Modal Trimming Method for Improving Local Optima of Nonlinear Programming Problems : Performance Evaluation Through Test Problems

2002 ◽  
Vol 2002.12 (0) ◽  
pp. 182-185
Author(s):  
Ryohei Yokoyama ◽  
Koichi Ito
Keyword(s):  
Performance Evaluation ◽  
Nonlinear Programming ◽  
Test Problems ◽  
Local Optima

A Method for Comparative Performance Evaluation of Structural Optimization Codes: Part I — Theory

1988 ◽  
Author(s):  
G. Subbarayan ◽  
D. L. Bartel ◽  
D. L. Taylor
Keyword(s):  
Performance Evaluation ◽  
Nonlinear Programming ◽  
Structural Optimization ◽  
Design Optimization ◽  
Performance Criteria ◽  
Test Problems ◽  
Comparative Performance ◽  
Systematic Procedure ◽  
The Past ◽  
Evaluation Scheme

Abstract This paper presents a systematic procedure for the comparative performance evaluation of nonlinear programming codes intended for applications in structural optimization. Part I discusses the issues in the evaluation of nonlinear programming codes and proposes a performance evaluation scheme for structural optimization codes. Aspects of performance evaluation such as the choice of test problems and appropriate set of performance criteria for structural optimization codes are described. A procedure to analyze codes based on their observed geometric behavior for test problems is also presented. The proposed method is contrasted with studies conducted in the past for comparative performance evaluation of nonlinear programming codes. Part II presents an application of the theory described in part I to evaluate two design optimization codes.

A Method for Comparative Performance Evaluation of Structural Optimization Codes: Part II — Applications

1988 ◽  
Author(s):  
G. Subbarayan ◽  
D. L. Bartel ◽  
D. L. Taylor
Keyword(s):  
Performance Evaluation ◽  
Nonlinear Programming ◽  
Structural Optimization ◽  
Design Optimization ◽  
Performance Criteria ◽  
Test Problems ◽  
Comparative Performance ◽  
Systematic Procedure ◽  
The Past ◽  
Evaluation Scheme

Abstract This paper presents a systematic procedure for the comparative performance evaluation of nonlinear programming codes intended for applications in structural optimization. Part I discusses the issues in the evaluation of nonlinear programming codes and proposes a performance evaluation scheme for structural optimization codes. Aspects of performance evaluation such as the choice of test problems and appropriate set of performance criteria for structural optimization codes are described. A procedure to analyze codes based on their observed geometric behavior for test problems is also presented. The proposed method is contrasted with studies conducted in the past for comparative performance evaluation of nonlinear programming codes. Part II presents an application of the theory described in part I to evaluate two design optimization codes.

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.

Development of a Common Platform for Testing Metamodel Based Design Optimization Methods

2013 ◽  
Author(s):  
Adel A. Younis ◽  
George H. Cheng ◽  
G. Gary Wang ◽  
Zuomin Dong
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Computation Time ◽  
Optimization Methods ◽  
Global Optimum ◽  
Test Problems ◽  
Test Bed ◽  
Test Procedures ◽  
Local Optima

Metamodel based design optimization (MBDO) algorithms have attracted considerable interests in recent years due to their special capability in dealing with complex optimization problems with computationally expensive objective and constraint functions and local optima. Conventional unimodal-based optimization algorithms and stochastic global optimization algorithms either miss the global optimum frequently or require unacceptable computation time. In this work, a generic testbed/platform for evaluating various MBDO algorithms has been introduced. The purpose of the platform is to facilitate quantitative comparison of different MBDO algorithms using standard test problems, test procedures, and test outputs, as well as to improve the efficiency of new algorithm testing and improvement. The platform consists of a comprehensive test function database that contains about 100 benchmark functions and engineering problems. The testbed accepts any optimization algorithm to be tested, and only requires minor modifications to meet the test-bed requirements. The testbed is useful in comparing the performance of competing algorithms through execution of same problems. It allows researchers and practitioners to test and choose the most suitable optimization tool for their specific needs. It also helps to increase confidence and reliability of the newly developed MBDO tools. Many new MBDO algorithms, including Mode Pursuing Sampling (MPS), Pareto Set Pursuing (PSP), and Space Exploration and Unimodal Region Elimination (SEUMRE), were tested in this work to demonstrate its functionality and benefits.

scholarly journals A Novel Parent Centric Crossover with the Log-Logistic Probabilistic Approach Using Multimodal Test Problems for Real-Coded Genetic Algorithms

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Ehtasham ul Haq ◽  
Ishfaq Ahmad ◽  
Ibrahim M. Almanjahie
Keyword(s):  
Optimization Problems ◽  
Probabilistic Approach ◽  
Population Diversity ◽  
Test Problems ◽  
Crossover Operator ◽  
Local Optima ◽  
Mutation Operators ◽  
Multiple Comparison Test ◽  
Power Mutation ◽  
Real Coded Genetic Algorithms

In this paper, a comprehensive empirical study is conducted to evaluate the performance of a new real-coded crossover operator called Fisk crossover (FX) operator. The basic aim of the proposed study is to preserve population diversity as well as to avoid local optima. In this context, a new crossover operator is designed and developed which is linked with Log-logistic probability distribution. For its global performance, a realistic comparison is made between FX versus double Pareto crossover (DPX), Laplace crossover (LX), and simulated binary crossover (SBX) operators. Moreover, these crossover operators are also used in conjunction with three mutation operators called power mutation (PM), Makinen, Periaux, and Toivanen mutation (MPTM), and nonuniform mutation (NUM) for inclusive evaluation. The performance of probabilistic-based algorithms is tested on a set of twenty-one well-known nonlinear optimization benchmark functions with diverse features. The empirical results show a substantial dominance of FX over other crossover operators with authentication of performance index (PI). Moreover, we also examined the significance of the proposed crossover scheme by administrating ANOVA and Gabriel pairwise multiple comparison test. Finally, the statistically significant results of the proposed crossover scheme have a definite edge over the other schemes, and it is also expected that FX has a great potential to solve complex optimization problems.

A comparative performance evaluation of 27 nonlinear programming codes

Computing ◽  
1983 ◽  
Vol 30 (4) ◽  
pp. 335-358 ◽  
Author(s):  
W. Hock ◽  
K. Schittkowski
Keyword(s):  
Performance Evaluation ◽  
Nonlinear Programming ◽  
Comparative Performance

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

Remarks on Sufficiency of Constraint-Bound Solutions in Optimal Design

1988 ◽  
Author(s):  
P. Y. Papalambros
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Design Problems ◽  
Local Optima ◽  
Solution Strategies ◽  
Active Constraints ◽  
Active Sets ◽  
Trade Offs ◽  
Design Variables ◽  
Monotonicity Analysis

Abstract Solution strategies for optimal design problems in nonlinear programming formulations may require verification of optimality for constraint-bound points. These points are candidate solutions where the number of active constraints is equal to the number of design variables. Models leading to such solutions will typically offer little insight to design trade-offs and it would be desirable to identify them early, or exclude them in a strategy using active sets. Potential constrained-bound solutions are usually identified based on the principles of monotonicity analysis. This article discusses some cases where these points are in fact global or local optima.

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