A two-phase variable neighborhood search for solving nonlinear optimal control problems

In this paper, a two-phase algorithm, namely IVNS, is proposed for solving nonlinear optimal control problems. In each phase of the algorithm, we use a variable neighborhood search (VNS), which performs a uniform distribution in the shaking step and the successive quadratic programming, as the local...

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Main Authors: Reza Ghanbari, Aghileh Heydari, Saeed Nezhadhosein
Format: Article
Language:English
Published: Ferdowsi University of Mashhad 2015-04-01
Series:Iranian Journal of Numerical Analysis and Optimization
Subjects:
Online Access:https://ijnao.um.ac.ir/article_24438_dff185ed536756612e3e85f9576d16d4.pdf
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author Reza Ghanbari
Aghileh Heydari
Saeed Nezhadhosein
author_facet Reza Ghanbari
Aghileh Heydari
Saeed Nezhadhosein
author_sort Reza Ghanbari
collection DOAJ
description In this paper, a two-phase algorithm, namely IVNS, is proposed for solving nonlinear optimal control problems. In each phase of the algorithm, we use a variable neighborhood search (VNS), which performs a uniform distribution in the shaking step and the successive quadratic programming, as the local search step. In the first phase, VNS starts with a completely random initial solution of control input values. To increase the accuracy of the solution obtained from the phase 1, some new time nodes are added and the values of the new control inputs are estimated by spline interpolation. Next, in the second phase, VNS restarts by the solution constructed by the phase 1. The proposed algorithm is implemented on more than 20 well-known benchmarks and real world problems, then the results are compared with some recently proposed algorithms. The numerical results show that IVNS can find the best solution on 84% of test problems. Also, to compare the IVNS with a common VNS (when the number of time nodes is same in both phases), a computational study is done. This study shows that IVNS needs less computational time with respect to common VNS, when the quality of solutions are not different signifcantly.
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spelling doaj.art-b34895fa417e4fd0b01ab64f1f8905872022-12-21T22:09:32ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692015-04-0151133610.22067/ijnao.v5i1.3420024438A two-phase variable neighborhood search for solving nonlinear optimal control problemsReza Ghanbari0Aghileh Heydari1Saeed Nezhadhosein2Ferdowsi University of MashhadPayame Noor UniversityPayame Noor UniversityIn this paper, a two-phase algorithm, namely IVNS, is proposed for solving nonlinear optimal control problems. In each phase of the algorithm, we use a variable neighborhood search (VNS), which performs a uniform distribution in the shaking step and the successive quadratic programming, as the local search step. In the first phase, VNS starts with a completely random initial solution of control input values. To increase the accuracy of the solution obtained from the phase 1, some new time nodes are added and the values of the new control inputs are estimated by spline interpolation. Next, in the second phase, VNS restarts by the solution constructed by the phase 1. The proposed algorithm is implemented on more than 20 well-known benchmarks and real world problems, then the results are compared with some recently proposed algorithms. The numerical results show that IVNS can find the best solution on 84% of test problems. Also, to compare the IVNS with a common VNS (when the number of time nodes is same in both phases), a computational study is done. This study shows that IVNS needs less computational time with respect to common VNS, when the quality of solutions are not different signifcantly.https://ijnao.um.ac.ir/article_24438_dff185ed536756612e3e85f9576d16d4.pdfnonlinear optimal control problemvariable neighborhood searchsuccessive quadratic programming
spellingShingle Reza Ghanbari
Aghileh Heydari
Saeed Nezhadhosein
A two-phase variable neighborhood search for solving nonlinear optimal control problems
Iranian Journal of Numerical Analysis and Optimization
nonlinear optimal control problem
variable neighborhood search
successive quadratic programming
title A two-phase variable neighborhood search for solving nonlinear optimal control problems
title_full A two-phase variable neighborhood search for solving nonlinear optimal control problems
title_fullStr A two-phase variable neighborhood search for solving nonlinear optimal control problems
title_full_unstemmed A two-phase variable neighborhood search for solving nonlinear optimal control problems
title_short A two-phase variable neighborhood search for solving nonlinear optimal control problems
title_sort two phase variable neighborhood search for solving nonlinear optimal control problems
topic nonlinear optimal control problem
variable neighborhood search
successive quadratic programming
url https://ijnao.um.ac.ir/article_24438_dff185ed536756612e3e85f9576d16d4.pdf
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