پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 691 |
| تعداد مقالات | 10,035 |
| تعداد مشاهده مقاله | 71,039,328 |
| تعداد دریافت فایل اصل مقاله | 62,488,786 |
On the structure of the equitably nondominated set of multi-objective optimization problems | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 25، دوره 15، شماره 7، مهر 2024، صفحه 289-298 اصل مقاله (440.43 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.30970.4529 | ||
| نویسندگان | ||
| davoud Foroutannia* ؛ Fatemeh Ahmadi | ||
| Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran | ||
| تاریخ دریافت: 04 خرداد 1402، تاریخ بازنگری: 27 خرداد 1402، تاریخ پذیرش: 25 تیر 1402 | ||
| چکیده | ||
| This paper is mainly concerned with some of the theoretical aspects of equitable multi-objective optimization. By using the equitability preference structure, we discuss some properties of the equitably nondominated set, such as nonemptiness, external stability and connectedness. Also, we introduce the concept of proper equitable nondominance, and show that these solutions can be obtained by minimizing a weighted sum of the sort of objective functions where all weights are positive and decreasing. Moreover, we present a hybrid scalarization problem to generate equitably nondominated solutions. This method also provides a necessary condition for the existence of properly equitable nondominated solutions. | ||
| کلیدواژهها | ||
| Nondominancy؛ Proper nondominance؛ Equitability؛ External stability؛ Connectedness؛ Multi-objective programming | ||
| مراجع | ||
|
[1] M. Ehrgott, Multicriteria Optimization, Springer Verlag, Berlin, 2005. [2] D. Foroutannia and A. Mahmodinejad, The concept of B-efficient solution in fair multi-objective optimization problems, Iran. J. Numer. Anal. Optim. 7 (2017), no. 1, 47–64. [3] M.M. Kostreva and W. Ogryczak, Linear optimization with multiple equitable criteria, RAIRO Oper. Res. 33 (1999), no. 3, 275–297. [4] M.M. Kostreva, W. Ogryczak and A. Wierzbicki, Equitable aggregations in multiple criteria analysis, Eur. J. Oper. Res. 158 (2004), no. 2, 362–377. [5] M.O. Lorenz, Methods of measuring the concentration of wealth, J. Am. Stat. Assoc. 9 (1905), 209–219. [6] D.T. Luc, Theory of Vector Optimization, Springer Verlag, Berlin, 1989. [7] A.W. Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications, Academic Press, New York, 1979. [8] W. Ogryczak, Multiple criteria linear programming model for portfolio selection, Ann. Oper. Res. 97 (2000), 143–162. [9] W. Ogryczak, Inequality measures and equitable approaches to location problems, Eur. J. Oper. Res. 122 (2000), no. 2, 374–391. [10] W. Ogryczak, H. Luss, M. Pioro, D. Nace, and A. Tomaszewski, Fair optimization and networks: a survey, J. Appl. Math., 2014 (2014), Article ID 612018. [11] W. Ogryczak, A. Wierzbicki, and M. Milewski, A multi-criteria approach to fair and efficient bandwidth allocation, Omega, 36 (2008), 451–463. [12] W. Ogryczak and M. Zawadzki, Conditional median: a parametric solution concept for location problems, Ann. Oper. Res. 110 (2002), 167–181. [13] L. Pourkarimi and M. Soleimani-damaneh, Existence, Proper Pareto reducibility, and connectedness of the nondominated set in multi-objective optimization, J. Nonlinear Convex Anal. 19 (2018), 1287–1295. [14] V.K. Singh, Equitable efficiency in Multiple Criteria Optimization, Ph.D. Thesis, Clemson University, 2007. | ||
|
آمار تعداد مشاهده مقاله: 13,571 تعداد دریافت فایل اصل مقاله: 17,543 |
||