A filtered beam search based heuristic algorithm for packing unit circles into a circular container

Abstract

A constructive method for addressing the circular packing problem is proposed based on the filtered beam search framework, with the goal of minimizing the radius of a circular container that can hold N unit circles without overlapping. To position each circle in the container, the proposed method employs a corner-occupying placement strategy. Since there are often multiple possible positions for a circle to be packed, the method employs two steps to select the best placement. The positions are quickly assessed in the first phase, known as the filtering phase. In the second phase, known as the beam selection phase, a computationally intensive strategy is used to evaluate the positions more accurately. To balance the accuracy and efficiency of the method, two parameters are utilized, namely filterwidth and beamwidth. These parameters control the pruning operations in the tree-based search procedure. The performance of the proposed method is assessed utilizing two sets of 19 publicly available instances from the literature, and a comparative analysis is conducted against five constructive-based algorithms and one global optimization method. The computational results demonstrate its competitive performance, surpassing all constructive-based reference algorithms. Furthermore, a thorough investigation is conducted into the suggested method's parameter settings and essential components.