Part Layout Optimization Using a Quadtree Representation

1988 ◽  
Author(s):  
E. Sandgren ◽  
T. Dworak
Keyword(s):  
Nonlinear Programming ◽  
Penalty Function ◽  
Function Method ◽  
Penalty Function Method ◽  
Nonlinear Programming Problem ◽  
Programming Formulation ◽  
Search Technique ◽  
Design Variables ◽  
Discrete Nature ◽  
Complex Parts

Abstract A nonlinear programming formulation is developed for minimizing the area required to position a set of pre-defined objects without overlap. The objects consist of polygons with an arbitrary number of edges. Nonconvex polygons are assumed which allows for the modelling of complex parts, including parte with holes. A quadtree representation is formed for each polygon and intersections are determined by traversing quadtrees for the potentially intersecting objects. The design variables are selected to be the x and y location and the rotation for each polygon that is to be positioned. An exterior penalty function method is used to generate the solution to the resulting nonlinear programming problem. A nongradient search technique is used due to the discrete nature of the overlap constraints. Example problems are presented and extensions to other classes of problems are discussed.

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.

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.

Minimum Sensitivity Design of Planar Kinematic Systems

1990 ◽  
Author(s):  
Umesh R. Patil ◽  
Prakash Krishnaswami
Keyword(s):  
Sensitivity Analysis ◽  
Nonlinear Programming ◽  
Function Method ◽  
Element Formulation ◽  
Penalty Function Method ◽  
Nonlinear Programming Problem ◽  
Kinematic System ◽  
Minimum Sensitivity ◽  
Robust System ◽  
General Method

Abstract In designing a kinematic system, it is desirable to ensure that the performance of the system is relatively insensitive to small changes in the nominal design, since this will result in a more robust system that can be manufactured economically with looser tolerances. A general method for minimizing the sensitivity of such systems is developed in this paper. The approach is based on the idea of converting the minimum sensitivity design problem into a nonlinear programming problem which is then solved using an exterior penalty function method. The constrained multi-element formulation is used for kinematic analysis and sensitivity analysis is performed using a direct differentation technique. The resulting algorithm is general enough to handle any planar kinematic system. The proposed method has been implemented in a computer program which has been tested on some sample problems. The results provide convincing proof of the power and feasibility of this method.

scholarly journals An objective penalty function method for nonlinear programming

2004 ◽  
Vol 17 (6) ◽  
pp. 683-689 ◽  
Author(s):  
Zhiqing Meng ◽  
Qiying Hu ◽  
Chuangyin Dang ◽  
Xiaoqi Yang
Keyword(s):  
Nonlinear Programming ◽  
Penalty Function ◽  
Function Method ◽  
Penalty Function Method ◽  
Objective Penalty Function
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