A Branch–Reduction–Bound algorithm for linear fractional multi-product planning problems

IF 1.1 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Xianfeng Ding, Meiling Hu
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引用次数: 0

Abstract

In this paper, we propose a Branch–Reduction–Bound (BRB) algorithm to solve fractional multiplicative product programming problems, with the aim of finding globally optimal solutions. The method introduces two innovative linear transformation techniques that simplify the solution process by converting the original problem into two equivalent linear relaxation problems. Building on this, a novel branch-and-delete rule is developed to efficiently manage sub-problem selection using a dynamic priority queue approach, and the computational process is further optimized through a region deletion rule. The synergy of these techniques significantly accelerates the algorithm's convergence rate, providing an efficient global optimization strategy. We compare the BRB algorithm with four other algorithms through numerical experiments, and the results confirm its feasibility, effectiveness, and superior computational efficiency, highlighting its advantages in solving complex optimization problems.

线性分式多积规划问题的分支-约简界算法
在本文中,我们提出了一种分支约简界(BRB)算法来求解分数乘积规划问题,目的是寻找全局最优解。该方法引入了两种创新的线性变换技术,通过将原问题转化为两个等效的线性松弛问题,简化了求解过程。在此基础上,提出了一种新的分支删除规则,采用动态优先队列方法有效地管理子问题的选择,并通过区域删除规则进一步优化计算过程。这些技术的协同作用显著加快了算法的收敛速度,提供了一种高效的全局优化策略。我们通过数值实验将BRB算法与其他四种算法进行了比较,结果证实了BRB算法的可行性、有效性和优越的计算效率,突出了其在解决复杂优化问题方面的优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Combinatorial Optimization
Journal of Combinatorial Optimization 数学-计算机:跨学科应用
CiteScore
2.00
自引率
10.00%
发文量
83
审稿时长
6 months
期刊介绍: The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering. The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.
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