Development of a Hybrid SQP-GRG Algorithm for Constrained Nonlinear Programming

1988 ◽  
Vol 110 (3) ◽  
pp. 308-315 ◽  
Author(s):  
A. Parkinson ◽  
M. Wilson
Keyword(s):  
Nonlinear Programming ◽  
Sequential Quadratic Programming ◽  
Hybrid Algorithm ◽  
Line Search ◽  
Programming Algorithm ◽  
Test Problems ◽  
Design Problems ◽  
Engineering Design Problems ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust, efficient, and feasible at intermediate iterations. Based on the strengths of the generalized reduced gradient (GRG) and sequential quadratic programming (SQP) algorithms, a hybrid SQP-GRG algorithm is developed. The hybrid algorithm uses the SQP search direction and a modified GRG line search. The resulting SQP-GRG algorithm is shown to be robust, feasible at intermediate iterations, and comparable in efficiency to Powell’s SQP algorithm on 26 test problems.

scholarly journals A comparative study on optimization methods for the constrained nonlinear programming problems

2005 ◽  
Vol 2005 (2) ◽  
pp. 165-173 ◽  
Author(s):  
Ozgur Yeniay
Keyword(s):  
Nonlinear Programming ◽  
Comparative Study ◽  
Sequential Quadratic Programming ◽  
Gradient Methods ◽  
Optimization Methods ◽  
Test Problems ◽  
Reduced Gradient ◽  
Constrained Nonlinear Programming ◽  
Generalized Reduced Gradient ◽  
Reduced Gradient Methods

Constrained nonlinear programming problems often arise in many engineering applications. The most well-known optimization methods for solving these problems are sequential quadratic programming methods and generalized reduced gradient methods. This study compares the performance of these methods with the genetic algorithms which gained popularity in recent years due to advantages in speed and robustness. We present a comparative study that is performed on fifteen test problems selected from the literature.

A Unified Outline of Nonlinear Programming Algorithms

1985 ◽  
Vol 107 (4) ◽  
pp. 449-453 ◽  
Author(s):  
K. Schittkowski
Keyword(s):  
Nonlinear Programming ◽  
Sequential Quadratic Programming ◽  
Gradient Methods ◽  
Reduced Gradient ◽  
Numerical Performance ◽  
Constrained Nonlinear Programming ◽  
Generalized Reduced Gradient ◽  
Performance Results ◽  
Programming Algorithms ◽  
Reduced Gradient Methods

The four most successful approaches for solving the constrained nonlinear programming problem are the penalty, multiplier, sequential quadratic programming, and generalized reduced gradient methods. A general algorithmic frame will be presented, which realizes any of these methods only by specifying a search direction for the variables, a multiplier estimate, and some penalty parameters in each iteration. This approach allows one to illustrate common mathematical features and, on the other hand, serves to explain the different numerical performance results we observe in practice.

A Hybrid Fuzzy Simplex Genetic Algorithm

2000 ◽  
Author(s):  
Mohamed B. Trabia
Keyword(s):  
Genetic Algorithm ◽  
Hybrid Algorithm ◽  
Simplex Algorithm ◽  
Standard Test ◽  
Initial Guess ◽  
Test Problems ◽  
Programming Technique ◽  
Design Problems ◽  
Engineering Design Problems ◽  
Novel Algorithm

Abstract Nelder and Mead Simplex (NMS) algorithm is an effective nonlinear programming technique. Trabia and Lu (1999) recently presented a novel algorithm, Fuzzy Simplex (FS), which improved the efficiency of Nelder and Mead Simplex by using fuzzy logic to determine the orientation and size of the simplex. While Fuzzy Simplex algorithm can be successfully used to search a wide variety of functions, it suffers, as other simplex algorithms, from its dependence on the initial guess and the original simplex size. This paper addresses this problem by combining the Fuzzy Simplex with Genetic Algorithm (GA) in a hybrid algorithm. Standard test problems are used to evaluate the efficiency of the algorithm. The algorithm is also applied successfully to several engineering design problems. The Hybrid GA Fuzzy Simplex algorithm generally results in a faster convergence.

Nonlinear Mixed Integer-Discrete-Continuous Programming and its Application to Engineering Design Problems

1989 ◽  
Author(s):  
J.-F. Fu ◽  
R. G. Fenton ◽  
W. L. Cleghorn
Keyword(s):  
Nonlinear Programming ◽  
Objective Function ◽  
Engineering Design ◽  
Optimization Algorithm ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Design Problems ◽  
Continuous Programming ◽  
Engineering Design Problems ◽  
Standard Values

Abstract An algorithm for solving nonlinear programming problems containing integer, discrete and continuous variables is presented. Based on a commonly employed optimization algorithm, penalties on integer and/or discrete violations are imposed on the objective function to force the search to converge onto standard values. Examples are included to illustrate the practical use of this algorithm.

A Fuzzy Adaptive Simplex Search Optimization Algorithm

1999 ◽  
Author(s):  
Mohamed B. Trabia ◽  
Xiao Bin Lu
Keyword(s):  
Fuzzy Logic ◽  
Optimization Algorithms ◽  
Test Problems ◽  
Objective Functions ◽  
Fuzzy Logic Controllers ◽  
Design Problems ◽  
Simplex Search ◽  
Search Optimization ◽  
Engineering Design Problems ◽  
Fuzzy Adaptive

Abstract Optimization algorithms usually use fixed parameters that are empirically chosen to reach the minimum for various objective functions. This paper shows how to incorporate fuzzy logic in optimization algorithms to make the search adaptive to various objective functions. This idea is applied to produce a new algorithm for minimization of a function of n variables using an adaptive form of the simplex method. The search starts by generating a simplex with n+1 vertices. The algorithm replaces the point with the highest function value by a new point. This process comprises reflecting the point with the highest function value in addition to expanding or contracting the simplex using fuzzy logic controllers whose inputs incorporate the relative weights of the function values at the simplex points. The efficiency of the algorithm is studied using a set of standard minimization test problems. This algorithm generally results in a faster convergence toward the minimum. The algorithm is also applied successfully to two engineering design problems.

scholarly journals A Mathematical Model for Optimal Strength and Alignment of a Marine Shafting System

1985 ◽  
Vol 29 (03) ◽  
pp. 212-222
Author(s):  
Zissimos Mourelatos ◽  
Panos Papalambros
Keyword(s):  
Mathematical Model ◽  
Nonlinear Programming ◽  
Programming Formulation ◽  
Solution Strategy ◽  
Reduced Gradient Method ◽  
Trade Offs ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Optimal Strength ◽  
Vertical Positioning

The design of a marine shafting system is modeled mathematically in order to perform optimization studies with respect to shaft strength as well as longitudinal and vertical positioning of the bearings. The objective criteria used are minimization of the bearing reaction influence numbers and even distribution of the bearing loading. Design trade-offs can be thus established. The problem is posed in a nonlinear programming formulation and is solved using a standard generalized reduced gradient method (GRG2), but in a specialized solution strategy. Two examples from actual ship designs are presented.

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