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

Y G Stoyan, M V Zlotnik and A M Chugay
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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

Journal of the Operational Research Society, 2012, vol. 63, issue 3, 379-391

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.

Date: 2012
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