IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v62y2015i2p565-588.html
   My bibliography  Save this article

An improved test set approach to nonlinear integer problems with applications to engineering design

Author

Listed:
  • J. Gago-Vargas
  • I. Hartillo
  • J. Puerto
  • J. Ucha

Abstract

Many problems in engineering design involve the use of nonlinearities and some integer variables. Methods based on test sets have been proposed to solve some particular problems with integer variables, but they have not been frequently applied because of computation costs. The walk-back procedure based on a test set gives an exact method to obtain an optimal point of an integer programming problem with linear and nonlinear constraints, but the calculation of this test set and the identification of an optimal solution using the test set directions are usually computationally intensive. In problems for which obtaining the test set is reasonably fast, we show how the effectiveness can still be substantially improved. This methodology is presented in its full generality and illustrated on two specific problems: (1) minimizing cost in the problem of scheduling jobs on parallel machines given restrictions on demands and capacity, and (2) minimizing cost in the series parallel redundancy allocation problem, given a target reliability. Our computational results are promising and suggest the applicability of this approach to deal with other problems with similar characteristics or to combine it with mainstream solvers to certify optimality. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • J. Gago-Vargas & I. Hartillo & J. Puerto & J. Ucha, 2015. "An improved test set approach to nonlinear integer problems with applications to engineering design," Computational Optimization and Applications, Springer, vol. 62(2), pages 565-588, November.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:2:p:565-588
    DOI: 10.1007/s10589-015-9739-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-015-9739-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-015-9739-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ouzineb, Mohamed & Nourelfath, Mustapha & Gendreau, Michel, 2008. "Tabu search for the redundancy allocation problem of homogenous series–parallel multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1257-1272.
    2. David W. Coit & Alice E. Smith & David M. Tate, 1996. "Adaptive Penalty Methods for Genetic Optimization of Constrained Combinatorial Problems," INFORMS Journal on Computing, INFORMS, vol. 8(2), pages 173-182, May.
    3. Castro, F. & Gago, J. & Hartillo, I. & Puerto, J. & Ucha, J.M., 2011. "An algebraic approach to integer portfolio problems," European Journal of Operational Research, Elsevier, vol. 210(3), pages 647-659, May.
    4. Duan Li & Xiaoling Sun, 2006. "Nonlinear Integer Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-32995-6, December.
    5. Martin Schlüter & Matthias Gerdts, 2010. "The oracle penalty method," Journal of Global Optimization, Springer, vol. 47(2), pages 293-325, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Umesh Balande & Deepti Shrimankar, 2020. "An oracle penalty and modified augmented Lagrangian methods with firefly algorithm for constrained optimization problems," Operational Research, Springer, vol. 20(2), pages 985-1010, June.
    2. Vahid Baradaran & Amir Hossein Hosseinian, 2020. "A bi-objective model for redundancy allocation problem in designing server farms: mathematical formulation and solution approaches," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 11(5), pages 935-952, October.
    3. Rashika Gupta & Manju Agarwal, 2006. "Penalty guided genetic search for redundancy optimization in multi-state series-parallel power system," Journal of Combinatorial Optimization, Springer, vol. 12(3), pages 257-277, November.
    4. Chang, Kuo-Hao & Kuo, Po-Yi, 2018. "An efficient simulation optimization method for the generalized redundancy allocation problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1094-1101.
    5. Ardakan, Mostafa Abouei & Talkhabi, Sajjad & Juybari, Mohammad N., 2022. "Optimal activation order vs. redundancy strategies in reliability optimization problems," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    6. Li, Chun-yang & Chen, Xun & Yi, Xiao-shan & Tao, Jun-yong, 2010. "Heterogeneous redundancy optimization for multi-state series–parallel systems subject to common cause failures," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 202-207.
    7. Dunker, Thomas & Radons, Gunter & Westkamper, Engelbert, 2005. "Combining evolutionary computation and dynamic programming for solving a dynamic facility layout problem," European Journal of Operational Research, Elsevier, vol. 165(1), pages 55-69, August.
    8. Abdossaber Peiravi & Mahdi Karbasian & Mostafa Abouei Ardakan, 2018. "K-mixed strategy: A new redundancy strategy for reliability problems," Journal of Risk and Reliability, , vol. 232(1), pages 38-51, February.
    9. Peiravi, Abdossaber & Nourelfath, Mustapha & Zanjani, Masoumeh Kazemi, 2022. "Universal redundancy strategy for system reliability optimization," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    10. Gholinezhad, Hadi & Zeinal Hamadani, Ali, 2017. "A new model for the redundancy allocation problem with component mixing and mixed redundancy strategy," Reliability Engineering and System Safety, Elsevier, vol. 164(C), pages 66-73.
    11. Guo, Jian-Xin & Huang, Chen, 2020. "Feasible roadmap for CCS retrofit of coal-based power plants to reduce Chinese carbon emissions by 2050," Applied Energy, Elsevier, vol. 259(C).
    12. Nourelfath, Mustapha & Châtelet, Eric & Nahas, Nabil, 2012. "Joint redundancy and imperfect preventive maintenance optimization for series–parallel multi-state degraded systems," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 51-60.
    13. Ling, Xiaoliang & Wei, Yinzhao & Si, Shubin, 2019. "Reliability optimization of k-out-of-n system with random selection of allocative components," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 186-193.
    14. Liu, Zhitao & Tan, CherMing & Leng, Feng, 2015. "A reliability-based design concept for lithium-ion battery pack in electric vehicles," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 169-177.
    15. Nikolaos Ploskas & Nikolaos V. Sahinidis, 2022. "Review and comparison of algorithms and software for mixed-integer derivative-free optimization," Journal of Global Optimization, Springer, vol. 82(3), pages 433-462, March.
    16. Nourelfath, Mustapha & Nahas, Nabil & Ben-Daya, Mohamed, 2016. "Integrated preventive maintenance and production decisions for imperfect processes," Reliability Engineering and System Safety, Elsevier, vol. 148(C), pages 21-31.
    17. Cascón, J.M. & González-Arteaga, T. & de Andrés Calle, R., 2019. "Reaching social consensus family budgets: The Spanish case," Omega, Elsevier, vol. 86(C), pages 28-41.
    18. Pourkarim Guilani, Pedram & Sharifi, Mani & Niaki, S.T.A. & Zaretalab, Arash, 2014. "Reliability evaluation of non-reparable three-state systems using Markov model and its comparison with the UGF and the recursive methods," Reliability Engineering and System Safety, Elsevier, vol. 129(C), pages 29-35.
    19. Yuji Nakagawa & Ross J. W. James & César Rego & Chanaka Edirisinghe, 2014. "Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models," Management Science, INFORMS, vol. 60(3), pages 695-707, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:62:y:2015:i:2:p:565-588. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.