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Solving an optimization packing problem of circles and non-convex polygons with rotations into a multiply connected region

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Author Info

  • Y G Stoyan

    (Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine)

  • M V Zlotnik

    (Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine)

  • A M Chugay

    (Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine)

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    Abstract

    This paper deals with the packing problem of circles and non-convex polygons, which can be both translated and rotated into a strip with prohibited regions. Using the Φ-function technique, a mathematical model of the problem is constructed and its characteristics are investigated. Based on the characteristics, a solution approach to the problem is offered. The approach includes the following methods: an optimization method by groups of variables to construct starting points, a modification of the Zoutendijk feasible direction method to search for local minima and a special non-exhaustive search of local minima to find an approximation to a global minimum. A number of numerical results are given. The numerical results are compared with the best known ones.

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    Bibliographic Info

    Article provided by Palgrave Macmillan in its journal Journal of the Operational Research Society.

    Volume (Year): 63 (2012)
    Issue (Month): 3 (March)
    Pages: 379-391

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    Handle: RePEc:pal:jorsoc:v:63:y:2012:i:3:p:379-391

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