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

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

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