Near optimal minimal convex hulls of disks

Abstract The minimal convex hulls of disks problem is to find such arrangements circular in the plane that minimize length hull boundary. mixed-integer non-linear programming model, named [17], works only for small moderate-sized problems. Here we propose a polylithic framework big instances by combining following algorithms and models: (i) A fast disk-packing algorithm based on Voronoi diagrams, (NLP) models packing disks, an NLP model minimizing discretized perimeter hull; (ii) convex-hull compute disk their lengths; (iii) taking output as its input. We present complete analytic solutions problems up four semi-analytic linear which yields exact strip with one thousand congruent disks. It turns out proposed approach fine large containing 1,000 Monolithic using usually outperform other approaches. better than results [17] provides benchmark suite further research.