.png){kind=icon}
.png){kind=icon}
Return
Spatial Algorithm for Mixed Integer Generalized Affine Multiplicative Problems
.png){kind=icon}
PRE
AI
DOI：10.1007/s10957-026-02959-7.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
In this paper, we propose a novel spatial branch-accelerate-bound algorithm to work out the mixed integer generalized affine multiplicative problem globally. To search for the global optimal solution of the mixed integer generalized affine multiplicative problem, we first transform it into an equivalent problem by introducing new variables and applying exponential transformations. Additionally, by utilizing the convex and concave hull approximation of exponential functions, the mixed integer affine relaxation problem of the equivalent problem can be constructed. Subsequently, by working out the mixed integer affine relaxation problem, the lower bound of the optimal value for the equivalent problem can be acquired. Afterwards, to accelerate the solving speed of the algorithm, by leveraging the special structure of the objective functions of equivalence and relaxation problems, as well as the characteristics of branch-and-bound algorithms, we propose some new spatial acceleration techniques. Based on the branch-and-bound scheme, we design a novel spatial branch-accelerate-bound algorithm for addressing the mixed integer generalized affine multiplicative problem by combining the mixed integer affine relaxation problem with the spatial acceleration techniques. Furthermore, we prove the global convergence of the algorithm and estimate its computational complexity in the worst-case scenario. Finally, numerical experimental results validate the effectiveness of the proposed algorithm, demonstrating its capability to find global optimal solutions for large-scale mixed integer generalized affine multiplicative problem.
Keywords:
Mixed integer generalized affine multiplicative problem
Global optimization
Mixed integer affine relaxation problem
Spatial branch-and-bound search
Acceleration technique
Journal
J
IF:
1.5
Papers:
178
Citations:
8.2K