Monkey Algorithm for Packing Circles with Binary Variables

The problem of packing non-congruent circles within a rectangular container is considered. The objective is to place the maximum number of circles inside the container such that no circle overlaps with another one. This problem is known to be NP-Hard. Dealing with these problems efficiently is difficult, so heuristic-based methods have been used. In this paper the problem of packing non-congruent circles is solved using the binary version of monkey algorithm. The proposed algorithm uses a grid for approximating the container and considering the grid points as potential positions for assigning centers of the circles. The algorithm consists of five main routines: the climb process, watch-jump process, repairing process, cooperation process and somersault process. Numerical results on packing non-congruent circles are presented to demonstrate the efficiency of the proposed approach. © 2019, Springer Nature Switzerland AG.