A Hybrid Epigraph Directions Method for Nonsmooth and Nonconvex Constrained Optimization via Generalized Augmented Lagrangian Duality and a Genetic Algorithm
Autor: | Hernando J. R. Franco, Afonso C. C. Lemonge, Tales Lima Fonseca, Wilhelm Passarella Freire |
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Jazyk: | angličtina |
Rok vydání: | 2018 |
Předmět: |
Mathematical optimization
Optimization problem Article Subject Computer science General Mathematics 0211 other engineering and technologies MathematicsofComputing_NUMERICALANALYSIS Mathematics::Optimization and Control Duality (optimization) 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences symbols.namesake Genetic algorithm 0101 mathematics Metaheuristic Epigraph 021103 operations research Augmented Lagrangian method lcsh:Mathematics General Engineering Constrained optimization lcsh:QA1-939 Hybrid algorithm lcsh:TA1-2040 symbols lcsh:Engineering (General). Civil engineering (General) Lagrangian |
Zdroj: | Mathematical Problems in Engineering, Vol 2018 (2018) |
ISSN: | 1563-5147 |
Popis: | The Interior Epigraph Directions (IED) method for solving constrained nonsmooth and nonconvex optimization problem via Generalized Augmented Lagrangian Duality considers the dual problem induced by a Generalized Augmented Lagrangian Duality scheme and obtains the primal solution by generating a sequence of iterates in the interior of the epigraph of the dual function. In this approach, the value of the dual function at some point in the dual space is given by minimizing the Lagrangian. The first version of the IED method uses the Matlab routine fminsearch for this minimization. The second version uses NFDNA, a tailored algorithm for unconstrained, nonsmooth and nonconvex problems. However, the results obtained with fminsearch and NFDNA were not satisfactory. The current version of the IED method, presented in this work, employs a Genetic Algorithm, which is free of any strategy to handle the constraints, a difficult task when a metaheuristic, such as GA, is applied alone to solve constrained optimization problems. Two sets of constrained optimization problems from mathematics and mechanical engineering were solved and compared with literature. It is shown that the proposed hybrid algorithm is able to solve problems where fminsearch and NFDNA fail. |
Databáze: | OpenAIRE |
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