An improved algorithm for the packing of unequal circles within a larger containing circle

Abstract

This paper describes an approved algorithm for the problems of unequal circle packing -the quasi-physical quasihuman algorithm. First, the quasi-physical approach for the general packing problems is described in solving the pure problems of unequal circle packing. The method is an analogy to the physical model in which a number of smooth cylinders are packed inside a container. A quasi-human strategy is then proposed to trigger a jump for a stuck object in order to get out of local minima. Our method has been tested in numerical experiments. The computational results are presented, showing the merits of the proposed method. Our algorithm can be thought as an adoptive algorithm of the Tabu search. Ó

New heuristics for packing unequal circles into a circular container

“…In this section, we evaluate our approach on a series of instances up to 100 circles from the literature [10,12,13,16,17,18,20], and compare our approach with the simulation approach proposed by Huang et al and Wang et al [9,10,18] in terms of solution quality and running time. We also study the behaviours of our approach when it is applied to pack equal circles.…”

“…The simulation approach in [9,10,18] is practically a Local Search based on an elasticity physics model, denoted by LS. We briefly present it below: the n circles are considered as elastic disks and squeezed inside the container.…”

“…But to our knowledge, no significant published research addresses the problem of packing unequal circles into a circular container, except a simulation approach based on an elasticity physics model, proposed by Huang et al [9,10] and Wang et al [18]. This approach can obtain good enough solutions for packing unequal circles and very good solutions for packing equal circles, but the computational time greatly increases for large instances.…”

“…Another feature of our approach is the use of a self look-ahead strategy to improve A1.0 and gives the second algorithm, denoted by A1.5. We evaluate our approach on a series of instances up to 100 circles from the literature [10,12,13,16,17,18,20] and compare it with existing approaches.…”

Orthogonal packing of identical rectangles within isotropic convex regions

“…In [25,26], Packmol was introduced as successful tool for building initial configurations for molecular dynamics simulations, based on the packing of spheres by nonlinear optimization. Hybrid methods that combine nonlinear models with heuristics have also been considered in [21,22,24,28,31,32], among others, for packing identical or different circular pieces within several types of objects. In [36], mixed integer linear and nonlinear formulations for staged cutting problems and 2-stage two-dimensional guillotine cutting patterns are reviewed.…”