Sparse Balanced Layout of Ellipsoids*

The authors consider the problem of generating spheroidal voids in a three- dimensional domain of complex geometry, with regard for the constraints on the “sparseness” of voids subject to the system balance. The problem is reduced to the optimized layout of ellipsoids of revolution in a convex container (cylinder or cuboid), taking into account the prohibited zones, constraints on the feasible distances between objects, and the balance condition. The problem is aimed at maximizing the minimum distance between each pair of ellipsoids and each ellipsoid and the boundary of the container. Adjusted quasi-phi-functions for analytical description of the allocation constraints are defined. A mathematical model is constructed in the form of a nonlinear programming problem. A solution method is proposed that uses the multistart strategy in combination with smart algorithms to search for feasible and locally optimal solutions. The results of computating experiments are presented.