scholarly journals A Filled Function Approach for Nonsmooth Constrained Global Optimization

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Weixiang Wang ◽  
Youlin Shang ◽  
Ying Zhang
Keyword(s):  
Global Optimization ◽  
Constrained Optimization ◽  
Unconstrained Optimization ◽  
Penalty Function ◽  
Optimization Problem ◽  
Solution Algorithm ◽  
Constrained Global Optimization ◽  
Filled Function ◽  
Global Minima ◽  
Constrained Optimization Problem

A novel filled function is given in this paper to find a global minima for a nonsmooth constrained optimization problem. First, a modified concept of the filled function for nonsmooth constrained global optimization is introduced, and a filled function, which makes use of the idea of the filled function for unconstrained optimization and penalty function for constrained optimization, is proposed. Then, a solution algorithm based on the proposed filled function is developed. At last, some preliminary numerical results are reported. The results show that the proposed approach is promising.

scholarly journals A Novel Penalty Function Approach to Constrained Optimization Problems with Genetic Algorithms

1998 ◽  
Vol 2 (6) ◽  
pp. 208-213 ◽  
Author(s):  
Xinghuo Yu ◽  
◽  
Weixing Zheng ◽  
Baolin Wu ◽  
Xin Yao ◽  
...  
Keyword(s):  
Constrained Optimization ◽  
Unconstrained Optimization ◽  
Penalty Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Function Approach ◽  
Constrained Optimization Problem ◽  
Constrained Optimization Problems ◽  
Unconstrained Optimization Problem ◽  
Penalty Function Approach

In this paper, a novel penalty function approach is proposed for constrained optimization problems with linear and nonlinear constraints. It is shown that by using a mapping function to "wrap" up the constraints, a constrained optimization problem can be converted to an unconstrained optimization problem. It is also proved mathematically that the best solution of the converted unconstrained optimization problem will approach the best solution of the constrained optimization problem if the tuning parameter for the wrapping function approaches zero. A tailored genetic algorithm incorporating an adaptive tuning method is then used to search for the global optimal solutions of the converted unconstrained optimization problems. Four test examples were used to show the effectiveness of the approach.

A Generalized Filled Function for Non-Smooth Constrained Global Optimization

2011 ◽  
Vol 204-210 ◽  
pp. 114-117
Author(s):  
Wei Xiang Wang ◽  
You Lin Shang ◽  
Lian Sheng Zhang
Keyword(s):  
Global Optimization ◽  
Numerical Experiments ◽  
Function Method ◽  
Optimization Problem ◽  
Solution Algorithm ◽  
Global Optimization Problem ◽  
Computational Results ◽  
Constrained Global Optimization ◽  
Filled Function ◽  
Filled Function Method

A generalized filled function method is developed in this paper to solve nonsmooth constrained global optimization problem. Theoretical properties of the proposed function is investigated, and a solution algorithm is proposed. Numerical experiments are also reported in this paper. The preliminary computational results show that the proposed method is promising.

scholarly journals Finding Global Minima with a Filled Function Approach for Non-Smooth Global Optimization

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Weixiang Wang ◽  
Youlin Shang ◽  
Ying Zhang
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Numerical Test ◽  
Function Approach ◽  
Global Optimization Problem ◽  
Computational Results ◽  
Filled Function ◽  
Global Minima ◽  
Smooth Case ◽  
Definition Of

A filled function approach is proposed for solving a non-smooth unconstrained global optimization problem. First, the definition of filled function in Zhang (2009) for smooth global optimization is extended to non-smooth case and a new one is put forwarded. Then, a novel filled function is proposed for non-smooth the global optimization and a corresponding non-smooth algorithm based on the filled function is designed. At last, a numerical test is made. The computational results demonstrate that the proposed approach is effcient and reliable.

scholarly journals Nonconvex constrained optimization by a filtering branch and bound

2020 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Kathrin Klamroth ◽  
Julia Niebling
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Constrained Optimization Problem ◽  
Numerical Tests ◽  
Nonconvex Constrained Optimization ◽  
Objective Value ◽  
Feasible Solutions ◽  
Quality Guarantee ◽  
Single Objective

AbstractA major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the $$\alpha $$ α BB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained optimization problem. Moreover, the multiobjective reformulation enables to identify the trade-off between constraint satisfaction and objective value which is also reflected in the quality guarantee. Numerical tests validate that we indeed can find feasible and often optimal solutions where the classical single-objective $$\alpha $$ α BB method fails, i.e., it terminates without ever finding a feasible solution.

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