Solving capacitated clustering problems

Mulvey, John M.; Beck, Michael P.

doi:10.1016/0377-2217(84)90155-3

Cited by 150 publications

(73 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We denote this variant of AP as capacitated AP (CAP). This model can be used to solve a special case of the NP-hard problem known as the capacitated clustering problem (CCP); (Mulvey & Beck, 1984), where L is an integer, and the demands, or weights of the points, are equal and fixed to 1.…”

Section: Deriving Message Updates For Capacitated Affinity Propagationmentioning

confidence: 99%

See 1 more Smart Citation

A Binary Variable Model for Affinity Propagation

2009

View full text Add to dashboard Cite

Affinity propagation (AP) was recently introduced as an unsupervised learning algorithm for exemplar-based clustering. We present a derivation of AP that is much simpler than the original one and is based on a quite different graphical model. The new model allows easy derivations of message updates for extensions and modifications of the standard AP algorithm. We demonstrate this by adjusting the new AP model to represent the capacitated clustering problem. For those wishing to investigate or extend the graphical model of the AP algorithm, we suggest using this new formulation since it allows a simpler and more intuitive model manipulation.

show abstract

Section: Deriving Message Updates For Capacitated Affinity Propagationmentioning

confidence: 99%

“…Further, in our experience, this model simplifies message derivation for modifications to the AP model. We demonstrate the ease of use of the new model by showing how AP can be easily extended to solve a capacitated clustering problem (Mulvey & Beck, 1984) where each cluster has an upper limit L on the number of points it can contain.…”

Section: Introductionmentioning

confidence: 99%

A Binary Variable Model for Affinity Propagation

2009

View full text Add to dashboard Cite

show abstract

“…Ethanol plants are located using a capacitated clustering heuristic, demand at gasoline terminals is based on the fraction of fuel that refineries process, and ethanol demand is assumed proportional to gasoline consumption (35)(36)(37).…”

Section: Ethanol Plantsmentioning

confidence: 99%

Cellulosic Ethanol from Municipal Solid Waste: A Case Study of the Economic, Energy, and Greenhouse Gas Impacts in California

Chester

Martin

2009

Environ. Sci. Technol.

View full text Add to dashboard Cite

As cellulosic ethanol technologies advance, states could use the organic content of municipal solid waste as a transportation fuel feedstock and simultaneously reduce externalities associated with waste disposal. We examine the major processes required to support a lignocellulosic (employing enzymatic hydrolysis) municipal solid waste-to-ethanol infrastructure computing cost, energy, and greenhouse gas effects for California. The infrastructure is compared against the Business As Usual case where the state continues to import most of its ethanol needs from the Midwest. Assuming between 60% and 90% practical yields for ethanol production, California could produce between 1.0 and 1.5 billion gallons per year of ethanol from 55% of the 40 million metric tonnes of waste currently sent to landfills annually. The classification of organic wastes and ethanol plant operation represent almost the entire system cost (between $3.5 and $4.5 billion annually) while distribution has negligible cost effects and savings from avoided landfilling is small. Fossil energy consumption from Business As Usual decreases between 82 and 130 PJ largely due to foregone gasoline consumption. The net greenhouse gas impacts are ultimately dependent on how well landfills control their emissions of decomposing organics. Based on the current landfill mix in the state, the cellulosic infrastructure would experience a slight gain in greenhouse gas emissions. However, net emissions can rise if organics diversion releases carbon that would otherwise be flared and sequestered. Emissions would be avoided if landfills are not capable of effectively controlling emissions during periods of active waste decay. There is currently considerable uncertainty surrounding the recovery efficiency of landfill emissions controls. In either case, burying lignin appears to be better than burning lignin because of its decay properties, energy and carbon content. We estimate the breakeven price for lignocellulosic ethanol between $2.90 and $3.47/gal (µ ) $3.13/gal).

show abstract

“…One can cite in this context, for instance, the work of Pierre Hansen (e.g. [2]), but most to the point here is the recent proposal from Liao and Guo [3], this proposal explicitly linking k-means with facility location, similarly as this was done several decades ago by Mulvey and Beck [4].…”

Section: Some Hints At Cluster Analysismentioning

confidence: 98%