This paper deals with the problem of circle packing, in which the largest radii circle is to be fit in a confined space filled with arbitrary circles of different radii and centers. A circle packing problem is one of a variety of cutting and packing problems. We suggest four different nature-inspired Meta-heuristic algorithms to solve this problem. Algorithms are based on the social behavior of other biology species such as birds, wolves, fireflies, and bats. Moreover, recent advancements in these algorithms are also considered for problem-solving. The circle packing problem is one of the NP-hard problems. It is challenging to solve NP-hard problems exactly, so the proposed algorithms provide an approximate solution within the allotted time. Standard statistical parameters are used for comparison, and simulation and results indicate that the problem is highly non-linear and sensitive.

翻译：本文研究圆填充问题，即在充满不同半径和中心位置的任意圆形的密闭空间中，求解最大半径圆的最优放置。圆填充问题属于裁剪与填充问题的一类。我们提出了四种不同的自然启发式元启发算法来解决这一问题。这些算法基于鸟类、狼群、萤火虫和蝙蝠等其他生物物种的社会行为。此外，这些算法的最新进展也被纳入问题求解的考虑范围。圆填充问题属于NP难问题。精确求解NP难问题极具挑战性，因此所提出的算法在限定时间内提供近似解。采用标准统计参数进行比较，仿真与结果表明该问题具有高度非线性和敏感性。