The main contribution of this paper is the procedure that constructs a good approximation to the non-dominated set of multiple objective linear fractional programming problem using the solutions to certain linear optimization problems. In our approach we propose a way to generate a discrete set of feasible solutions that are further used as starting points in any procedure for deriving efficient solutions. The efficient solutions are mapped into non-dominated points that form a 0th order approximation of the Pareto front. We report the computational results obtained by solving random generated instances, and show that the approximations obtained by running our procedure are better than those obtained by running other procedures suggested in the recent literature. We evaluated the quality of each approximation using classic metrics.
Accepté le :
DOI : 10.1051/ro/2018083
Mots-clés : Fractional programming, multiple objective programming, efficient solution, non-dominated point, 0th order approximation
@article{RO_2019__53_4_1229_0,
author = {Stanojevi\'c, Bogdana and Stanojevi\'c, Milan},
title = {A computationally efficient algorithm to approximate the pareto front of multi-objective linear fractional programming problem},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1229--1244},
publisher = {EDP-Sciences},
volume = {53},
number = {4},
year = {2019},
doi = {10.1051/ro/2018083},
mrnumber = {3986368},
zbl = {1425.90107},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2018083/}
}
TY - JOUR AU - Stanojević, Bogdana AU - Stanojević, Milan TI - A computationally efficient algorithm to approximate the pareto front of multi-objective linear fractional programming problem JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 1229 EP - 1244 VL - 53 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2018083/ DO - 10.1051/ro/2018083 LA - en ID - RO_2019__53_4_1229_0 ER -
%0 Journal Article %A Stanojević, Bogdana %A Stanojević, Milan %T A computationally efficient algorithm to approximate the pareto front of multi-objective linear fractional programming problem %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 1229-1244 %V 53 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2018083/ %R 10.1051/ro/2018083 %G en %F RO_2019__53_4_1229_0
Stanojević, Bogdana; Stanojević, Milan. A computationally efficient algorithm to approximate the pareto front of multi-objective linear fractional programming problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 4, pp. 1229-1244. doi : 10.1051/ro/2018083. http://www.numdam.org/articles/10.1051/ro/2018083/
[1] and , The controlled estimation method in the multiobjective linear fractional problem. Comput. Oper. Res. 31 (2004) 1821–1832. | DOI | MR | Zbl
[2] , Multicriteria linear fractional programming. Ph.D. thesis. University of British Columbia (1980).
[3] and , Bicriteria linear fractional programming. J. Optim. Theory App. 36 (1982) 203–220. | DOI | MR | Zbl
[4] , Computing non-dominated solutions in MOLFP. Eur. J. Oper. Res. 181 (2007) 1464–1475. | DOI | Zbl
[5] and , A reference point technique to compute non-dominated solutions in MOLFP. J. Math. Sci. 161 (2009) 820–830. | DOI | MR | Zbl
[6] , and , A dual variant of Benson’s “outer approximation algorithm’’ for multiple objective linear programming. J. Global Optim. 57 (2012) 757–778. | DOI | MR | Zbl
[7] , and , Finding representative systems for discrete bicriterion optimization problems. Oper. Res. Lett. 35 (2007) 336–344. | DOI | MR | Zbl
[8] , and , Constructing a pareto front approximation for decision making. Math. Methods Oper. Res. 73 (2011) 209–234. | DOI | MR | Zbl
[9] and , A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems. Eur. J. Oper. Res. 232 (2014) 479–488. | DOI | MR | Zbl
[10] and , Multiple objective linear fractional programming. Manage. Sci. 27 (1981) 1024–1039. | DOI | Zbl
[11] , , , and , A linear programming approach to test efficiency in multi-objective linear fractional programming problems. App. Math. Model. 34 (2010) 4179–4183. | DOI | MR | Zbl
[12] , and , Equispaced pareto front construction for constrained bi-objective optimization. Math. Comput. Model. 57 (2013) 2122–2131. | DOI | MR | Zbl
[13] and , Global solutions to fractional programming problem with ratio of nonconvex functions. Appl. Math. Comput. 255 (2015) 66–72. | MR | Zbl
[14] and , Approximation methods in multiobjective programming. J. Optim. Theory App. 126 (2005) 473–501. | DOI | MR | Zbl
[15] , and , Maximizing for the sum of ratios of two convex functions over a convex set. Comput. Oper. Res. 40 (2013) 2301–2307. | DOI | MR | Zbl
[16] , Fractional Programming: Theory, Methods and Applications. Kluwer Academic Publishers, Alphen aan den Rijn (1997). | DOI | MR | Zbl
[17] and , On the efficiency test in multi-objective linear fractional programming problems by Lotfi et al. 2010. Appl. Math. Model. 37 (2013) 7086–7093. | DOI | MR | Zbl
[18] , and , An iterative approach to solve multiobjective linear fractional programming problems. Appl. Math. Model. 38 (2014) 38–49. | DOI | MR | Zbl
[19] , and , An approximation to the nondominated set of a multiobjective linear fractional programming problem. Optimization 65 (2016) 1539–1552. | DOI | MR | Zbl
[20] and , Metrics for quality assessment of a multiobjective design optimization solution set. J. Mech. Des. 123 (2001) 18–25. | DOI
Cité par Sources :
