Balanced Circular Packing Problems with Distance Constraints

Abstract

The packing of different circles in a circular container under balancing and distance conditions is considered. Two problems are studied: the first minimizes the container’s radius, while the second maximizes the minimal distance between circles, as well as between circles and the boundary of the container. Mathematical models and solution strategies are provided and illustrated with computational results.

Keywords

• dense circular packing
• sparse circular packing
• balance
• mathematical models
• nonlinear optimization
• Shor’s r-algorithm