PACKING DIFFERENT-SIZED CIRCLES INTO A RECTANGULAR CONTAINER

This paper is motivated by the problem of fitting pipes of different d iameters into a shipping container. Here we study the subproblem of fi tting circles of different sizes into a rectangle since that problem i s a central part of the larger problem. We formulate this situation as a nonlinear mixed integer programming problem and develop a number of heuristic procedures for (approximately) solving this problem. The he uristics are based on a variety of solution building rules that emulat e the process of packing a container. Some of these methods, including a genetic algorithm, were based on a more structured design intended to provide solutions which are 'stable' from a stowage viewpoint. Thes e heuristics are described in detail and their relative performances a re compared for a sample set of 66 randomly generated problems. Based on this sample, the best performing heuristic methods were a quasi-ran dom technique and a genetic algorithm of the 'stable' solution structu re.