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：平衡圆形装箱问题旨在确定给定数量加权圆的位置，以最小化圆形容器的半径，同时满足平衡约束条件。这类问题具有NP-hard性质，且受到高维度和强约束条件的影响。本文提出一种基于虚拟力系统的群智能算法，用于求解平衡圆形装箱问题。在该方法中，对每个组件施加力系统，通过利用动力学基本原理，可在考虑约束条件的同时最小化目标函数。所提出的算法在包含多达300个圆的各种平衡圆形装箱问题基准测试集上进行了实验验证。与现有文献结果相比，报告的结果证明了该方法的有效性。