Numerical optimization: Handling nonlinear constraints

Author(s):  
Zbigniew Michalewicz
1996 ◽  
Vol 4 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Zbigniew Michalewicz ◽  
Marc Schoenauer

Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.


1999 ◽  
Vol 7 (1) ◽  
pp. 19-44 ◽  
Author(s):  
Slawomir Koziel ◽  
Zbigniew Michalewicz

During the last five years, several methods have been proposed for handling nonlinear constraints using evolutionary algorithms (EAs) for numerical optimization problems. Recent survey papers classify these methods into four categories: preservation of feasibility, penalty functions, searching for feasibility, and other hybrids. In this paper we investigate a new approach for solving constrained numerical optimization problems which incorporates a homomorphous mapping between n-dimensional cube and a feasible search space. This approach constitutes an example of the fifth decoder-based category of constraint handling techniques. We demonstrate the power of this new approach on several test cases and discuss its further potential.


1978 ◽  
Vol 100 (2) ◽  
pp. 292-296 ◽  
Author(s):  
J. Y. Moradi ◽  
M. Pappas

A new procedure for numerical optimization of constrained nonlinear problems is described. The method makes use of an efficient “Boundary Tracking” strategy to move on the constraint surfaces. In a comparison study it was found to be an effective method for treating nonlinear mathematical programming problems particularly those with difficult nonlinear constraints.


2013 ◽  
pp. 36-41
Author(s):  
Olivier Brugière ◽  
Guillaume Balarac ◽  
Christophe Corre ◽  
Olivier Métais ◽  
Emmanuel Flores ◽  
...  

2016 ◽  
Vol 10 (4) ◽  
pp. 215 ◽  
Author(s):  
Ioannis Kassanos ◽  
Marios Chrysovergis ◽  
John Anagnostopoulos ◽  
George Charalampopoulos ◽  
Stamelos Rokas ◽  
...  

Author(s):  
А. В. Поляк ◽  
М. М. Гуйван ◽  
О. М. Малінін

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