PACKING OF ELLIPSOIDS IN A CONVEX CONTAINER
DOI:
https://doi.org/10.26906/SUNZ.2018.1.080Keywords:
packing, ellipsoids, convex container, non-overlapping, containment, quasi-phi-functions, nonlinear optimisationAbstract
We consider the problem of optimal packing of a given collection of unequal ellipsoids into an arbitrary convex container of minimal sizes. To describe non-overlapping, containment and distance constraints we derive phifunctions and quasi-phi-functions. We propose a relaxation approach related to constructing a phi-function forcontainment constraints to avoid equations of more than four degree. We formulate the packing problem in the formof a nonlinear programming problem and propose a solution method that allows us to search for local optimalpackings. We provide computational results illustrated with figures.Downloads
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