Applied and Computational Mathematics

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Development of a Hybrid Algorithm for Efficiently Solving Mixed Integer-Continuous Optimization Problems

Received: 14 June 2016    Accepted:     Published: 15 June 2016
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Abstract

Problems with mixed integer-continuous design variables are a class of complicated optimization problems that commonly exist in practical engineering design work. In this paper, a hybrid algorithm combining metamodel-based Multipoint Approximation Method (MAM) and Hooke-Jeeves direct search technique is presented to efficiently seek the optimum solutions for mixed integer-continuous optimization problems. First, optimal continuous values are obtained by the Sequential Quadratic Programming method (SQP) on the approximated functions in a current trust region. Then, continuous values are rounded to the nearest integer values for discrete variables. Utilizing integer values as a starting point, the Hooke-Jeeves assisted MAM is applied to search for the discrete optimal solution in the sub-space of discrete variables as well as accordingly update the sub-optimal values for continuous design variables by SQP. The proposed hybrid algorithm is examined by the well established benchmark example and the obtained results demonstrate the superiority of the developed algorithm over GA in terms of computational cost and the quality of solutions.

DOI 10.11648/j.acm.20160503.13
Published in Applied and Computational Mathematics (Volume 5, Issue 3, June 2016)
Page(s) 107-113
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Integer-Continuous Optimization, Multipoint Approximation Method, Metamodel, Direct Search, Hybrid Algorithm

References
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[11] D. Liu, V. V. Toropov, “Implementation of discrete capability into the enhanced multipoint approximation method for solving mixed integer-continuous optimization problems,” International Journal for Computational Methods in Engineering Science & Mechanics, 17. pp. 22-35, 2016
[12] T. G. Kolda, R. M. Lewis, V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev., vol. 45, pp. 385-482, 2003.
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[17] G. E. P. Box, N. R. Draper, “Empirical model-building and response surfaces,” New York: John Wiley and Sons, 1987.
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Author Information
  • School of Mathematics, Faculty of Science, University of East Anglia, Norwich, UK

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    Dianzi Liu. (2016). Development of a Hybrid Algorithm for Efficiently Solving Mixed Integer-Continuous Optimization Problems. Applied and Computational Mathematics, 5(3), 107-113. https://doi.org/10.11648/j.acm.20160503.13

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    Dianzi Liu. Development of a Hybrid Algorithm for Efficiently Solving Mixed Integer-Continuous Optimization Problems. Appl. Comput. Math. 2016, 5(3), 107-113. doi: 10.11648/j.acm.20160503.13

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    Dianzi Liu. Development of a Hybrid Algorithm for Efficiently Solving Mixed Integer-Continuous Optimization Problems. Appl Comput Math. 2016;5(3):107-113. doi: 10.11648/j.acm.20160503.13

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  • @article{10.11648/j.acm.20160503.13,
      author = {Dianzi Liu},
      title = {Development of a Hybrid Algorithm for Efficiently Solving Mixed Integer-Continuous Optimization Problems},
      journal = {Applied and Computational Mathematics},
      volume = {5},
      number = {3},
      pages = {107-113},
      doi = {10.11648/j.acm.20160503.13},
      url = {https://doi.org/10.11648/j.acm.20160503.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20160503.13},
      abstract = {Problems with mixed integer-continuous design variables are a class of complicated optimization problems that commonly exist in practical engineering design work. In this paper, a hybrid algorithm combining metamodel-based Multipoint Approximation Method (MAM) and Hooke-Jeeves direct search technique is presented to efficiently seek the optimum solutions for mixed integer-continuous optimization problems. First, optimal continuous values are obtained by the Sequential Quadratic Programming method (SQP) on the approximated functions in a current trust region. Then, continuous values are rounded to the nearest integer values for discrete variables. Utilizing integer values as a starting point, the Hooke-Jeeves assisted MAM is applied to search for the discrete optimal solution in the sub-space of discrete variables as well as accordingly update the sub-optimal values for continuous design variables by SQP. The proposed hybrid algorithm is examined by the well established benchmark example and the obtained results demonstrate the superiority of the developed algorithm over GA in terms of computational cost and the quality of solutions.},
     year = {2016}
    }
    

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    AB  - Problems with mixed integer-continuous design variables are a class of complicated optimization problems that commonly exist in practical engineering design work. In this paper, a hybrid algorithm combining metamodel-based Multipoint Approximation Method (MAM) and Hooke-Jeeves direct search technique is presented to efficiently seek the optimum solutions for mixed integer-continuous optimization problems. First, optimal continuous values are obtained by the Sequential Quadratic Programming method (SQP) on the approximated functions in a current trust region. Then, continuous values are rounded to the nearest integer values for discrete variables. Utilizing integer values as a starting point, the Hooke-Jeeves assisted MAM is applied to search for the discrete optimal solution in the sub-space of discrete variables as well as accordingly update the sub-optimal values for continuous design variables by SQP. The proposed hybrid algorithm is examined by the well established benchmark example and the obtained results demonstrate the superiority of the developed algorithm over GA in terms of computational cost and the quality of solutions.
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