Reduced Outer Space Algorithm for Globally Computing Affine Sum-of-Ratios Problems

Hongwei Jiao, Junqiao Ma () and Youlin Shang ()
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Hongwei Jiao: School of Mathematical Sciences, Henan Institute of Science and Technology, Hualan Street, Henan, Xinxiang 453003, P. R. China
Junqiao Ma: School of Mathematical Sciences, Henan Institute of Science and Technology, Hualan Street, Henan, Xinxiang 453003, P. R. China
Youlin Shang: School of Mathematical Sciences, Henan University of Science and Technology, Kaiyuan Street, Henan, Luoyang 471023, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2025, vol. 42, issue 03, 1-21

Abstract: This paper investigates the affine sum-of-ratios problem (SRP) which has numerous applications in many fields of economy and engineering. For globally computing the affine SRP, based on equivalent transformation and new affine relaxation problem, a reduced outer space branch-and-bound algorithm is designed. The designed algorithm has been proven to converge to a global optimal solution of the problem (SRP) eventually. Meanwhile, the maximum iteration time for the algorithm in the worst case is estimated by analyzing its computational complexity. Finally, numerical experimental results indicate that the presented algorithm is robust and effective.

Keywords: Global optimization; reduced outer space algorithm; affine sum-of-ratios; affine relaxation method; branch-and-bound (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0217595924500155

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