The problem of packing equal spheres in a spherical container is a classic global optimization problem, which has attracted enormous studies in academia and found various applications in industry. This problem is computationally challenging, and many efforts focus on small-scale instances with the number of spherical items less than 200 in the literature. In this work, we propose an efficient local search heuristic algorithm named solution space exploring and descent for solving this problem, which can quantify the solution's quality to determine the number of exploring actions and quickly discover a high-quality solution. Besides, we propose an adaptive neighbor object maintenance method to speed up the convergence of the continuous optimization process and reduce the time consumption. Computational experiments on a large number of benchmark instances with $5 \leq n \leq 400$ spherical items show that our algorithm significantly outperforms the state-of-the-art algorithm. In particular, it improves the 274 best-known results and matches the 84 best-known results out of the 396 well-known benchmark instances.

翻译：等圆球体在球形容器中的装填问题是一个经典的全局优化问题，在学术界引起了广泛研究，并在工业领域有着多种应用。该问题具有极高的计算挑战性，现有文献中多数研究集中于球体数量小于200的小规模实例。本文提出了一种高效的局部搜索启发式算法——解空间探索与下降法，该方法通过量化解的质量来确定探索次数，并能快速发现高质量解。此外，我们还提出了一种自适应邻域对象维护方法，以加速连续优化过程的收敛并降低时间消耗。对含$5 \leq n \leq 400$个球体的大量基准实例进行的计算实验表明，我们的算法显著优于现有最优算法。特别地，在396个已知基准实例中，该算法改进了274个当前最佳已知结果，并匹配了84个最佳已知结果。