Fuzzy Quadratic Programming with Non-negative Parameters: A Solving method based on Decomposition

Taghi-Nezhad, Nemat Allah; Babakordi, Fatemeh

doi:10.22105/dmor.2019.84073

Document Type : Original Article

Authors

Department of Mathematics, Faculty of Basic Science, Gonbad Kavous University, Gonbad Kavous, Iran.

https://doi.org/10.22105/dmor.2019.84073

Abstract

Quadratic programming problem is one of the important problem of classic optimization problems that the aim is to find the maximum or minimum amount of a quadratic function under linear constraints. In this paper, the quadratic programming problem where its parameters are all nonnegative fuzzy numbers is discussed and a new algorithm based on fuzzy operations and fuzzy arithmetic is presented where reduced the fuzzy model into three smaller and more simple crisp problem. Then, by solving these crisp models using conventional algorithms such as SQP and by combining these solutions, the optimal solution of the fuzzy problem is obtained. Finally, an example is solved to implement the proposed algorithm and show the applicability of it.

Keywords

Main Subjects

Fuzzy Optimization

References

Glover, F., Lü, Z., & Hao, J. K. (2010). Diversification-driven tabu search for unconstrained binary quadratic problems. 4OR, 8(3), 239-253.

Kochenberger, G., Hao, J. K., Glover, F., Lewis, M., Lü, Z., Wang, H., & Wang, Y. (2014). The unconstrained binary quadratic programming problem: a survey. Journal of combinatorial optimization, 28(1), 58-81.

Takapoui, R., Moehle, N., Boyd, S., & Bemporad, A. (2017). A simple effective heuristic for embedded mixed-integer quadratic programming. International journal of control, 1-11.

Taghi-Nezhad, N. A., Taleshian, F., & Shahini, M. (In Press). A new approach for solving interval quadratic programming problem. Iranian journal of optimization.

Liuzzi, G., Locatelli, M., & Piccialli, V. (2019). A new branch-and-bound algorithm for standard quadratic programming problems. Optimization methods and software, 34(1), 79-97.

Taleshian, F., Fathali, J., & Allah Taghi-Nezhad, N. (2018). Fuzzy majority algorithms for the 1-median and 2-median problems on a fuzzy tree. Fuzzy information and engineering, 10(2), 225-248.

Taleshian, F., & Fathali, J. (2016). A mathematical model for fuzzy-median problem with fuzzy weights and variables. Advances in operations research. http://dx.doi.org/10.1155/2016/7590492

Nasseri, S. H., Taghi-Nezhad, N. A., & Ebrahimnejad, A. (2017). A novel method for ranking fuzzy quantities using center of incircle and its application to a petroleum distribution center evaluation problem. International journal of industrial and systems engineering, 27(4), 457-484.

Molai, A. A. (2014). A new algorithm for resolution of the quadratic programming problem with fuzzy relation inequality constraints. Computers & industrial engineering, 72, 306-314.

Taghi-Nezhad, N. A., & Taleshian, F. (2018). A solution approach for solving fully fuzzy quadratic programming problems. Journal of applied research on industrial engineering, 5(1), 50-61.

Ghanbari, R., Ghorbani-Moghadam, K., & Mahdavi-Amiri, N. (2019). A variables neighborhood search algorithm for solving fuzzy quadratic programming problems using modified Kerre’s method. Soft computing, 1-11.

Goodarzi, F. K., Taghinezhad, N. A., & Nasseri, S. H. (2014). A new fuzzy approach to solve a novel model of open shop scheduling problem. University politehnica of Bucharest scientific bulletin-series a-applied mathematics and physics, 76(3), 199-210.

Ezzati, R., Khorram, E., & Enayati, R. (2015). A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Applied mathematical modelling, 39(12), 3183-3193.

Journal of Decisions and Operations Research

Fuzzy Quadratic Programming with Non-negative Parameters: A Solving method based on Decomposition

References

References

Volume 3, Issue 4
March 2019
Pages 325-332

Fuzzy Quadratic Programming with Non-negative Parameters: A Solving method based on Decomposition

References

References

Volume 3, Issue 4March 2019Pages 325-332

Volume 3, Issue 4
March 2019
Pages 325-332