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.

Valorization of scrap tires pyrolysis oil (STPO) through a 2-stage hydrotreating-hydrocracking strategy. Process variables and kinetic modeling

232 p.

Frame presentations: variants of the reals, rings of functions, their Dedekind completions, and the unit circle

176 p.

Identification of Sex and Female’s Reproductive Stage in Commercial Fish Species through the Quantification of Ribosomal Transcripts in Gonads

The estimation of maturity and sex of fish stocks in European waters is a requirement of the EU Data Collection Framework as part of the policy to improve fisheries management. On the other hand, research on fish biology is increasingly focused in molecular approaches, researchers needing correct identification of fish sex and reproductive stage without necessarily having in house the histological know-how necessary for the task. Taking advantage of the differential gene transcription occurring during fish sex differentiation and gametogenesis, the utility of 5S ribosomal RNA (5S rRNA) and General transcription factor IIIA (gtf3a) in the molecular identification of sex and gametogenic stage was tested in different economically-relevant fish species from the Bay of Biscay. Gonads of 9 fish species (, Atlantic, Atlantic-chub and horse mackerel, blue whiting, bogue, European anchovy, hake and pilchard and megrim), collected from local commercial fishing vessels were histologically sexed and 5S and 18S rRNA concentrations were quantified by capillary electrophoresis to calculate a 5S/18S rRNA index. Degenerate primers permitted cloning and sequencing of gtf3a fragments in 7 of the studied species. 5S rRNA and gtf3a transcript levels, together with 5S/18S rRNA index, distinguished clearly ovaries from testis in all of the studied species. The values were always higher in females than in males. 5S/18S rRNA index values in females were always highest when fish were captured in early phases of ovary development whilst, in later vitellogenic stages, the values decreased significantly. In megrim and European anchovy, where gonads in different oogenesis stages were obtained, the 5S/18S rRNA index identified clearly gametogenic stage. This approach, to the sexing and the quantitative non-subjective identification of the maturity stage of female fish, could have multiple applications in the study of fish stock dynamics, fish reproduction and fecundity and fish biology in general.