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.

The forward problem for the electromagnetic Helmholtz equation

157 p.

Diseño de un mecanismo de amplificación para una garra de 1 grado de libertad.

[ES]El presente Trabajo de Fin de Grado tiene la finalidad de contribuir al desarrollo de una línea de investigación mediante la implementación de un mecanismo que amplifique el movimiento de un grado de libertad. Dicho proyecto consiste en optimizar un mecanismo ya existente formado por un músculo neumático de un grado de libertad de forma que se mejore el rango de utilización de dicho mecanismo ampliando la carrera final de éste. Para ello se llevará a cabo un análisis de distintos mecanismos multiplicadores, el diseño de la mejor opción entre todos ellos y la final fabricación de un prototipo funcional. También se llevará a cabo el diseño y fabricación de las piezas auxiliares que, si bien, no forman parte explícita del mecanismo multiplicador, son necesarias para la posterior implantación de dicho mecanismo en el mecanismo ya existente, formado por un mecanismo mecatrónico de cinemática plana 5R dotado de un músculo neumático y una ventosa.