ANALYSING THE IMPACT OF PENALTY CONSTANT ON PENALTY FUNCTION THROUGH PARTICE SWARM OPTIMIZATION

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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Application of a New Penalty Function Method to Design Optimization

Journal of Engineering for Industry ◽

10.1115/1.3439160 ◽

1977 ◽

Vol 99 (1) ◽

pp. 31-36 ◽

Cited By ~ 22

Author(s):

S. B. Schuldt ◽

G. A. Gabriele ◽

R. R. Root ◽

E. Sandgren ◽

K. M. Ragsdell

Keyword(s):

Linear Programming ◽

Nonlinear Programming ◽

Design Optimization ◽

Penalty Function ◽

Function Method ◽

Test Problems ◽

Penalty Function Method ◽

Method Of Multipliers ◽

Non Linear Programming ◽

Linear Programming Problems

This paper presents Schuldt’s Method of Multipliers for nonlinear programming problems. The basics of this new exterior penalty function method are discussed with emphasis upon the ease of implementation. The merit of the technique for medium to large non-linear programming problems is evaluated, and demonstrated using the Eason and Fenton test problems.

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IMPROVED PARTICLE SWARM OPTIMIZATION FOR NON-LINEAR PROGRAMMING PROBLEM WITH BARRIER METHOD

International Journal of Students Research in Technology & Management ◽

10.18510/ijsrtm.2017.5410 ◽

2017 ◽

Vol 5 (4) ◽

pp. 72-80

Author(s):

Raju Prajapati ◽

Om Prakash Dubey ◽

Randhir Kumar

Keyword(s):

Linear Programming ◽

Particle Swarm Optimization ◽

Programming Language ◽

Particle Swarm ◽

Barrier Method ◽

Lagrangian Multipliers ◽

Swarm Optimization ◽

Non Linear Programming ◽

Non Linear ◽

Linear Programming Problems

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.

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