Global Optimization Approach to Unequal Global Optimization Approach to Unequal Sphere Packing Problems in 3D

A. Sutou and Y. Dai
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A. Sutou: Central Research Laboratory, Hitachi
Y. Dai: University of Illinois at Chicago

Journal of Optimization Theory and Applications, 2002, vol. 114, issue 3, No 9, 694 pages

Abstract: Abstract The problem of the unequal sphere packing in a 3-dimen-sional polytope is analyzed. Given a set of unequal spheres and a poly-tope, the double goal is to assemble the spheres in such a way that (i) they do not overlap with each other and (ii) the sum of the volumes of the spheres packed in the polytope is maximized. This optimization has an application in automated radiosurgical treatment planning and can be formulated as a nonconvex optimization problem with quadratic constraints and a linear objective function. On the basis of the special structures associated with this problem, we propose a variety of algorithms which improve markedly the existing simplicial branch-and-bound algorithm for the general nonconvex quadratic program. Further, heuristic algorithms are incorporated to strengthen the efficiency of the algorithm. The computational study demonstrates that the proposed algorithm can obtain successfully the optimization up to a limiting size.

Keywords: nonconvex quadratic programming; unequal sphere packing problem; simplicial branch-and-bound algorithm; LP relax-ation; heuristic algorithms (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (8)

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DOI: 10.1023/A:1016083231326

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