Scenario Cluster Lagrangian Decomposition in two stage stochastic mixed 0-1 optimization

In this paper we introduce four scenario Cluster based Lagrangian Decomposition (CLD) procedures for obtaining strong lower bounds to the (optimal) solution value of two-stage stochastic mixed 0-1 problems. At each iteration of the Lagrangian based procedures, the traditional aim consists of obtaining the solution value of the corresponding Lagrangian dual via solving scenario submodels once the nonanticipativity constraints have been dualized. Instead of considering a splitting variable representation over the set of scenarios, we propose to decompose the model into a set of scenario clusters. We compare the computational performance of the four Lagrange multiplier updating procedures, namely the Subgradient Method, the Volume Algorithm, the Progressive Hedging Algorithm and the Dynamic Constrained Cutting Plane scheme for different numbers of scenario clusters and different dimensions of the original problem. Our computational experience shows that the CLD bound and its computational effort depend on the number of scenario clusters to consider. In any case, our results show that the CLD procedures outperform the traditional LD scheme for single scenarios both in the quality of the bounds and computational effort. All the procedures have been implemented in a C++ experimental code. A broad computational experience is reported on a test of randomly generated instances by using the MIP solvers COIN-OR and CPLEX for the auxiliary mixed 0-1 cluster submodels, this last solver within the open source engine COIN-OR. We also give computational evidence of the model tightening effect that the preprocessing techniques, cut generation and appending and parallel computing tools have in stochastic integer optimization. Finally, we have observed that the plain use of both solvers does not provide the optimal solution of the instances included in the testbed with which we have experimented but for two toy instances in affordable elapsed time. On the other hand the proposed procedures provide strong lower bounds (or the same solution value) in a considerably shorter elapsed time for the quasi-optimal solution obtained by other means for the original stochastic problem.

Generating cluster submodels from a multistage stochastic mixed integer optimization model using break stage

We present a scheme to generate clusters submodels with stage ordering from a (symmetric or a nonsymmetric one) multistage stochastic mixed integer optimization model using break stage. We consider a stochastic model in compact representation and MPS format with a known scenario tree. The cluster submodels are built by storing first the 0-1 the variables, stage by stage, and then the continuous ones, also stage by stage. A C++ experimental code has been implemented for reordering the stochastic model as well as the cluster decomposition after the relaxation of the non-anticipativiy constraints until the so-called breakstage. The computational experience shows better performance of the stage ordering in terms of elapsed time in a randomly generated testbed of multistage stochastic mixed integer problems.

Cluster analisiaren aplikazio bat ekonomian Donostiako auzoen ikerketa

Lan honekin Donostiako bizitza kalitatea ikertu nahi dute, hau da etxebizitzetako bizilagunen eta etxebizitzen egitura eta erabileraren arteko erlazio posiblea. Biztanle mota, etxebizitza mota eta Donostiako eremu homogeneoen arteko lotura bilatzen saiatuko dira, Aldagai Anitzeko Analisia, batez ere Osagai Nagusizko Analisia, erabiliz aldagai kopurua murrizteko eta faktore edo osagai gutxitan aldagaien informazio gehiena jasotzeko. Jarraian, Cluster aplikatuko dute auzo homogeneoen taldeak osatzeko.

Estrategias de Marketing para la gestión público-privada del comercio de Guipúzcoa. Un modelo basado en el análisis cluster.

Este artículo trata sobre el desarrollo de áreas comerciales en los alrededores de las ciudades y de cómo el centro urbano ha ido perdiendo atractivo comercial. Esta situación, común en la mayor parte de los países de nuestro entorno, plantea importantes problemas para el comercio tradicional de centro ciudad, que ve como gran parte de sus clientes optan por la oferta de la periferia, con la siguiente fuga de ingresos.

Towards a standard methodology to evaluate internal cluster validity indices

The evaluation and comparison of internal cluster validity indices is a critical problem in the clustering area. The methodology used in most of the evaluations assumes that the clustering algorithms work correctly. We propose an alternative methodology that does not make this often false assumption. We compared 7 internal cluster validity indices with both methodologies and concluded that the results obtained with the proposed methodology are more representative of the actual capabilities of the compared indices.

Orígenes, elementos determinantes y resultados de un exitoso proceso de colaboración entre competidores y otros agentes: el cluster de la Alta Cocina Vasca

[ES] El País Vasco es internacionalmente reconocido por su gastronomía y sus grandes cocineros; de hecho, es el territorio del mundo con más estrellas Michelin por kilómetro cuadrado. Esta notoriedad e imagen repercuten muy positivamente en todo el sector gastronómico y en la imagen y proyección turística del País Vasco y se ha logrado gracias a la labor sostenida de un grupo inicial de cocineros, a los que siguieron otros, que realizan importantes esfuerzos de colaboración, sin dejar de competir entre ellos (tratándose de un claro ejemplo de coopetition). El análisis de la relación entre estos grandes cocineros vascos y su entorno, permite identificar un cluster que actualmente se encuentra en fase de madurez con un futuro esperanzador y que ha arrojado importantes beneficios al sector, a cada uno de sus integrantes y a la región en su conjunto muy especialmente en términos de innovación, notoriedad y reputación. Para la realización de este trabajo se ha utilizado, además de la revisión bibliográfica y documental pertinente, una metodología cualitativa, consistente en la realización de entrevistas en profundidad a los siete cocineros fundadores y patronos del Basque Culinary Center (primera Facultad Universitaria de Estudios Gastronómicos de Europa, dependiente de la Universidad de Mondragón). El trabajo es uno de los frutos extraídos de un contrato de colaboración entre el Instituto de Economía Aplicada a la empresa de la UPV/EHU e Innobasque (Agencia Vasca para la Innovación), en el que esta última fijó tanto los objetivos de la investigación como la metodología a utilizar.

Subtypes of Patients Experiencing Exacerbations of COPD and Associations with Outcomes

Chronic obstructive pulmonary disease (COPD) is a complex and heterogeneous condition characterized by occasional exacerbations. Identifying clinical subtypes among patients experiencing COPD exacerbations (ECOPD) could help better understand the pathophysiologic mechanisms involved in exacerbations, establish different strategies of treatment, and improve the process of care and patient prognosis. The objective of this study was to identify subtypes of ECOPD patients attending emergency departments using clinical variables and to validate the results using several outcomes. We evaluated data collected as part of the IRYSS-COPD prospective cohort study conducted in 16 hospitals in Spain. Variables collected from ECOPD patients attending one of the emergency departments included arterial blood gases, presence of comorbidities, previous COPD treatment, baseline severity of COPD, and previous hospitalizations for ECOPD. Patient subtypes were identified by combining results from multiple correspondence analysis and cluster analysis. Results were validated using key outcomes of ECOPD evolution. Four ECOPD subtypes were identified based on the severity of the current exacerbation and general health status (largely a function of comorbidities): subtype A (n = 934), neither high comorbidity nor severe exacerbation; subtype B (n = 682), moderate comorbidities; subtype C (n = 562), severe comorbidities related to mortality; and subtype D (n = 309), very severe process of exacerbation, significantly related to mortality and admission to an intensive care unit. Subtype D experienced the highest rate of mortality, admission to an intensive care unit and need for noninvasive mechanical ventilation, followed by subtype C. Subtypes A and B were primarily related to other serious complications. Hospitalization rate was more than 50% for all the subtypes, although significantly higher for subtypes C and D than for subtypes A and B. These results could help identify characteristics to categorize ECOPD patients for more appropriate care, and help test interventions and treatments in subgroups with poor evolution and outcomes.