Balanced circular bin packing problems consist in positioning a given number of weighted circles in order to minimize the radius of a circular container while satisfying equilibrium constraints. These problems are NP-hard, highly constrained and dimensional. This paper describes a swarm algorithm based on a virtual-force system in order to solve balanced circular bin packing problems. In the proposed approach, a system of forces is applied to each component allowing to take into account the constraints and minimizing the objective function using the fundamental principle of dynamics. The proposed algorithm is experimented and validated on benchmarks of various balanced circular bin packing problems with up to 300 circles. The reported results allow to assess the effectiveness of the proposed approach compared to existing results from the literature.

翻译：均衡圆形装箱问题是指在满足平衡约束的条件下，定位给定数量的加权圆，以最小化圆形容器的半径。这些问题属于NP难问题，具有高度约束性和维度性。本文描述了一种基于虚拟力系统的群体算法，用于解决均衡圆形装箱问题。在该方法中，每个组件上施加一个力系统，从而能够考虑约束条件，并利用动力学基本原理解析地最小化目标函数。所提出的算法在多达300个圆的各种均衡圆形装箱问题基准测试上进行了实验与验证。报告的结果评估了所提方法相较于文献中现有结果的有效性。