A novel branch‐and‐bound algorithm for solving linear multiplicative programming problems

Peng Hu, Hengyang Gu, Bowen Wang
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Abstract

This article proposes a rectangular branch‐and‐bound algorithm for solving linear multiplication problems (LMP) globally. In order to obtain a reliable lower bound of the original problem, this article designs a novel linear relaxation programming problem (LRP) that has not been seen in the existing literature. Based on the basic framework of the rectangular branch and bound algorithm, this article proposes an algorithm that can obtain a global solution. According to the structure of linear relaxation programming, the article designs a region reduction technology to improve the efficiency of the algorithm. This article also provides convergence analysis to ensure the reliability of the algorithm. Finally, several numerical experiments are used to demonstrate the effectiveness and robustness of the algorithm.
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解决线性乘法编程问题的新型分支与边界算法
本文提出了一种全局求解线性乘法问题(LMP)的矩形分支与边界算法。为了获得原始问题的可靠下界,本文设计了一个新颖的线性松弛编程问题(LRP),这在现有文献中尚未见到。基于矩形分支与边界算法的基本框架,本文提出了一种可以获得全局解的算法。根据线性松弛编程的结构,文章设计了一种区域缩减技术,以提高算法的效率。本文还提供了收敛性分析,以确保算法的可靠性。最后,通过几个数值实验证明了算法的有效性和鲁棒性。
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