Node selection through upper bounding local search methods in branch & bound solvers for NCOPs

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Victor Reyes, Ignacio Araya
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引用次数: 0

Abstract

Interval-based branch & bound solvers are commonly used for solving Nonlinear Continuous global Optimization Problems (NCOPs). In each iteration, the solver strategically chooses and processes a node within the search tree. The node is bisected and the two generated offspring nodes are processed by filtering methods. For each of these nodes, the solver also searches for new feasible solutions in order to update the best candidate solution. The cost of this solution is used for pruning non-optimal branches of the search tree. Thus, node selection and finding new solutions, stands as pivotal aspects in the functionality of these kind of solvers. The ability to find close-to-optimal solutions early in the search process may discard extensive non-optimal search space regions, thereby effectively reducing the overall size of the search tree. In this work, we propose three novel node selection algorithms that use the feasible solutions obtained through a cost-effective iterative method. Upon updating the best candidate solution, these algorithms strategically choose the node containing this solution for subsequent processing. The newly introduced strategies have been incorporated as node selection methods in a state-of-the-art branch & bound solver, showing promising results in a set of 57 benchmark instances.

Abstract Image

在 NCOP 的分支与边界求解器中通过上界局部搜索方法选择节点
基于区间的分支求解器通常用于解决非线性连续全局优化问题(NCOPs)。在每次迭代中,求解器都会战略性地选择并处理搜索树中的一个节点。节点被一分为二,生成的两个子节点通过过滤方法进行处理。对于每个节点,求解器还会搜索新的可行方案,以更新最佳候选方案。该解决方案的成本用于修剪搜索树的非最优分支。因此,节点选择和寻找新的解决方案是这类求解器功能的关键所在。在搜索过程的早期找到接近最优解的能力可以舍弃大量的非最优搜索空间区域,从而有效减少搜索树的整体大小。在这项工作中,我们提出了三种新颖的节点选择算法,它们使用通过经济有效的迭代法获得的可行解。在更新最佳候选解决方案后,这些算法会战略性地选择包含该解决方案的节点进行后续处理。新引入的策略已被作为节点选择方法纳入最先进的分支&约束求解器,在一组 57 个基准实例中显示出良好的效果。
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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