The circle packing problem: A theoretical comparison of various convexification techniques

IF 0.8 4区 管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Aida Khajavirad
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引用次数: 0

Abstract

We consider the problem of packing a given number of congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex quadratically constrained optimization problem, which possesses many local optima. We consider several popular convexification techniques, giving rise to linear programming relaxations and semidefinite programming relaxations for the circle packing problem. We compare the strength of these relaxations theoretically, thereby proving the conjectures by Anstreicher. Our results serve as a theoretical justification for the ineffectiveness of existing machinery for convexification of non-overlapping constraints.
圆包装问题:各种凸化技术的理论比较
我们把在单位正方形中填入给定数量、半径最大的全等圆的问题视为一个数学优化问题。由于存在非重叠约束,这个问题是一个臭名昭著的非凸二次约束优化难题,其中有许多局部最优点。我们考虑了几种流行的凸化技术,为圆包装问题提出了线性规划松弛和半定量规划松弛。我们从理论上比较了这些松弛的强度,从而证明了 Anstreicher 的猜想。我们的结果从理论上证明了现有非重叠约束凸化机制的无效性。
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来源期刊
Operations Research Letters
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.
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