On the combined inverse-square effect of multiple points in multidimensional space

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2024-07-01 DOI:10.1016/j.orl.2024.107139

Keaton Coletti , Pawel Kalczynski , Zvi Drezner

引用次数: 0

Abstract

The inverse-square law states that a source's effect is inversely proportional to the distance from that source squared. In continuous location problems, objective functions often obey the inverse-square law. This work shows that for any region in D dimensions, the maximum inverse-square effect is on the region's boundary if $D < 4$ , the minimum is on the boundary if $D > 4$ , and both the maximum and minimum are on the boundary if $D = 4$ .

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论多维空间中多个点的联合反平方效应

平方反比定律指出，信号源的影响与信号源距离的平方成反比。在连续定位问题中，目标函数通常遵循平方反比定律。这项研究表明，对于任何 D 维区域，如果 D<4 ，最大反平方效应位于区域边界；如果 D>4 ，最小反平方效应位于边界；如果 D=4 ，最大反平方效应和最小反平方效应都位于边界。

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

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

期刊介绍： Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.