Methodology to Solve Multi-Dimentional Sphere Packing Problems

This paper discusses the problem of optimally packing spheres of various dimensions into containers of arbitrary geometrical shapes. According to the international classification, this problem belongs to Sphere Packing Problems (SPPs). The aim of this work is to create an integrated methodology for solving SPPs.В статті розглядається задача оптимального розміщення куль різної розмірності в контейнерах довільних геометричних форм. Згідно з міжнародною класифікацією ця задача належить до класу SPP (Sphere Packing Problems). Метою даної роботи є створення єдиної методології розв’язання задач SPP.В статье рассматривается задача оптимального размещения шаров различной размерности в контейнерах произвольных геометрических форм. Согласно международной классификации эта задача относится к классу SPP (Sphere Packing Problems). Целью данной работы является создание единой методологии решения задач SPP

A Vitual-Force Based Swarm Algorithm for Balanced Circular Bin Packing Problems

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.Comment: 23 pages including reference

改进区域划分的圆Packing变分算法

通过改进基于Power图的区域划分,提出一种收敛速度更快的圆packing算法.首先固定容器面积,将输入圆缩小一定的倍数,随机撒在容器中;之后对圆心点进行三角化,并根据相邻圆的半径比值对容器进行区域划分;再让所有圆在不超出自己区域边界的条件下尽量等比例增长至最大;最后将划分区域-长大的过程迭代下去,得到最大增长倍数.实验结果表明,该算法能够使得圆packing的过程更快地达到收敛.国家自然科学基金(61472332);;福建省自然科学基金(2018J01104

Packing Circles Within Circular Containers: A New Heuristic Algorithm For The Balance Constraints Case

In this work we propose a heuristic algorithm for the layout optimization for disks installed in a rotating circular container. This is a unequal circle packing problem with additional balance constraints. It proved to be an NP-hard problem, which justifies heuristics methods for its resolution in larger instances. The main feature of our heuristic is based on the selection of the next circle to be placed inside the container according to the position of the system's center of mass. Our approach has been tested on a series of instances up to 55 circles and compared with the literature. Computational results show good performance in terms of solution quality and computational time for the proposed algorithm.36227930