scholarly journals A metaheuristic penalty approach for the starting point in nonlinear programming

2020 ◽  
Vol 54 (2) ◽  
pp. 451-469
Author(s):  
David R. Penas ◽  
Marcos Raydan
Keyword(s):  
Nonlinear Programming ◽  
Feasible Solution ◽  
Packing Problem ◽  
Merit Function ◽  
Test Problems ◽  
Huge Amount ◽  
Novel Approach ◽  
Starting Point ◽  
Metaheuristic Techniques ◽  
Optimization Schemes

Solving nonlinear programming problems usually involve difficulties to obtain a starting point that produces convergence to a local feasible solution, for which the objective function value is sufficiently good. A novel approach is proposed, combining metaheuristic techniques with modern deterministic optimization schemes, with the aim to solve a sequence of penalized related problems to generate convenient starting points. The metaheuristic ideas are used to choose the penalty parameters associated with the constraints, and for each set of penalty parameters a deterministic scheme is used to evaluate a properly chosen metaheuristic merit function. Based on this starting-point approach, we describe two different strategies for solving the nonlinear programming problem. We illustrate the properties of the combined schemes on three nonlinear programming benchmark-test problems, and also on the well-known and hard-to-solve disk-packing problem, that possesses a huge amount of local-nonglobal solutions, obtaining encouraging results both in terms of optimality and feasibility.

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.

Pracniques: construction of nonlinear programming test problems

1965 ◽  
Vol 8 (2) ◽  
pp. 113 ◽  
Author(s):  
J. B. Rosen ◽  
S. Suzuki
Keyword(s):  
Nonlinear Programming ◽  
Test Problems

Cluster Analysis for the Cognitive Selection of Nonlinear Programming Algorithms

1990 ◽  
Author(s):  
Jin-xian Ma ◽  
Shi-huai Xie ◽  
Yong Chen
Keyword(s):  
Cluster Analysis ◽  
Nonlinear Programming ◽  
Expert System ◽  
Mechanical Design ◽  
Test Problems ◽  
Comparative Performance ◽  
Nonlinear Programming Algorithms ◽  
Cognitive Selection ◽  
Programming Algorithms ◽  
Selection Of

Abstract In recent years, cluster analysis has played an increasingly important role in statistical pattern recognition. Hoeltzel and Chieng have shown an example on cognitive selection of nonlinear programming algorithms in a mechanical design expert system. In this paper, an improved dynamic clustering of 3000 samples came from a comparative performance evaluation of six typical nonlinear programming softwares with randomly generated test problems has been made. Explanations resulting from the cluster analysis have been used to build rules to form the knowledge base of an optimization expert system.

scholarly journals Nonlinear Programming Test Problems

1966 ◽  
Vol 9 (1) ◽  
pp. 115-116
Author(s):  
M. J. Box
Keyword(s):  
Nonlinear Programming ◽  
Test Problems
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