Main Article Content
Abstract
The Non-Linear Programming Problems (NLPP) are computationally hard to solve as compared to the Linear Programming Problems (LPP). To solve NLPP, the available methods are Lagrangian Multipliers, Sub gradient method, Karush-Kuhn-Tucker conditions, Penalty and Barrier method etc. In this paper, we are applying Barrier method to convert the NLPP with equality constraint to an NLPP without constraint. We use the improved version of famous Particle Swarm Optimization (PSO) method to obtain the solution of NLPP without constraint. SCILAB programming language is used to evaluate the solution on sample problems. The results of sample problems are compared on Improved PSO and general PSO.
Keywords
Non-Linear Programming Problem
Barrier Method
Particle Swarm Optimization
, Equality and Inequality Constraints
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How to Cite
Prajapati, R., Dubey, O. P., & Kumar, R. (2017). IMPROVED PARTICLE SWARM OPTIMIZATION FOR NON-LINEAR PROGRAMMING PROBLEM WITH BARRIER METHOD. International Journal of Students’ Research in Technology & Management, 5(4), 72–80. https://doi.org/10.18510/ijsrtm.2017.5410
References
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[1] Eberhart, R.C. and Kennedy, J., 1995, December. Particle swarm optimization. Proc. IEEE International Conf. on Neural Networks (Perth, Australia), IEEE service centre, Piscataway, NJ, vol.4,pp. 1942 – 1948.
[2] Eberhart, R.C. and Kennedy, J., 1995, October. A new optimizer using particle swarm theory. In Proceedings of the sixth international symposium on micro machine and human science, Vol.1, pp39-43.
[3] Melgani, F. and Bazi, Y., 2008. Classification of electrocardiogram signals with support vector machines and particle swarm optimization. Information Technology in Biomedicine, IEEE Transactions on, 12(5), pp.667-677.
[4] [Abido, M.A., 2002. Optimal design of power-system stabilizers using particle swarm optimization. Energy Conversion, IEEE Transactions on, 17(3), pp.406-413.
[5] Omran, M., Salman, A. and Engelbrecht, A.P., 2002, November. Image classification using particle swarm optimization. In Proceedings of the 4th Asia-Pacific conference on simulated evolution and learning, Vol. 1, pp. 18-22.
[6] Shi, Y. and Eberhart, R., 1998, May. A modified particle swarm optimizer. InEvolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on (pp. 69-73).
[7] Angeline, P.J., 1998, May. Using selection to improve particle swarm optimization. In Proceedings of IEEE International Conference on Evolutionary Computation (Vol. 89).
[8] Eberhart, R.C. and Shi, Y., 2000. Comparing inertia weights and constriction factors in particle swarm optimization. In Evolutionary Computation, 2000. Proceedings of the 2000 Congress on, Vol. 1, pp. 84-88.
[9] Li, W.T., Shi, X.W. and Hei, Y.Q., 2008. An improved particle swarm optimization algorithm for pattern synthesis of phased arrays. Progress In Electromagnetics Research, 82, pp.319-332.
[10] Robinson, J., Sinton, S. and Rahmat-Samii, Y., 2002. Particle swarm, genetic algorithm, and their hybrids: optimization of a profiled corrugated horn antenna. In Antennas and Propagation Society International Symposium, 2002. IEEE, Vol. 1, pp. 314-317.
[11] [11] Niknam, T., Amiri, B., Olamaei, J. and Arefi, A., 2009. An efficient hybrid evolutionary optimization algorithm based on PSO and SA for clustering.Journal of Zhejiang University Science A, 10 (4), pp.512-519.
[12] Kaveh, A. and Talatahari, S., 2008. A hybrid particle swarm and ant colony optimization for design of truss structures. Asian Journal of Civil Engineering,9(4), pp.329-348.
[13] [13] Hu, X. and Eberhart, R., 2002, July. Solving constrained nonlinear optimization problems with particle swarm optimization. In Proceedings of the sixth world multiconference on systemics, cybernetics and informatics, Vol. 5, pp. 203-206.
[14] [14] Parsopoulos, K.E. and Vrahatis, M.N., 2002. Particle swarm optimization method for constrained optimization problems. Intelligent Technologies–Theory and Application: New Trends in Intelligent Technologies, 76, pp.214-220.
[15] Bai, Q., 2010, February. Analysis of Particle Swarm Optimization Algorithm.Computer Information Science, Vol. 3. No. 1 pp. 180-184.
[16] Yiqing, L., Xigang, Y. and Yongjian, L., 2007. An improved PSO algorithm for solving non-convex NLP/MINLP problems with equality constraints.Computers & chemical engineering, 31(3), pp.153-162.
[17] Hu, X., Eberhart, R.C. and Shi, Y., 2003, April. Engineering optimization with particle swarm. In Swarm Intelligence Symposium, 2003. SIS'03. Proceedings of the 2003 IEEE (pp. 53-57). IEEE.
[18] Parsopoulos, K.E. and Vrahatis, M.N., 2002. Recent approaches to global optimization problems through particle swarm optimization. Natural computing, 1(2-3), pp.235-306.
[19] http://www.sce.carleton.ca/faculty/chinneck/po/Chapter18.pdf
References
[1] Eberhart, R.C. and Kennedy, J., 1995, December. Particle swarm optimization. Proc. IEEE International Conf. on Neural Networks (Perth, Australia), IEEE service centre, Piscataway, NJ, vol.4,pp. 1942 – 1948.
[2] Eberhart, R.C. and Kennedy, J., 1995, October. A new optimizer using particle swarm theory. In Proceedings of the sixth international symposium on micro machine and human science, Vol.1, pp39-43.
[3] Melgani, F. and Bazi, Y., 2008. Classification of electrocardiogram signals with support vector machines and particle swarm optimization. Information Technology in Biomedicine, IEEE Transactions on, 12(5), pp.667-677.
[4] [Abido, M.A., 2002. Optimal design of power-system stabilizers using particle swarm optimization. Energy Conversion, IEEE Transactions on, 17(3), pp.406-413.
[5] Omran, M., Salman, A. and Engelbrecht, A.P., 2002, November. Image classification using particle swarm optimization. In Proceedings of the 4th Asia-Pacific conference on simulated evolution and learning, Vol. 1, pp. 18-22.
[6] Shi, Y. and Eberhart, R., 1998, May. A modified particle swarm optimizer. InEvolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on (pp. 69-73).
[7] Angeline, P.J., 1998, May. Using selection to improve particle swarm optimization. In Proceedings of IEEE International Conference on Evolutionary Computation (Vol. 89).
[8] Eberhart, R.C. and Shi, Y., 2000. Comparing inertia weights and constriction factors in particle swarm optimization. In Evolutionary Computation, 2000. Proceedings of the 2000 Congress on, Vol. 1, pp. 84-88.
[9] Li, W.T., Shi, X.W. and Hei, Y.Q., 2008. An improved particle swarm optimization algorithm for pattern synthesis of phased arrays. Progress In Electromagnetics Research, 82, pp.319-332.
[10] Robinson, J., Sinton, S. and Rahmat-Samii, Y., 2002. Particle swarm, genetic algorithm, and their hybrids: optimization of a profiled corrugated horn antenna. In Antennas and Propagation Society International Symposium, 2002. IEEE, Vol. 1, pp. 314-317.
[11] [11] Niknam, T., Amiri, B., Olamaei, J. and Arefi, A., 2009. An efficient hybrid evolutionary optimization algorithm based on PSO and SA for clustering.Journal of Zhejiang University Science A, 10 (4), pp.512-519.
[12] Kaveh, A. and Talatahari, S., 2008. A hybrid particle swarm and ant colony optimization for design of truss structures. Asian Journal of Civil Engineering,9(4), pp.329-348.
[13] [13] Hu, X. and Eberhart, R., 2002, July. Solving constrained nonlinear optimization problems with particle swarm optimization. In Proceedings of the sixth world multiconference on systemics, cybernetics and informatics, Vol. 5, pp. 203-206.
[14] [14] Parsopoulos, K.E. and Vrahatis, M.N., 2002. Particle swarm optimization method for constrained optimization problems. Intelligent Technologies–Theory and Application: New Trends in Intelligent Technologies, 76, pp.214-220.
[15] Bai, Q., 2010, February. Analysis of Particle Swarm Optimization Algorithm.Computer Information Science, Vol. 3. No. 1 pp. 180-184.
[16] Yiqing, L., Xigang, Y. and Yongjian, L., 2007. An improved PSO algorithm for solving non-convex NLP/MINLP problems with equality constraints.Computers & chemical engineering, 31(3), pp.153-162.
[17] Hu, X., Eberhart, R.C. and Shi, Y., 2003, April. Engineering optimization with particle swarm. In Swarm Intelligence Symposium, 2003. SIS'03. Proceedings of the 2003 IEEE (pp. 53-57). IEEE.
[18] Parsopoulos, K.E. and Vrahatis, M.N., 2002. Recent approaches to global optimization problems through particle swarm optimization. Natural computing, 1(2-3), pp.235-306.
[19] http://www.sce.carleton.ca/faculty/chinneck/po/Chapter18.pdf
[2] Eberhart, R.C. and Kennedy, J., 1995, October. A new optimizer using particle swarm theory. In Proceedings of the sixth international symposium on micro machine and human science, Vol.1, pp39-43.
[3] Melgani, F. and Bazi, Y., 2008. Classification of electrocardiogram signals with support vector machines and particle swarm optimization. Information Technology in Biomedicine, IEEE Transactions on, 12(5), pp.667-677.
[4] [Abido, M.A., 2002. Optimal design of power-system stabilizers using particle swarm optimization. Energy Conversion, IEEE Transactions on, 17(3), pp.406-413.
[5] Omran, M., Salman, A. and Engelbrecht, A.P., 2002, November. Image classification using particle swarm optimization. In Proceedings of the 4th Asia-Pacific conference on simulated evolution and learning, Vol. 1, pp. 18-22.
[6] Shi, Y. and Eberhart, R., 1998, May. A modified particle swarm optimizer. InEvolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on (pp. 69-73).
[7] Angeline, P.J., 1998, May. Using selection to improve particle swarm optimization. In Proceedings of IEEE International Conference on Evolutionary Computation (Vol. 89).
[8] Eberhart, R.C. and Shi, Y., 2000. Comparing inertia weights and constriction factors in particle swarm optimization. In Evolutionary Computation, 2000. Proceedings of the 2000 Congress on, Vol. 1, pp. 84-88.
[9] Li, W.T., Shi, X.W. and Hei, Y.Q., 2008. An improved particle swarm optimization algorithm for pattern synthesis of phased arrays. Progress In Electromagnetics Research, 82, pp.319-332.
[10] Robinson, J., Sinton, S. and Rahmat-Samii, Y., 2002. Particle swarm, genetic algorithm, and their hybrids: optimization of a profiled corrugated horn antenna. In Antennas and Propagation Society International Symposium, 2002. IEEE, Vol. 1, pp. 314-317.
[11] [11] Niknam, T., Amiri, B., Olamaei, J. and Arefi, A., 2009. An efficient hybrid evolutionary optimization algorithm based on PSO and SA for clustering.Journal of Zhejiang University Science A, 10 (4), pp.512-519.
[12] Kaveh, A. and Talatahari, S., 2008. A hybrid particle swarm and ant colony optimization for design of truss structures. Asian Journal of Civil Engineering,9(4), pp.329-348.
[13] [13] Hu, X. and Eberhart, R., 2002, July. Solving constrained nonlinear optimization problems with particle swarm optimization. In Proceedings of the sixth world multiconference on systemics, cybernetics and informatics, Vol. 5, pp. 203-206.
[14] [14] Parsopoulos, K.E. and Vrahatis, M.N., 2002. Particle swarm optimization method for constrained optimization problems. Intelligent Technologies–Theory and Application: New Trends in Intelligent Technologies, 76, pp.214-220.
[15] Bai, Q., 2010, February. Analysis of Particle Swarm Optimization Algorithm.Computer Information Science, Vol. 3. No. 1 pp. 180-184.
[16] Yiqing, L., Xigang, Y. and Yongjian, L., 2007. An improved PSO algorithm for solving non-convex NLP/MINLP problems with equality constraints.Computers & chemical engineering, 31(3), pp.153-162.
[17] Hu, X., Eberhart, R.C. and Shi, Y., 2003, April. Engineering optimization with particle swarm. In Swarm Intelligence Symposium, 2003. SIS'03. Proceedings of the 2003 IEEE (pp. 53-57). IEEE.
[18] Parsopoulos, K.E. and Vrahatis, M.N., 2002. Recent approaches to global optimization problems through particle swarm optimization. Natural computing, 1(2-3), pp.235-306.
[19] http://www.sce.carleton.ca/faculty/chinneck/po/Chapter18.pdf