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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2013 / Cilt: 3 - Sayı: 2

A multi-parametric programming algorithm for special classes of non-convex multilevel optimization problems

Abay Molla KASSA
Semu Mitiku KASSA
Pages
133–144
Publication Date
2022-10-11
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, a ?-convergence proof is given for the algorithm.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A global solution strategy for multilevel optimization problems with special non-convexityformulation in the objectives of the inner level problems is presented based on branch-and-bound andmulti-parametric programming approach.
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Key Findings & Data:An algorithm to such problems is proposed by convexifyingthe inner level problem while the variables from upper level problems are considered as parameters.The resulting convex parametric under-estimator problem is solved using multi-parametric programming approach.
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Conclusion & Impact:Moreover, a ?-convergence proof is given for the algorithm.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

A global solution strategy for multilevel optimization problems with special non-convexityformulation in the objectives of the inner level problems is presented based on branch-and-bound andmulti-parametric programming approach. An algorithm to such problems is proposed by convexifyingthe inner level problem while the variables from upper level problems are considered as parameters.The resulting convex parametric under-estimator problem is solved using multi-parametric programming approach. A branch-and-bound procedure is employed until a pre-specified positive tolerance issatisfied. Moreover, a ?-convergence proof is given for the algorithm.

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Cite This Article

KASSA, A. M., KASSA, S. M. (2022). A multi-parametric programming algorithm for special classes of non-convex multilevel optimization problems. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 3 - Sayı: 2, 133–144. https://ajindex.com/articles/440740

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References (15)

  1. Migdalas, A., Pardalos, M.P., and V¨arbrand, P., Multilevel optimization: algorithm, theory and applications. Kluwer Acadamic Publisher, (1992)
  2. Vicente, N.L. and Calamai, H.P., Bilevel and multilevel programming: a bibliography review. Journal of Global Optimization, 5, 1 - 9 (1994)
  3. Hansen, P., Jaumard, B., and Savard, G., New branch-and-bound rules for linear bilevel programming. SIAM Journal on Scientific and Statistical Computing, 13, 1194 - 1217 (1992)
  4. Blair, C., The computational complexity of multi-level linear programs. Annals of Operations Research, 34, 13 - 19 (1992)
  5. Bard, J.F., An investigation of the linear three level programming problem. IEEE Transactions on Systems, Man, and Cybernetics, 14, 711 - 717 (1984)
  6. Zhang, G., Lu, J., Montero, J., Zeng, Y., Model, solution concept, and Kth-best algorithm for linear trilevel programming. Information Sciences, 180, 481 - 492 (2010)
  7. Mersha, A.Y., Dempe S., Feasible direction method for bilevel programming problem. Optimization, 61(5), 597 - 616 (2012)
  8. G¨um¨us, Z.H., Floudas C.A., Global Optimization of Nonlinear Bilevel Programming Problems. Journal of Global Optimization, 20, 1 - 31 (2001)
  9. Tilahun, S.L., Kassa S.M., and Ong, H.C., A new algorithm for multilevel optimization problems using evolutionary strategy, inspired by natural selection. In: Anthony, A., Ishizuka, M., and Lukose, D., (Eds.): PRICAI 2012, LNAI 7458, Springer-Verlag, Berlin Heidelberg, 577 - 588 (2012)
  10. Fa´ısca, P.N., Dua, V., Rustem, B., Saraiva, M.P., Pistikopoulos, N.E., Parametric global optimisation for bilevel programming. Journal of Global Optimization, 38, 609 - 623 (2006)
  11. Fa´ısca, P.N., Saraiva, M.P., Rustem, B., Pistikopoulos, N.E., A multiparametric programming approach for multilevel hierarchical and decentralized optimization problems. Computational Management Science, 6, 377 - 397 (2009)
  12. Fiacco, V.A., Sensitivity analysis for nonlinear programming using penalty methods. Mathematical Programming, 10, 287 - 311 (1976)
  13. Dua, V., Pistikopoulos, N.E., An algorithm for the solution of multiparametric mixed integer linear programming problems. Annals of Operations Research, 99, 123 - 139 (2001)
  14. Pistikopoulos, N.E., Georgiadis C.M. and Dua V., (Editors) Multiparametric programming: Theory, algorithm, and application. 15] Fiacco, V.A., Introduction to sensitivity and stability analysis in nonlinear programming. Acadamic press, (1983)
  15. Al-Khayyal, F.A.,