Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Signomial Geometric Programming Approach to Solve Multi-Objective Non-Linear Fractional Programming Problem

Document Type : Original Paper

Authors
Mansour Saraj 1
Abbas Hosseni 2
1 Associated Prof, Faculty of Mathematical Science, Shahid Chamran University of Ahwaz
2 Dept of Mathematics, Shahid Chamran University of Ahvaz
10.22055/jamm.2025.49000.2347
Abstract
In this paper, we present a new method for solving multi-objective nonlinear fractional programming problems, which pose significant challenges in the optimization field due to their inherent complexities. To enhance efficiency and accuracy in solving these types of problems, firstly, by using Dinkelbach’s algorithm, the problem is transformed into a nonlinear programming problem, that this transformation facilitates the problem-solving process. Subsequently, we utilize a signomial geometric programming approach to find the optimal solution. The results obtained demonstrate a significant improvement in findings ompared to traditional methods, in terms of accuracy and efficiency. Finally, in last paper, by

providing a numerical example, we examine the efficiency and accuracy of the proposed algorithm.
Keywords
کلمات کلیدی: برنامه ریزی هندسی سیگنومیال
روش چارنز و کوپر
الگوریتم دینکل باخ
برنامه ریزی کسری غیرخطی چند هدفه
Subjects
[1] Bazikar, F. and Saraj, M., 2014. Solving linear multi-objective geometric programming problems via
reference point approach. Sains Malaysiana, 43(8), pp. 1271-1274.
[2] Cooper, A.C.W. and Charnes, W., 1962. Programming with linear fractional functionals. Naval Research logistics quarterly, 9(3), pp. 181-186. doi: 10.1002/nav.3800090303.
[3] Dinkelbach, W., 1967. On nonlinear fractional programming. Management science, 13(7), pp. 492-
498. doi: 10.1287/mnsc.13.7.492
[4] Duffin, R.J. and Peterson, E.L., 1973. Geometric programming with signomials. Journal of Optimization Theory and Applications, 11(1), pp. 3-35. doi: 10.1007/BF00934288.
[5] Duffin, R.J., Peterson, E.L. and Zener, C.M., 1968. Geometric Programming Theory and Application.
John Wiley and Sons, New York, 10(2), pp. 235-236. doi: 10.1137/1010047.
[6] Ehrgott, M., 2005. Multicriteria optimization. (Vol. 491). Springer Science & Business Media. doi:
10.1007/3-540-27659-9.
[7] Islam, S. and Roy, T.K., 2005. Modified geometric programming problem and its applications. Journal
of Applied Mathematics and Computing, 17(1), pp. 121-144. doi: 10.1007/BF02936045.
[8] Li, H., 2015. A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems. Annals of Operations Research, 235(1), pp. 543-558. doi:
10.1007/s10479-015-1878-5.
[9] Mandal, W.A. and Islam, S., 2019. Modified signomial geometric programming (MSGP) and
its applications. Independent Journal of Management & Production, 10(2), pp. 440-458. doi:
10.14807/ijmp.v10i2.537.
[10] Mishra, S. and Ota, R.R., 2022. Signomial geometric programming approach to solve Non-Linear
fractional programming problems. International Journal of Applied and Computational Mathematics,
8(1), pp. 37-44. doi: 10.1007/s40819-022-01248-x.
[11] Öz, E., Güzel, N. and Alp, S., 2017. An alternative approach to the solution of multiobjective geometric programming problems. Open Journal of Optimization, 6(1), pp. 11-25. doi:
10.4236/ojop.2017.61002.
[12] Ródenas, R.G., López, M.L. and Verastegui, D., 1999. Extensions of Dinkelbach’s algorithm for
solving non-linear fractional programming problems. Top 7, 33–70. doi: 10.1007/BF02564711
[13] Stancu-Minasian, I.M., 1997. Fractional programming: theory, methods and applications (Vol. 409).
Springer Science & Business Media. doi: 10.1007/978-94-009-0035-6.

  • Receive Date 11 February 2025
  • Revise Date 29 July 2025
  • Accept Date 28 October 2025