Computing non-dominated solutions in MOLFP In this paper we present a technique to compute the maximum of a weighted sum of the objective functions in multiple objective linear fractional programming (MOLFP). The basic idea of the technique is to divide (by the approximate `middle’) the non-dominated region in two sub-regions and to analyze each of them in order to discard one if it can be proved that the maximum of the weighted sum is in the other. The process is repeated with the remaining region. The process will end when the remaining regions are so little that the differences among their non-dominated solutions are lower than a pre-defined error. Through the discarded regions it is possible to extract conditions that establish weight indifference regions. These conditions define the variation range of the weights that necessarily leads to the same non-dominated solution. An example, illustrating the concept, is presented. Some computational results indicating the performance of the technique are also presented.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Arya, Rubi; Singh, Pitam: Fuzzy parametric iterative method for multi-objective linear fractional optimization problems (2017)
  2. Bhati, Deepak; Singh, Pitam; Arya, Rubi: A taxonomy and review of the multi-objective fractional programming (MOFP) problems (2017)
  3. Jahanshahloo, G. R.; Talebian, B.; Lotfi, F. Hosseinzadeh; Sadeghi, J.: Finding a solution for multi-objective linear fractional programming problem based on goal programming and data envelopment analysis (2017)
  4. Mirdehghan, S. Morteza; Rostamzadeh, Hassan: Finding the efficiency status and efficient projection in multiobjective linear fractional programming: a linear programming technique (2016)
  5. Jiao, Hong-Wei; Liu, San-Yang: A practicable branch and bound algorithm for sum of linear ratios problem (2015)
  6. Mehdi, Meriem Ait; Chergui, Mohamed El-Amine; Abbas, Moncef: An improved method for solving multiobjective integer linear fractional programming problem (2014)
  7. Costa, João Paulo; Alves, Maria João: Enhancing computations of nondominated solutions in MOLFP via reference points (2013)
  8. Zerdani, Ouiza; Moulai, Mustapha: Optimization over an integer efficient set of a multiple objective linear fractional problem (2011)
  9. Costa, J. P.; Alves, M. J.: A reference point technique to compute nondominated solutions in MOLFP (2009)
  10. Chergui, Mohamed El-Amine; Moulaï, Mustapha: An exact method for a discrete multiobjective linear fractional optimization (2008)
  11. Costa, João Paulo: Computing non-dominated solutions in MOLFP (2007)
  12. Costa, João Paulo: An interactive method for multiple objective linear fractional programming problems (2005)