Solving the sum-of-ratios problem by a stochastic search algorithm



In spite of the recent progress in fractional programming, the sum-of-ratios problem remains untoward. Freund and Jarre proved that this is an NP-complete problem. Most methods overcome the difficulty using the deterministic type of algorithms, particularly, the branch-and-bound method. In this paper, we propose a new approach by applying the stochastic search algorithm introduced by Birbil, Fang and Sheu to a transformed image space. The algorithm then computes and moves sample particles in the q − 1 dimensional image space according to randomly controlled interacting electromagnetic forces. Numerical experiments on problems up to sum of eight linear ratios with a thousand variables are reported. The results also show that solving the sum-of-ratios problem in the image space as proposed is, in general, preferable to solving it directly in the primal domain.


Sum-of-ratios problems Min-max problems Dinkelbach-type method Branch-and-bound method Stochastic search method 


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© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  • Wei-Ying Wu
    • 1
  • Ruey-Lin Sheu
    • 2
  • Ş. İlker Birbil
    • 3
  1. 1.Department of Statistics and ProbabilityMichigan State UniversityEast LansingUSA
  2. 2.Department of MathematicsNational Cheng Kung UniversityTainanTaiwan
  3. 3.Faculty of Engineering and Natural SciencesSabancı UniversityOrhanli-TuzlaTurkey

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