A heuristic for the circle packing problem with a variety of containers

López, Claudia O.; Beasley, John E.

doi:10.1016/j.ejor.2011.04.024

Cited by 82 publications

(36 citation statements)

References 19 publications

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“…It should also be noted that Lopez & Beasley's [5] paper on circle packing is the most recent study done on the subject.…”

Section: N})mentioning

confidence: 99%

“…This ultimately improves the solution, because as a stationary point of one formulation is reached and the formulation of the problem is changed, the stationary point may be moved and improved on. Mladenovic et al [7] and Lopez & Beasley [5] exploited this characteristic of optimisation by defining the positions of some circles in Cartesian and of others in Polar coordinates. Their algorithm then changes the circles that are expressed in Polar coordinates to Cartesian coordinates, and vice versa, with each iteration of the algorithm.…”

Section: Formulation Space Searchmentioning

confidence: 99%

“…Lopez & Beasley [5] developed an altered and improved heuristic algorithm that was also based on FSS. The FSS uses different formulations of the same problem to obtain improved solutions compared with singular formulation algorithms.…”

Section: Formulation Space Searchmentioning

confidence: 99%

“…It should also be noted that they focused their efforts on developing a solution for two dimensional containers -especially circular containers. Lopez & Beasley [5] formulated the solution as follows: Let • C be the set of circles whose centres are expressed as Cartesian coordinates, so for circle i ∈ C its centre is at (xi, yi) in Cartesian coordinates.…”

Section: Formulation Space Searchmentioning

confidence: 99%

“…The circle packing problem (CPP) is described by Lopez & Beasley [5]: "Finding the maximum radius of a specified number of circles that can be fitted, without any overlaps, into a two dimensional container of fixed size". Circle packing problems can be solved by using two distinct objective functions.…”

Section: Introduction To the Circle Packing Problemmentioning

confidence: 99%

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An Operations Research and Simulation�based Study on Improving the Efficiency of a Slurry Drying Tower

Jongh

Botha

2013

sajie

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This paper relates to a company that produces washing powders. The focus is on improving the efficiency of gas usage (per unit of powder produced) in the furnace that produces hot air. This hot air is an integral part of washing powder production: it dries the viscous slurry and transforms it into the base powder used in all washing powders. The cost of gas is the factory's largest expense. This paper attempts to increase the productivity and profitability of the operations by applying operations research using MATLAB and the non-linear optimiser called SNOPT (sparse non-linear optimiser). Using these techniques, a proposed solution that aims to balance the amount of open space between spraying slurry, as well as the overlap of spraying slurry within the furnace, is obtained. This is achieved by optimising the positioning of the top layer of 24 lances. The placement of the bottom layer of lances is done by positioning them in the areas of biggest overlap. These improvements result in a positive impact on the amount of gas burnt within the furnace to dry slurry to powder. OPSOMMINGHierdie navorsing handel oor 'n aangeleentheid wat verband hou met die aktiwiteite van 'n onderneming wat waspoeiers vervaardig. Daar word gepoog om die rendement van 'n verhittingsoond wat lug verhit vir die droging van poeier te verbeter. Die drogingsproses vind plaas deur viskeuse bry te droog tot poeier, wat gebruik kan word as bestanddeel van gewone waspoeier. Hierdie artikel beoog om produktiwiteit en wins van die proses te verhoog deur 'n operasionele navorsingsbenadering toe te pas wat gebruik maak van 'n boeket van toepaslike programmatuur soos o.a. SNOPT ("sparse non-linear optimizer") en Matlab. 'n voorgestelde oplossing is verkry deur van die bogenoemde metodes gebruik te maak, die oplossing beoog om die hoeveelheid oop spasies tussen die viskeuse bry en ook die oorvleueling van die viskeuse bry in die verhittingsoond te balanseer. Dit word bereik deur die optimale posisies te verkry vir die boonste 24 lansiere. Die onderste laag lansiere word geposisioneer in die areas waar die grootste oorvleueling plaasvind. Hierdie verbeterings het 'n positiewe impak op die hoeveelheid gas wat in die verhittingsoond gebrand word. a aa a a a aa a a a a a 1

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“…It should also be noted that Lopez & Beasley's [5] paper on circle packing is the most recent study done on the subject.…”

Section: N})mentioning

confidence: 99%

Section: Formulation Space Searchmentioning

confidence: 99%

Section: Formulation Space Searchmentioning

confidence: 99%

Section: Formulation Space Searchmentioning

confidence: 99%

Section: Introduction To the Circle Packing Problemmentioning

confidence: 99%