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.

Semi-automatic generation of learning domain modules for technology supported learning systems

In a time when Technology Supported Learning Systems are being widely used, there is a lack of tools that allows their development in an automatic or semi-automatic way. Technology Supported Learning Systems require an appropriate Domain Module, ie. the pedagogical representation of the domain to be mastered, in order to be effective. However, content authoring is a time and effort consuming task, therefore, efforts in automatising the Domain Module acquisition are necessary.Traditionally, textbooks have been used as the main mechanism to maintain and transmit the knowledge of a certain subject or domain. Textbooks have been authored by domain experts who have organised the contents in a means that facilitate understanding and learning, considering pedagogical issues.Given that textbooks are appropriate sources of information, they can be used to facilitate the development of the Domain Module allowing the identification of the topics to be mastered and the pedagogical relationships among them, as well as the extraction of Learning Objects, ie. meaningful fragments of the textbook with educational purpose.Consequently, in this work DOM-Sortze, a framework for the semi-automatic construction of Domain Modules from electronic textbooks, has been developed. DOM-Sortze uses NLP techniques, heuristic reasoning and ontologies to fulfill its work. DOM-Sortze has been designed and developed with the aim of automatising the development of the Domain Module, regardless of the subject, promoting the knowledge reuse and facilitating the collaboration of the users during the process.

Viability Conditions for a Compartmentalized Protometabolic System: A Semi-Empirical Approach

In this work we attempt to find out the extent to which realistic prebiotic compartments, such as fatty acid vesicles, would constrain the chemical network dynamics that could have sustained a minimal form of metabolism. We combine experimental and simulation results to establish the conditions under which a reaction network with a catalytically closed organization (more specifically, an (M, R)-system) would overcome the potential problem of self-suffocation that arises from the limited accessibility of nutrients to its internal reaction domain. The relationship between the permeability of the membrane, the lifetime of the key catalysts and their efficiency (reaction rate enhancement) turns out to be critical. In particular, we show how permeability values constrain the characteristic time scale of the bounded protometabolic processes. From this concrete and illustrative example we finally extend the discussion to a wider evolutionary context.

On the optimal usage of labelled examples in semi-supervised multi-class classification problems

In recent years, the performance of semi-supervised learning has been theoretically investigated. However, most of this theoretical development has focussed on binary classification problems. In this paper, we take it a step further by extending the work of Castelli and Cover [1] [2] to the multi-class paradigm. Particularly, we consider the key problem in semi-supervised learning of classifying an unseen instance x into one of K different classes, using a training dataset sampled from a mixture density distribution and composed of l labelled records and u unlabelled examples. Even under the assumption of identifiability of the mixture and having infinite unlabelled examples, labelled records are needed to determine the K decision regions. Therefore, in this paper, we first investigate the minimum number of labelled examples needed to accomplish that task. Then, we propose an optimal multi-class learning algorithm which is a generalisation of the optimal procedure proposed in the literature for binary problems. Finally, we make use of this generalisation to study the probability of error when the binary class constraint is relaxed.

Recent HERMES results from inclusive and semi-inclusive hadron production

4th International Workshop on Transverse Polisarization Phenomena in Hard Processes (TRANSVERSITY 2014)