Open AccessCovering a square with six circles by deterministic global optimization
Author(s) -
Sonia Cafieri,
Pierre Hansen,
Frédéric Messine
Publication year - 2019
Publication title -
aip conference proceedings
Language(s) - English
Resource type - Conference proceedings
eISSN - 1551-7616
pISSN - 0094-243X
DOI - 10.1063/1.5089991
Subject(s) - square (algebra) , radius , global optimization , mathematics , mathematical optimization , computer science , combinatorics , geometry , computer security
We consider the problem of covering a square with exactly 6 identical circles of minimal radius. In the literature, a covering is presented by Melissen and Schuur, and conjectured to be optimal. We adress the problem proposing a mathematical programming formulation and solving it to global optimality. We prove that the conjectured optimal covering is indeed the global optimum.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom