Solving the Sum-of-Ratios Problem byStochastic Search Algorithm

• Main Authors: Wei-Ying Wu, 吳韋瑩
• Other Authors: Ruey-Lin Sheu
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/02654251841867886727

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 93 === 　In spite of recent progress in fractional programming, the sum-of-ratios problem remains untoward. Freund and Jarre proved that this is an NP-complete problem. Most of the existing methods overcome the difficulty using the deterministic type of algorithms, particularly the branch-and-bound method. They can solve only the sum of a few ratios. In this paper, we propose a new approach using the stochastic search algorithm by Birbil, Fang and Sheu. It computes each sample point by solving a single ratio problem and then moves the sample points according to randomly controlled interacting ``electromagnetic' forces. To test, we perform numerical experiments on problems up to the sum of sixteen linear ratios and the results are very positive.