Quasi-Packing Different Spheres with Ratio Conditions in a Spherical Container

This paper considers the optimized packing of different spheres into a given spherical container under non-standard placement conditions. A sphere is considered placed in if at least certain part container. Spheres are allowed to overlap with each other according predefined parameters. Ratio conditions introduced establish correspondence between number packed radii. The aims maximize total subject ratio, partial overlapping and quasi-containment nonlinear mixed-integer optimization model proposed for this ratio quasi-packing problem. heuristic algorithm developed that reduces original problem sequence continuous open dimension problems scaled spheres. Computational results finding global solutions small instances good feasible large provided.