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Covering a square with six circles by deterministic global optimization

Abstract : 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.
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Submitted on : Monday, February 18, 2019 - 9:27:38 PM
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Sonia Cafieri, Pierre Hansen, Frédéric Messine. Covering a square with six circles by deterministic global optimization. LeGO 2018: 14th International Workshop on Global Optimization, Sep 2018, Leiden, Netherlands. pp.020024, ⟨10.1063/1.5089991⟩. ⟨hal-02023555⟩

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