Abstract
This paper presents an outcome space branch-and-bound algorithm for minimizing a class of linear ratio optimization problems (LROPs), requiring just nonnull denominators in the given domain. The solution methodology uses an affine relaxation of a bilinear approximation model, which is equivalent to the original problem. By combining the relaxation model with the branch-and-bound framework, an outcome space branch-and-bound algorithm is devised for solving LROPs. The algorithm can reduce the computational complexity, as branching is performed in the outcome space with a size equal to the number of fractions, rather than the variable dimension space. Finally, the numerical results indicate the computational feasibility and good performance of the algorithm.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China (No. 61877046, No. 61373174, No. 11602184).
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Communicated by Ernesto G. Birgin.
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Liu, S., Ge, L. An outcome space algorithm for minimizing a class of linear ratio optimization problems. Comp. Appl. Math. 40, 225 (2021). https://doi.org/10.1007/s40314-021-01614-3
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DOI: https://doi.org/10.1007/s40314-021-01614-3
Keywords
- Global optimization
- Linear ratio optimization problem
- Branch-and-bound
- Affine relaxation programming problem