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AUTHOR(S): 

Sudhir G. Akojwar, Pravin R. Kshirsagar

 

TITLE

Performance Evolution of Optimization Techniques for Mathematical Benchmark Functions

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ABSTRACT

This paper demonstrates several optimization techniques which comprise Genetic algorithm (GA), Ant Colony optimization (ACO) and Particle swarm optimization (PSO). The proposed paper enforces the concept of artificial intelligence to detect minima / maxima by applying set of mathematical benchmark functions. For Optimization technique, artificial intelligence used which comprise of several algorithms like Particle swarm optimization, genetic algorithm, ant colony optimization, neural network and fuzzy system. The proposed work will use particle swarm intelligence and genetic intelligence. This paper bestows comparison between PSO and GA according to performance. In random search algorithm, GA cannot detect the global optimization solution. The benchmark functions used under these algorithms are Rosenbrock, Griewank, Ackley and Sphere. They have multiple local minima / maxima and single global minima / maxima. Neural network has propensity to strikes at local minima / maxima. Result demonstrates that discomfort of neural network is thoroughly segregated by particle swarm intelligence and genetic algorithm.

KEYWORDS

Particle swarm optimization, Ant colony optimization, Genetic Algorithm, Artificial Intelligence, Evolutionary Algorithms

REFERENCES

[1] Russell Eberhart and James Kennedy, A New Optimizer Using Particle Swarm Theory, 6th international symposium on Micro Machine and Human Science, IEEE, 1995.

[2] Kennedy, I., Eberhart, R., Particle Swarm Optimization, Proc. IEEE International Conference on Neural Networks (Perth, Australia), IEEE Service Center, Piscataway, NJ, Iv: 1942- 1948, I995.

[3] Shi, Y., Eberhart, R., Parameter Selection in Particle Swarm Optimization, Proceedings of the 7th Annual Conference on Evolutionary Programming, pp. 591-601, 1998.

[4] R.C. Eberhart and Y. Shi. Comparing inertia weights and constriction factors in particle swarm optimization. Proceedings of the 2000 Congress on Evolutionary Computation, 1:84 - 88, 2000.

[5] M. Clerc and J. Kennedy. The particle swarm stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6:58 - 73, 2002.

[6] S. Ujjin and P. J. Bentley, Particle Swarm Optimization Recommender System, IEEE Swarm Intelligence Symposium, 2003, 24-26 April 2003, pp. 124-131.

[7] Valdez, F. and Melin P. Parallel Evolutionary Computing using a cluster for Mathematical Function Optimization, Nafips. San Diego CA, USA, 598-602. June 2007.

[8] K. F. Man, K. S. Tang, and S. Kwong, Genetic algorithms: Concepts and applications, IEEE transactions on industrial electronics, vol. 43, no. 5, October 1996.

[9] Dongshu yan, jintao zhang, bo Yuma, Genetic algorithm for finding minimal multihomogeneous bezout number, 7th IEEE/ACIS international conference on computer and information science.

[10] H. Wright, Genetic algorithms for real parameter optimization, Foundations of Genetic Algorithms, J. E. Rawlins, Ed. San Mateo, CA: Morgan Kaufmdnn, 1991, pp. 205-218.

[11] John A. Miller, Walter D. Potter, Ravi V. Gandham and Chinto N. Lapena, An evaluation of local improvement operators for genetic algorithms, IEEE transaction on systems, man and cybernetics, vol. 23. No. 5 Sept. /Oct. 1993.

[12] Zhiyong li, Wei Zhou, Bo Xu, Kenli li, An ant colony genetic algorithm based on pheromone diffusion, 4th international conference on natural computation, 2008 IEEE.

[13] Thomas Stutzle and Holger H. Hoos, Min-Max Ant System, Future generation computer systems, Elsevier, 2000.

[14] Van den Bergh, Particle Swarm Weight Initialization in Multi-Layer Perceptron Artificial Neural Networks, Accepted for ICAI. Durban, South Africa, 1999, pp. 41-45.

[15] R. Mendes, P. Cone, M. Rocha, Particle swarm for feed forward neural network training, Proc. International Joint Conference on Neural Networks, pp. 1895-1899.2002.

[16] Goldberg D. E. Genetic algorithms in search optimization, and machine learning. AddisonWesley, 1989.

[17] Handbook of Genetic Algorithms. New York: Van Nostrand Reinhold, 1991.

[18] Ant colony optimization, Marco Dorigo and Thomas Stutzle, A Bradford Book, The MIT Press, Cambridge, Massachusetts, London, England.

[19] Ant colony optimization, Artificial ants as a computational Intelligence techniques, Marco Dorigo, Mauro Birattari, and Thomas Stutzle, Universite Libre de Bruxelles, Belgium.

[20] Li Ting Wu Li, An Enhanced Parallel Back propagation Learning Algorithm for Multilayer Perceptron, Proceedings of the 7th World Congress on Intelligent Control and Automation, June 25 - 27, 2008, Chongqing, China.

[21] En Hui Zheng, Min Yang, Tuning of Neural networks based on Genetic Algorithm and statistical learning theory, 3rd international conference on machine learning and cybernetics, Shanghai, 26-29 August, 2004.

[22] Nikolay Y. Nikolaev and Hitoshi Iba, Learning polynomial feed forward neural networks by genetic programming and back propagation.

[23] Bin Gao, Jing-Hua Zhu and Wen-chang Lang A Novel Hybrid Optimization Algorithm Based on GA and ACO for Solving Complex Problem, International Journal of Multimedia and Ubiquitous Engineering, Vol.10, No.8 (2015), pp.243-252

[24] Radha Thangaraj, Millie Pant, Ajith Abraham, Pascal Bouvry, Particle swarm optimization: Hybridization perspectives and experimental illustrations, Elsevier, 2010, pp 1-19

[25] Rania Hassan, Babak Cohanim, Olivier de Weck, A Comparison of particle swarm optimization and the genetic algorithm, American Institute of Aeronautics and Astronautics, pp 1 – 13

[26] V. Saishanmuga Raja, S.P. Rajagopalan A Comparative analysis of optimization techniques for artificial neural network in biomedical applications, Journal of Computer Science 10 (1): 106-114, 2014 ISSN: 1549- 3636, 2014 Science Publications, pp. 106 -119

[27] Mohd Nadhir Ab Wahab, Samia Nefti-Meziani, Adham Atyab, A Comprehensive Review of Swarm Optimization Algorithms, PLOS ONE DOI:10.1371/journal.pone.0122827 May 18, 2015, pp. 1-36,

[28] V.Selvi , Dr.R.Umarani, Comparative Analysis of Ant Colony and Particle Swarm Optimization Techniques, International Journal of Computer Applications (0975 – 8887), Volume 5– No.4, August 2010, pp. 1-6

[29] Ginnu George, Kumudha Raimond, A Survey on Optimization Algorithms for Optimizing the Numerical Functions, International Journal of Computer Applications (0975 – 8887) Volume 61– No.6, January 2013, pp. 41-46

[30] Riccardo Poli, An Analysis of Publications on Particle Swarm Optimisation Applications, University of Essex, UK, Technical Report CSM-469, ISSN: 1744-8050, May 2007, pp. 1- 57

Cite this paper

Sudhir G. Akojwar, Pravin R. Kshirsagar. (2016) Performance Evolution of Optimization Techniques for Mathematical Benchmark Functions. International Journal of Computers, 1, 231-236

 

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