یک روش جدید برای حل مساله برنامه ریزی درجه دوم بازه ای

Subject Areas : Non linear Programming

نعمت اله  تقی نژاد ¹ (Department of Mathematics, Faculty of basic sciences, Gonbad Kavous University, Gonbad, Iran)
فاطمه  تالشیان ² (Department of Mathematics, Shahrood University of Technology, Iran)
مهدی  شهینی ³ (Department of Mathematics, Faculty of basic sciences, Gonbad Kavous University, Gonbad, Iran)

Received: 2017-12-28 Accepted : 2018-07-15 Published : 2019-06-01

Keywords: برنامه ریزی درجه دوم, عدد بازه ای, برنامه ریزی بازه ای, برنامه ریزی درجه دوم بازه ای,

Abstract :

در این مقاله یک مسئله برنامه ریزی درجه دوم بازه ای(IQP) مورد بحث قرار می گیرد، جایی که ضریب محدودیت ها و سمت راست قیود با داده های بازه ای نمایش داده شده است. در ابتدا، یک روش معمول برای حل مسئله برنامه نویسی خطی بازه ای مورد بررسی قرار میگیرد سپس این ایده به مساله IQP گسترش می یابد.بر اساس این روش، هر مسئله IQP به دو مسئله برنامه ریزی درجه دوم کلاسیک تجزیه میشود که با استفاده از الگوریتم SQPحل میشود. در انتها نیز نتایج عددی ارائه می شوند.    

References:

Aboudolas, A. K., Papageorgiou, M., Kouvelas, A., & Kosmatopoulos, E. (2010). A rolling-horizon quadratic-programming approach to the signal control problem in large-scale congested urban road network. Transportation Research Part C: Emerging Technologies, 8(5), 680-694.

Allahdadi, M., Nehi, H. M., Ashayerinasab, H. A., & Javanmard, M. (2016). Improving the modified interval linear programming method by new techniques. Information Sciences, 339, 224-236.

Ashayerinasab, H., MishmastNehi, H., & M., A. (2018). Solving the interval linear programming problem: A new algorithm for a general case. Expert Systems With Applications, 93, 39–49.

Bayo, N. L., Grau, J. M., Ruiz, P. M., & Sua´rez, M. M. (2010). Initial Guess of the Solution of Dynamic Optimization of Chemical Processes. Journal of Mathematical Chemistry, 48(1), 27-38.

Bazaraa, M. S., Sherali, H. D., & Shetty, C. M. (1993). Nonlinear Programming: Theory and Algorithm: Second Edition. NJ, USA: John Wiley & Sons.

Ding, K., & Huang, N. J. (2008). A new class of interval projection neural networks for solving interval quadratic program. Chaos Solitons and Fractals, 35(4), 718–725.

Ebrahimnejad, A., Ghomi, S. J., & & Mirhosseini-Alizamini, S. M. (2018). A revisit of numerical approach for solving linear fractional programming problem in a fuzzy environment. Applied Mathematical Modelling, 57, 459-473.

Frasch, J. V., Sager, S., & Diehl, M. (2015). A parallel quadratic programming method for dynamic optimization problems. Mathematical Programming Computation, 7(3), 289-329.

Gill, P. E., & Wong, E. (2015). Methods for convex and general quadratic programming. Mathematical Programming Computation, 7(1), 71-112.

Gupta. (1995). Applications of Quadratic Programming. Journal of Information and Optimization Sciences, 16(1), 177-194.

Hertoga, D., Roosa, B., & Terlakya, T. (1991). A Polynomial Method of Weighted Centers for Convex Quadratic Programming. Journal of Information and Optimization Sciences, 12(2), 187-205.

Hladík, M. (2014). How to determine basis stability in interval linear programming. Optimization Letters, 8(1), 375-389.

Hladík, M. (2017). On strong optimality of interval linear programming. Optimization Letters, 11(7), 1459-1468.

Ishizaki, A. T., Koike, M., Ramdani, N., Ueda, Y., Masuta, T., Oozeki, T., . . . Imura, J. I. (2016). Interval quadratic programming for day-ahead dispatch of uncertain predicted demand,. Automatica, 64, 163-173.

Jafari, H. S. (2010). Solving Nonlinear Klein-Gordon Equation with A Quadratic Nonlinear Term Using Homotopy Analysis Method. Iranian Journal of Optimization, 2(2), 162-172.

Khalili Goodarzi, F., 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.

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.

Kozlov, M. K., Tarasov, S. P., & Khachiyan, L. G. (1980). The polynomial solvability of convex quadratic programming. USSR Computational Mathematics and Mathematical Physics, 20(5), 223-228.

Lio, S. T., & Wang, R. T. (2007). A numerical solution method to interval quadratic programming. Applied Mathematics and Computation, 189, 1274-1281.

Lodwick, W. (2011). Interval Analysis, Fuzzy Set Theory and Possibility Theory in Optimization. Certainty Optimization, 1-68.

Mishmast Nehi, H., Ashayerinasab, H.A. & Allahdadi, M. Oper Res Int J (2018). https://doi.org/10.1007/s12351-018-0383-4

Mohd, I. B. (2006). A global optimization using interval arithmetic. Journal of Fundamental Science, 2, 76-88.

Nasseri, S. H., Taghi-Nezhad, N. A., & Ebrahimnejad, A. (2017a). 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.

Nasseri, S. H., Taghi-Nezhad, N., & Ebrahimnejad, A. (2017b). A Note on Ranking Fuzzy Numbers with an Area Method using Circumcenter of Centroids. Fuzzy Information and Engineering, 9(2), 259-268.

Pardalos, P. M., & Vavasis, S. A. (1991). Quadratic programming with one negative eigenvalue is NP-hard. J. Global Optim, 1(1), 15-22.

Rezai Balf, F., Hosseinzadeh Lotfi, F., & Alizadeh Afrouzi, M. (2010). The interval Malmquist productivity index in DEA. Iranian Journal of Optimization, 4(1), 311-322.

Shaocheng, T. (1994). Interval number and fuzzy number linear programming. Fuzzy Sets and Systems, 66, 301-306.

Taghi-Nezhad, N., Taleshian, F. (2018). A Solution Approach for Solving Fully Fuzzy Quadratic Programming Problems. Journal of Applied Research on Industrial Engineering, 5(1), 50-61. doi: 10.22105/jarie.2018.111797.1028

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.

Taleshian, F., & Fathali, J. (2016). A Mathematical Model for Fuzzy-Median Problem with Fuzzy Weights and Variables. Advances in Operations Research. doi:10.1155/2016/7590492

Taleshian, F., Fathali, J., & Taghi-Nezhad, N. A. (in press). Fuzzy majority algorithms for the 1-median and 2-median problems on a fuzzy tree. Fuzzy Information and Engineering.

Wang, S., & Huang, G. H. (2013). Interactive fuzzy boundary interval programming for air quality management under uncertainty. Water, Air, & Soil Pollution, 224, 1573-1589.

Yang, Y., & Cao, J. (2008). A feedback neural network for solving convex constraint optimization problems. Applied Mathematics and Computation, 201(1-2), 340–350.

Zhou, J., Cheng, S., & Li, M. (2012). University of Michigan-schanghai. Sequantal quadratic programming for robust optimization with interval uncertainty, 134, 1-13.