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...
| Main Authors: | , , |
|---|---|
| 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 |
| _version_ | 1831543848064516096 |
|---|---|
| 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. |
| first_indexed | 2024-12-17T00:58:18Z |
| format | Article |
| id | doaj.art-b34895fa417e4fd0b01ab64f1f890587 |
| institution | Directory Open Access Journal |
| issn | 2423-6977 2423-6969 |
| language | English |
| last_indexed | 2024-12-17T00:58:18Z |
| publishDate | 2015-04-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| 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 |
| work_keys_str_mv | AT rezaghanbari atwophasevariableneighborhoodsearchforsolvingnonlinearoptimalcontrolproblems AT aghilehheydari atwophasevariableneighborhoodsearchforsolvingnonlinearoptimalcontrolproblems AT saeednezhadhosein atwophasevariableneighborhoodsearchforsolvingnonlinearoptimalcontrolproblems AT rezaghanbari twophasevariableneighborhoodsearchforsolvingnonlinearoptimalcontrolproblems AT aghilehheydari twophasevariableneighborhoodsearchforsolvingnonlinearoptimalcontrolproblems AT saeednezhadhosein twophasevariableneighborhoodsearchforsolvingnonlinearoptimalcontrolproblems |