Application of a New Penalty Function Method to Design Optimization

1977 ◽  
Vol 99 (1) ◽  
pp. 31-36 ◽  
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.

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

2018 ◽  
Vol 6 (2) ◽  
pp. 01-06
Author(s):  
Raju Prajapati ◽  
Om Prakash Dubey
Keyword(s):  
Linear Programming ◽  
Penalty Function ◽  
Inequality Constraint ◽  
Test Problems ◽  
Swarm Optimization ◽  
Non Linear Programming ◽  
Linear Programming Problems ◽  
The Impact ◽  
The Given ◽  
Computational Purpose

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.

scholarly journals DEVELOPMENT OF SOFTWARE FOR SOLVING PROBLEMS WITH THE PENALTY FUNCTION METHOD

2020 ◽  
Vol 7 (1) ◽  
pp. 84-87
Author(s):  
Galina E. Egorova ◽  
Tatyana S. Zaitseva
Keyword(s):  
Nonlinear Programming ◽  
Convex Programming ◽  
Penalty Function ◽  
Function Method ◽  
Theoretical Research ◽  
Penalty Function Method ◽  
Indirect Methods ◽  
Economic Problems ◽  
Definition Of

The penalty function method is one of the most popular and universal methods of convex programming and belongs to the group of indirect methods for solving nonlinear programming problems. Thе article discusses the algorithm for solving problems by the penalty function method, provides an example of a solution. A complete definition of the concepts used in the theoretical material of the method, and examples of its application are also given. It is worth noting that these methods are widely used to solve technical and economic problems. Also they are quite often used both in theoretical research and in the development of algorithms. The result of the work is the development of software for solving problems using the penalty function method.

Computational Enhancements to the Method of Multipliers

1980 ◽  
Vol 102 (3) ◽  
pp. 517-523 ◽  
Author(s):  
R. R. Root ◽  
K. M. Ragsdell
Keyword(s):  
Nonlinear Programming ◽  
Penalty Function ◽  
Transformation Method ◽  
Numerical Results ◽  
Test Problems ◽  
Method Of Multipliers ◽  
Transformation Technique ◽  
Code Bias ◽  
Overall Efficiency

Transformation or penalty function techniques have enjoyed wide popularity for the solution of nonlinear programming problems in recent years. Many methods have been proposed in this class, including the Method of Multipliers. In this paper we present two enhancements which may be used with any transformation technique. The first is a technique for direct handling of variable bounds, and the second is a problem scaling algorithm. Both techniques have been implemented in connection with a Method of Multipliers code, BIAS, and applied to 23 test problems. The numerical results indicate a significant increase in the robustness and overall efficiency of the transformation method employed.

Sign in / Sign up

Export Citation Format

Share Document