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

  • Authors:

  • Wei-Ying Wu;Ruey-Lin Sheu;Ş. İlker Birbil

  • Affiliations:

  • Department of Statistics and Probability, Michigan State University, East Lansing, USA 48824;Department of Mathematics, National Cheng Kung University, Tainan, Taiwan 701;Faculty of Engineering and Natural Sciences, Sabanc1 University, Orhanli-Tuzla, Turkey 34956

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2008

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Abstract

In spite of the recent progress in fractional programming, thesum-of-ratios problem remains untoward. Freund and Jarre provedthat this is an NP-complete problem. Most methods overcome thedifficulty using the deterministic type of algorithms,particularly, the branch-and-bound method. In this paper, wepropose a new approach by applying the stochastic search algorithmintroduced by Birbil, Fang and Sheu to a transformed image space.The algorithm then computes and moves sample particles in theq - 1 dimensional image space according torandomly controlled interacting electromagnetic forces. Numericalexperiments on problems up to sum of eight linear ratios with athousand variables are reported. The results also show that solvingthe sum-of-ratios problem in the image space as proposed is, ingeneral, preferable to solving it directly in the primaldomain.