Top

Neural Computing and Applications

Published in:

07-03-2016 | Original Article

Branch and bound computational method for multi-objective linear fractional optimization problem

Authors: Deepak Bhati, Pitam Singh

Published in: Neural Computing and Applications | Issue 11/2017

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Present research deals with more efficient solution of a multi-objective linear fractional (MOLF) optimization problem by using branch and bound method. The MOLF optimization problem is reduced into multi-objective optimization problem by a transformation. The reduced multi-objective optimization problem is converted into single objective optimization problem by giving suitable weight for each objective. The equivalency theorems are established. Weak duality concept is used to compute the bounds for each partition and some theoretical results are also established. The proposed method is motivated by the work of Shen et al. (J Comput Appl Math 223:145–158, 2009). Matlab code is designed for the proposed method to run all the simulated results and it is applied on two numerical problems. The efficiency of the method is measured by comparing with earlier established method.

previous article A novel hybrid algorithm for solving continuous single-objective defensive location problem

next article An improved delay-partitioning approach to stability criteria for generalized neural networks with interval time-varying delays

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Schaible S, Shi J (2003) Fractional programming: the sum-of-ratio case. Optim Method Softw 18(2):219–229MathSciNetCrossRefMATH

Henson MA (1981) On sufficiency of the Kuhn–Tucker conditions. J Math Anal Appl 80:545–550MathSciNetCrossRefMATH

Horst R, Tuy H (1996) Global optimization: deterministic approaches. Springer, BerlinCrossRefMATH

Kuhn HW, Tucker AW (1951) Nonlinear programming. In: Neyman J (ed) Proceedings of the second Berkeley symposium on mathematical statistics and probability. University of California Press, Berkeley

Mishra SK et al (2009) Generalized convexity and vector optimization. Nonconvex optimization and its applications. Springer, Berlin

Saad OM (2006) Finding propoer efficient solutions in fuzzy multi-objectve programming. J Stat Manag Syst 9(2):485–496CrossRef

Singh C, Hanson MA (1991) Multi-objectve fractional programming duality theory. Navel Res Logist 38:925–933CrossRefMATH

Leber M, Kaderali L, Schnhuth A, Schrader R (2005) A fractional programming approach to efficient DNA melting temperature calculation. Bioinformatics 21(10):2375–2382CrossRef

Goedhart MH, Spronk J (1995) Financial planning with fractional goals. Eur J Oper Res 82(1):111–124CrossRefMATH

10.

Fasakhodi AA, Nouri SH, Amini M (2010) Water resources sustainability and optimal cropping pattern in farming systems: a multi-objective fractional goal programming approach. Water Res Manag 24:4639–4657CrossRef

11.

Costa JP (2005) An interactive method for multi objective linear fractional programming problem. OR Spectrum 27:633–652CrossRefMATH

12.

Costa JP, Alves MJ (2009) A reference point technique to compute non-dominated solutions in MOLFP. J Math Sci 161(6):820–831MathSciNetCrossRefMATH

13.

Valipour A, Yaghoobi MA, Mashinchi M (2014) An intertive approach to solve multi objective linear fractional programming problems. Appl Math Model 38:38–49MathSciNetCrossRef

14.

Yano H, Sakawa M (1989) Interactive fuzzy decision making for generalized multi objective linear fractional programming problems with fuzzy parameters. Fuzzy Sets Syst 32(3):245–261CrossRefMATH

15.

Chakraborty M, Gupta S (2002) Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Sets Syst 125:335–342MathSciNetCrossRefMATH

16.

Guzel N, Sivri M (2005) Taylor series solution of multi-objective linear fractional programming problem. Trakya Univ J Sci 6(2):80–87

17.

Guzel N (2013) A proposal to the solution of multi-objective linear fractional programming problem. Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2013. Article ID 435030:1–4

18.

Linderoth J (2005) A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs. Math Program Ser 103:251–282MathSciNetCrossRefMATH

19.

Sharma V (2012) Multi-objective integer nonlinear fractional programming problem: a cutting plane approach. OPSEARCH 49(2):133–153MathSciNetCrossRefMATH

20.

Konno H, Fukaishi K (2000) Branch and bound algorithm for solving low rank linear multiplicative and fractional programming problems. J Glob Optim 18:283–299MathSciNetCrossRefMATH

21.

Benson HP (2008) Global maximization of a generalized concave multiplicative function. J Optim Theory Appl 137:105–120MathSciNetCrossRefMATH

22.

Benson HP (2010) Branch-and-bound outer approximation algorithm for sum-of-ratios fractional programs. J Optim Theory Appl 146:1–18MathSciNetCrossRefMATH

23.

Shen PP, Duan YP, Pei YG (2009) A simplicial branch and duality bound algorithm for the sum of convex-convex ratios problem. J Comput Appl Math 223:145–158MathSciNetCrossRefMATH

24.

Zhou XG, Cao BY (2013) A Simplicial branch and bound duality bounds algorithm to linear multiplicative programming. J Appl Math Volume 2013: 1–10, Article ID: 984168

25.

Kim DS (2005) Multiobjective fractional programming with a modified objective function. Commun Korean Math Soc 20:837–847MathSciNetCrossRefMATH

26.

Schaible S (1977) A note on the sum of a linear and linear fractional functions. Naval Res Logist Q 24:691–693CrossRefMATH

27.

Benson HP (2007) Solving sum of ratios fractional programs via concave minimization. J Optim Theory Appl 135:1–17MathSciNetCrossRefMATH

28.

Kanno H, Tsuchiya K, Yamamoto R (2007) Minimization of ratio of function defined as sum of the absolute values. J Optim Theory Appl 135:399–410MathSciNetCrossRefMATH

29.

Chen HJ, Schaible S, Sheu RL (2009) Generic algorithm for generalized fractional programming. J Optim Theory Appl 141:93–105MathSciNetCrossRefMATH

30.

Hackman ST, Passy U (2002) Maximizing linear fractional function on a pareto efficient frontier. J Optim Theory Appl 113(1):83–103MathSciNetCrossRefMATH

31.

Benson HP (2003) Generating sum of ratios test problems in global optimization. J Optim Theory Appl 119(3):615–621MathSciNetCrossRefMATH

32.

Benson HP (2004) On the global optimization of sums of linear fractional functions over a convex set. J Optim Theory Appl 121(1):19–39MathSciNetCrossRefMATH

33.

Benson HP (2002) Global optimization algorithm for the nonlinear sum of ratios problem. J Optim Theory Appl 112(1):1–29MathSciNetCrossRefMATH

34.

Benson HP (2001) Global optimization algorithm for the non-linear sum of ratios problem. J Math Anal Appl 263:301–315MathSciNetCrossRef

35.

Shen P, Jin L (2010) Using canonical partition to globally maximizing the non-linear sum of ratios. Appl Math Model 34:2396–2413MathSciNetCrossRefMATH

36.

Wang YJ, Zhang KC (2004) Global optimization of non-linear sum of ratios problem. Appl Math Appl 158:319–330MathSciNetMATH

37.

Shen PP, Wang CF (2006) Global optimization for sum of ratios problem with coefficient. Appl Math Comput 176:219–229MathSciNetMATH

38.

Jiao H, Shen P (2007) A note on the paper global optimization of non-linear sum of ratios. Appl Math Comput 188:1812–1815MathSciNetMATH

39.

Shen P, Chen Y, Yuan M (2009) Solving sum of quadratic ratios fractional programs via monotonic function. Appl Math Comput 212:234–244MathSciNetMATH

40.

Shen P, Li W, Bai X (2013) Maximizing for the sum of ratios of two convex functions over a convex set. Comput Oper Res 40:2301–2307MathSciNetCrossRefMATH

41.

Shen PP, Wang CF (2008) Global optimization for sum of generalization fractional functions. J Comput Appl Math 214:1–12MathSciNetCrossRefMATH

42.

Jin L, Hou XP (2014) Global optimization for a class non-linear sum of ratios problems Problems in Engineering Volume 2014: Article ID: 103569

43.

Gao Y, Jin S (2013) A global optimization algorithm for sum of linear ratios problem. J Appl Math Volume 2013: 1–10, Article ID: 276245

Title: Branch and bound computational method for multi-objective linear fractional optimization problem
Authors: Deepak Bhati
Pitam Singh
Publication date: 07-03-2016
Publisher: Springer London
Published in: Neural Computing and Applications / Issue 11/2017
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-016-2243-6

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Other articles of this Issue 11/2017

PSO-based feature selection and neighborhood rough set-based classification for BCI multiclass motor imagery task

Transient response characteristic of memristor circuits and biological-like current spikes

Berth and quay crane coordinated scheduling using multi-objective chaos cloud particle swarm optimization algorithm

New fuzzy method for improving the precision of productivity predictions for a factory

A manifold framework of multiple-kernel learning for hyperspectral image classification

Symbiotic organisms search algorithm for optimal power flow problem based on valve-point effect and prohibited zones

Premium Partner