Gaussian and Cauchy Functions in the Filled Function Method – Why and What Next: On the Example of Optimizing Road Tolls

Abstract: In many practical problems, we need to find the values of the parameters that optimize the desired objective function. For example, for the toll roads, it is important to set the toll values that lead to the fastest return on investment. There exist many optimization algorithms, the pro...

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Autores principales: Flores Muñiz, José Guadalupe, Kalashnikov, Vyacheslav V., Kreinovich, Vladik, Kalashnykova, Nataliya I.
Formato: Artículo
Lenguaje:inglés
Publicado: Budapest Tech Polytechnical Institution. 2017
Materias:
Acceso en línea:http://eprints.uanl.mx/18225/1/516.pdf
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author Flores Muñiz, José Guadalupe
Kalashnikov, Vyacheslav V.
Kreinovich, Vladik
Kalashnykova, Nataliya I.
author_facet Flores Muñiz, José Guadalupe
Kalashnikov, Vyacheslav V.
Kreinovich, Vladik
Kalashnykova, Nataliya I.
author_sort Flores Muñiz, José Guadalupe
collection Repositorio Institucional
description Abstract: In many practical problems, we need to find the values of the parameters that optimize the desired objective function. For example, for the toll roads, it is important to set the toll values that lead to the fastest return on investment. There exist many optimization algorithms, the problem is that these algorithms often end up in a local optimum. One of the promising methods to avoid the local optima is the filled function method, in which we, in effect, first optimize a smoothed version of the objective function, and then use the resulting optimum to look for the optimum of the original function. It turns out that empirically, the best smoothing functions to use in this method are the Gaussian and the Cauchy functions. In this paper, we show that from the viewpoint of computational complexity, these two smoothing functions are indeed the simplest. The Gaussian and Cauchy functions are not a panacea: in some cases, they still leave us with a local optimum. In this paper, we use the computational complexity analysis to describe the next-simplest smoothing functions which are worth trying in such situations. Keywords: optimization; toll roads; filled function method; Gaussian and Cauchy smoothing
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spelling eprints-182252020-03-11T20:36:38Z http://eprints.uanl.mx/18225/ Gaussian and Cauchy Functions in the Filled Function Method – Why and What Next: On the Example of Optimizing Road Tolls Flores Muñiz, José Guadalupe Kalashnikov, Vyacheslav V. Kreinovich, Vladik Kalashnykova, Nataliya I. QC Física Abstract: In many practical problems, we need to find the values of the parameters that optimize the desired objective function. For example, for the toll roads, it is important to set the toll values that lead to the fastest return on investment. There exist many optimization algorithms, the problem is that these algorithms often end up in a local optimum. One of the promising methods to avoid the local optima is the filled function method, in which we, in effect, first optimize a smoothed version of the objective function, and then use the resulting optimum to look for the optimum of the original function. It turns out that empirically, the best smoothing functions to use in this method are the Gaussian and the Cauchy functions. In this paper, we show that from the viewpoint of computational complexity, these two smoothing functions are indeed the simplest. The Gaussian and Cauchy functions are not a panacea: in some cases, they still leave us with a local optimum. In this paper, we use the computational complexity analysis to describe the next-simplest smoothing functions which are worth trying in such situations. Keywords: optimization; toll roads; filled function method; Gaussian and Cauchy smoothing Budapest Tech Polytechnical Institution. 2017 Article PeerReviewed text en cc_by_nc_nd http://eprints.uanl.mx/18225/1/516.pdf http://eprints.uanl.mx/18225/1.haspreviewThumbnailVersion/516.pdf Flores Muñiz, José Guadalupe y Kalashnikov, Vyacheslav V. y Kreinovich, Vladik y Kalashnykova, Nataliya I. (2017) Gaussian and Cauchy Functions in the Filled Function Method – Why and What Next: On the Example of Optimizing Road Tolls. Acta polytechnica hungarica, 14 (3). pp. 237-250. ISSN 1785-8860 http://doi.org/10.12700/APH.14.3.2017.3.14 doi:10.12700/APH.14.3.2017.3.14
spellingShingle QC Física
Flores Muñiz, José Guadalupe
Kalashnikov, Vyacheslav V.
Kreinovich, Vladik
Kalashnykova, Nataliya I.
Gaussian and Cauchy Functions in the Filled Function Method – Why and What Next: On the Example of Optimizing Road Tolls
thumbnail https://rediab.uanl.mx/themes/sandal5/images/online.png
title Gaussian and Cauchy Functions in the Filled Function Method – Why and What Next: On the Example of Optimizing Road Tolls
title_full Gaussian and Cauchy Functions in the Filled Function Method – Why and What Next: On the Example of Optimizing Road Tolls
title_fullStr Gaussian and Cauchy Functions in the Filled Function Method – Why and What Next: On the Example of Optimizing Road Tolls
title_full_unstemmed Gaussian and Cauchy Functions in the Filled Function Method – Why and What Next: On the Example of Optimizing Road Tolls
title_short Gaussian and Cauchy Functions in the Filled Function Method – Why and What Next: On the Example of Optimizing Road Tolls
title_sort gaussian and cauchy functions in the filled function method why and what next on the example of optimizing road tolls
topic QC Física
url http://eprints.uanl.mx/18225/1/516.pdf
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