Binary monkey algorithm for approximate packing non-congruent circles in a rectangular container

Abstract 
A Packing problem consists in the best arrangement of several objects inside a bounded area named as the container. This arrangement must fulfill with technological constraints, for example, objects should not be overlapping. Some packing models for circular objects are typically formulated as non-convex optimization problems; where the continuous variables are the coordinates of the objects, so they are limited to not finding optimal solutions. Due to the combinatorial nature in the arrangement of such objects, heuristic methods are being used extensively which combine methods of global search and methods of local exhaustive search of local minima or their approximations. In this paper, we will address the packing problem for non-congruent (different size) circles with the binary version of the monkey algorithm which incorporates a cooperation process and a greedy strategy. We use a rectangular grid for covering the container. Every node in the grid represent potential positions for a circle. In this sense, binary monkey algorithm for the knapsack problem, can be used to solve de 0–1 approximate packing problem for non-congruet circles. The binary monkey problem uses two additional processes of the original monkey algorithm, these two processes are a greedy process and a cooperation processes.