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Avtomatika i Telemekhanika, 2017, Issue 9, Pages 131–144 (Mi at14374)  
Optimization, System Analysis, and Operations Research

Optimal placement of rectangles on a plane with fixed objects

G. G. Zabudskiia, T. I. Keinerb

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Omsk, Russia
b Dostoevsky Omsk State University, Omsk, Russia
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Abstract: Consider a region on a plane with a set of points with positive weights and rectangles that have to be place in that region without intersections. Either the maximal sum of weights of the points in rectangles or the total sum must be minimal. We consider the case of two rectangles. The original continuous problem is reduced to a discrete one by introducing equivalence classes. We propose polynomial combinatorial algorithms for solving the problem. We conduct a computational experiment to compare the efficiency of developed algorithms with the IBM ILOG CPLEX suite with an integer programming model.
Keywords: placement problem, influence zone, equivalence classes, minimax criterion, minisum criterion, plane, rectangles.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00740
The research shown in Section 3.2 was supported by the Russian Foundation for Basic Research, project no. 16-01-00740.
Presented by the member of Editorial Board: A. A. Lazarev

Received: 25.02.2016
English version:
Automation and Remote Control, 2017, Volume 78, Issue 9, Pages 1651–1661
DOI: https://doi.org/10.1134/S0005117917090090
Bibliographic databases:
Document Type: Article
PACS: 02.60.Pn
MSC: 90B80
Language: Russian
Citation: G. G. Zabudskii, T. I. Keiner, “Optimal placement of rectangles on a plane with fixed objects”, Avtomat. i Telemekh., 2017, no. 9, 131–144; Autom. Remote Control, 78:9 (2017), 1651–1661
Citation in format AMSBIB
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