## Abstract

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.

Original language | English |
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Pages (from-to) | 91-109 |

Number of pages | 19 |

Journal | Journal of Global Optimization |

Volume | 42 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2008 Sep 1 |

## All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics