No. 1, 2006, pp. 373-389. doi:10.1016/j.amc.2006.05.095

[15] B. S. Kermanshahi, Y. Wu, K. Yasuda and R. Yokoyama, “Environmental Marginal Cost Evaluation by Non-Inferiority Surface,” IEEE Transaction on Power Systems, Vol. 5, No. 4, 1990, pp. 1151-1159. doi:10.1109/59.99365