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Abstract
Non Linear Programming Problems (NLPP) are tedious to solve as compared to Linear Programming Problem (LPP). The present paper is an attempt to analyze the impact of penalty constant over the penalty function, which is used to solve the NLPP with inequality constraint(s). The improved version of famous meta heuristic Particle Swarm Optimization (PSO) is used for this purpose. The scilab programming language is used for computational purpose. The impact of penalty constant is studied by considering five test problems. Different values of penalty constant are taken to prepare the unconstraint NLPP from the given constraint NLPP with inequality constraint. These different unconstraint NLPP is then solved by improved PSO, and the superior one is noted. It has been shown that, In all the five cases, the superior one is due to the higher penalty constant. The computational results for performance are shown in the respective sections.
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References
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References
[2] Fiacco, A.V. and McCormick, G.P., Nonlinear programming: sequential unconstrained minimization techniques. Society for Industrial and Applied Mathematics, 1990.
[3] Kelley, C.T., Iterative methods for optimization. Society for Industrial and Applied Mathematics, 1999.
[4] Eberhart, R. and Kennedy, J., A new optimizer using particle swarm theory. Micro Machine and Human Science, 1995. MHS'95, Proceedings of the Sixth International Symposium, pp. 39-43. IEEE.
[5] Eberhart, R.C. and Shi, Y., Comparing inertia weights and constriction factors in particle swarm optimization. Evolutionary Computation, 2000. Proceedings of the 2000 Congress, Vol. 1, pp. 84-88. IEEE.
[6] Angeline, P.J., Using selection to improve particle swarm optimization. Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence, The 1998 IEEE International Conference pp. 84-89.
[7] Li, W.T., Shi, X.W. and Hei, Y.Q., An improved particle swarm optimization algorithm for pattern synthesis of phased arrays. Progress In Electromagnetics Research, 2008, 82, pp.319-332.
[8] Vardhan, L.A. and Vasan, A., Evaluation of penalty function methods for constrained optimization using particle swarm optimization. Image Information Processing (ICIIP), 2013 IEEE Second International Conference, pp. 487-492.
[9] Parsopoulos, K.E. and Vrahatis, M.N., Particle swarm optimization method for constrained optimization problems. Intelligent Technologies–Theory and Application: New Trends in Intelligent Technologies, 2002, 76(1), pp.214-220.
[10] https://web.stanford.edu/group/sisl/k12/optimization/MO-unit5-pdfs/5.6penaltyfunctions.pdf (Retrieved: 28th October 2017)