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.

Development of kelp rockfish, Sebastes atrovirens (Jordan and Gilbert 1880), and brown rockfish, S. auriculatus (Girard 1854), from birth to pelagic juvenile stage, with notes on early larval development of black-and-yellow rockfish, S. chrysomelas (Jordan and Gilbert 1880), reared in the laboratory (Pisces: Sebastidae).

Larval kelp (Sebastes atrovirens), brown (S. auriculatus), and blackand-yellow (S. chrysomelas) rockfish were reared from known adults, to preflexion stage, nine days after birth for S. chrysomelas, to late postflexion stage for S. atrovirens, and to pelagic juvenile stage for S. auriculatus. Larval S. atrovirens and S. chrysomelas were about 4.6 mm body length (BL) and S. auriculatus about 5.2 mm BL at birth. Both S. atrovirens and S. auriculatus underwent notochord flexion at about 6–9 mm BL. Sebastes atrovirens transform to the pelagic juvenile stage at about 14–16 mm BL and S. auriculatus transformed at ca. 25 mm BL. Early larvae of all three species were characterized by melanistic pigment dorsally on the head, on the gut, on most of the ventral margin of the tail, and in a long series on the dorsal margin of the tail. Larval S. atrovirens and S. auriculatus developed a posterior bar on the tail during the flexion or postflexion stage. In S. atrovirens xanthic pigment resembled the melanistic pattern throughout larval development. Larval S. auriculatus lacked xanthophores except on the head until late preflexion stage, when a pattern much like the melanophore pattern gradually developed. Larval S. chrysomelas had extensive xanthic pigmentation dorsally, but none ventrally, in preflexion stage. All members of the Sebastes subgenus Pteropodus (S. atrovirens, S. auriculatus, S. carnatus, S. caurinus, S. chrysomelas, S. dalli, S. maliger, S. nebulosus, S. rastrelliger) are morphologically similar and all share the basic melanistic pigment pattern described here. Although the three species reared in this study can be distinguished on the basis of xanthic pigmentation, it seems unlikely that it will be possible to reliably identify field-collected larvae to species using traditional morphological and melanistic pigmentation characters. (PDF file contains 36 pages.)

High and stable conversion efficiency obtaining in single-stage multi-crystal optical parametric chirped pulse amplification system

An optical parametric chirped-pulse amplification system is demonstrated to provide 32.9% pump-to-signal conversion efficiency . Special techniques are used to make the signal and pump pulses match with each other in both spectral and temporal domains. The broadband 9.5-mJ pulses are produced at the repetition rate of 1 Hz with the gain of over 1.9 x 10(8). The output energy fluctuation of 7.8% is achieved for the saturated amplification process against the pump fluctuation of 10%.

Inter-stage line ratio of He- and Li-like Ti emissions for the electron temperature measurement

Under coronal conditions, the steady state rate-equations are used to calculate the inter-stage line ratios between Li-like Is(2)2p(P-2(3/2))-> 1s(2)2s -> ((2) S-1/2) and He-like 1s2p (P-1(1))-> 1s(2) (S-1(0)) transitions for Ti in the electronic temperature ranges from 0.1 keV to 20 keV. The results show that the. temperature sensitivities are higher at the electronic temperature less than 5000 eV and the temperature sensitivities will decrease with the increase of electronic temperature.

Generation of 17-TW 23-fs pulses with a two-stage Ti : Sapphire amplifier at repetition rate 10 Hz

We have developed a two-stage Ti:sapphire amplifier system which can produce 17-TW/23-fs pulses at a repetition rate 10 MHz. A birefringent plate is used in the regenerative amplifier to alleviate gain narrowing, while an all-reflective cylindrical-mirror-based pulse stretcher and an acousto-optic programmable dispersive filter (AOPDF) are used to compensate for the higher order dispersion of the system.