An efficient algorithm and complexity result for solving the sum of general affine ratios problem

In this paper, with the unique hypothesis that the denominator is not equal to 0, an efficient outer space rectangle branch-and-bound algorithm is presented to globally solve the sum of general affine ratios problem. By using equivalent transformation and the characteristics of general single ratio...

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Vydáno v:Chaos, solitons and fractals Ročník 164; s. 112701
Hlavní autoři: Jiao, Hongwei, Ma, Junqiao
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.11.2022
Témata:
Accelerating technic
Branch-and-bound
Complexity analysis
Global optimization
Sum of general affine ratios
90C32
Branch-and-bound
Sum of general affine ratios
Complexity analysis
Global optimization
90C26
Accelerating technic
ISSN:0960-0779, 1873-2887
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Shrnutí:In this paper, with the unique hypothesis that the denominator is not equal to 0, an efficient outer space rectangle branch-and-bound algorithm is presented to globally solve the sum of general affine ratios problem. By using equivalent transformation and the characteristics of general single ratio function, a linear program relaxation problem is constructed for computing the lower bound of the global minimum value of the original problem. Moreover, to enhance the running speed of the presented algorithm, we design an outer space accelerating technic for deleting the entire outer space rectangle or a part of the entire examined outer space rectangle, in which there contains no the global minimum point of the equivalent problem. Furthermore, through the complexity analysis of the presented algorithm, we estimate its maximum iteration times. In addition, we prove the global convergence of the presented algorithm, report and analyze the numerical computational results for indicating the validity of the presented algorithm. Finally, two practical problems from power transportation and production planning are solved to verify the usefulness of the presented algorithm. •We present a novel outer space branch-and-bound algorithm for the SGAR.•The algorithm economizes the required computations by dividing space.•The main calculation involves solving a series of linear programming problems.•We give the complexity analysis of the algorithm for the first time.•The computing efficiency is significantly higher than the existing algorithms.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2022.112701