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.

Biomolecule storage on non-modified thermoplastic microfluidic chip by ink-jet printing of ionogels

[EN] This paper reports an innovative technique for reagents storage in microfluidic devices by means of a one-step UV-photoprintable ionogel-based microarray on non-modified polymeric substrates. Although the ionogel and the ink-jet printing technology are well published, this is the first study where both are used for long-term reagent storage in lab-on-a-chip devices. This technology for reagent storage is perfectly compatible with mass production fabrication processes since pre-treatment of the device substrate is not necessary and inkjet printing allows for an efficient reagent deposition process. The functionality of this microarray is demonstrated by testing the release of biotin-647 after being stored for 1 month at room temperature. Analysis of the fluorescence of the ionogel-based microarray that contains biotin-647 demonstrated that 90% of the biotin-647 present was released from the ionogel-based microarray after pumping PBS 0.1% Tween at 37 °C. Moreover, the activity of biotin-647 after being released from the ionogel-based microarray was investigated trough the binding capability of this biotin to a microcontact printed chip surface with avidin. These findings pave the way for a novel, one-step, cheap and mass production on-chip reagents storage method applicable to other reagents such as antibodies and proteins and enzymes.

Crank-Nicholson method for rate equations in powder random lasers

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2014)