An Exact Approach to Early/Tardy Scheduling with Release Dates

In this paper we consider the single machine earliness/tardiness scheduling problem with di?erent release dates and no unforced idle time. The problem is decomposed into a weighted earliness subproblem and a weighted tardiness subproblem. Lower bounding procedures are proposed for each of these subproblems, and the lower bound for the original problem is then simply the sum of the lower bounds for the two subproblems. The lower bounds and several versions of a branch-and-bound algorithm are then tested on a set of randomly generated problems, and instances with up to 30 jobs are solved to optimality. To the best of our knowledge, this is the first exact approach for the early/tardy scheduling problem with release dates and no unforced idle time.scheduling, early/tardy, release dates, lower bounds, branch-and-bound

Improved Lower Bounds for the Early/Tardy Scheduling Problem with No Idle Time

In this paper we consider the single machine earliness/tardiness scheduling problem with no idle time. Two of the lower bounds previously developed for this problem are based on lagrangean relaxation and the multiplier adjustment method, and require an initial sequence. We investigate the sensitivity of the lower bounds to the initial sequence, and experiment with di?erent dispatch rules and some dominance conditions. The computational results show that it is possible to obtain improved lower bounds by using a better initial sequence. The lower bounds are also incorporated in a branch-and-bound algorithm, and the computational tests show that one of the new lower bounds has the best performance for larger instances.scheduling, early/tardy, lower bound

Heuristics for the Early/Tardy Scheduling Problem with Release Dates

In this paper we consider the single machine earliness/tardiness scheduling problem with di?erent release dates and no unforced idle time. We analyse the performance of several dispatch rules, a greedy procedure and a decision theory local search heuristic. The dispatch rules use a lookahead parameter whose value must be specified. We perform some experiments to determine an appropriate value for this parameter. The use of dominance rules to improve the solutions obtained by these heuristics is also considered. The computational results show that the use of the dominance rules can indeed improve the solution quality with little additional computational e?ort. To the best of our knowledge, this is the first analysis of heuristic performance for the early/tardy scheduling problem with release dates and no unforced idle time.scheduling, early/tardy, release dates, heuristics

Improved Heuristics for the Early/Tardy Scheduling Problem with No Idle Time

In this paper we consider the single machine earliness/tardiness scheduling problem with no idle time. We present two new heuristics, a dispatch rule and a greedy procedure, and also consider the best of the existing dispatch rules. Both dispatch rules use a lookahead parameter that had previously been set at a fixed value. We develop functions that map some instance statistics into appropriate values for that parameter. We also consider the use of dominance rules to improve the solutions obtained by the heuristics. The computational results show that the function-based versions of the heuristics outperform their fixed value counterparts and that the use of the dominance rules can indeed improve solution quality with little additional computational effort.scheduling, early/tardy, heuristics, dispatch rules, dominance rules

Beam search algorithms for the early/tardy scheduling problem with release dates

In this paper we consider the single machine earliness/tardiness scheduling problem with di?erent release dates and no unforced idle time. We present several heuristic algorithms based on the beam search technique. These algorithms include classical beam search procedures, with both priority and total cost evaluation functions, as well as the filtered and recovering variants. Both priority evaluation functions and problem-specific properties were considered for the filtering step used in the filtered and recovering beam search heuristics. Extensive preliminary tests were performed to determine appropriate values for the parameters used by each algorithm. The computational results show that the recovering beam search algorithms outperform their filtered counterparts in both solution quality and computational requirements, while the priority-based filtering procedure proves superior to the rules-based alternative. The beam search procedure with a total cost evaluation function provides very good results, but is computationally expensive and can therefore only be applied to small or medium size instances. The recovering algorithm is quite close in solution quality and is significantly faster, so it can be used to solve even large instances.scheduling, early/tardy, beam search, heuristics

A Software Tool to Model Genetic Regulatory Networks. Applications to the Modeling of Threshold Phenomena and of Spatial Patterning in Drosophila

We present a general methodology in order to build mathematical models of genetic regulatory networks. This approach is based on the mass action law and on the Jacob and Monod operon model. The mathematical models are built symbolically by the Mathematica software package GeneticNetworks. This package accepts as input the interaction graphs of the transcriptional activators and repressors of a biological process and, as output, gives the mathematical model in the form of a system of ordinary differential equations. All the relevant biological parameters are chosen automatically by the software. Within this framework, we show that concentration dependent threshold effects in biology emerge from the catalytic properties of genes and its associated conservation laws. We apply this methodology to the segment patterning in Drosophila early development and we calibrate the genetic transcriptional network responsible for the patterning of the gap gene proteins Hunchback and Knirps, along the antero-posterior axis of the Drosophila embryo. In this approach, the zygotically produced proteins Hunchback and Knirps do not diffuse along the antero-posterior axis of the embryo of Drosophila, developing a spatial pattern due to concentration dependent thresholds. This shows that patterning at the gap genes stage can be explained by the concentration gradients along the embryo of the transcriptional regulators

Nanostructured 3D Constructs Based on Chitosan and Chondroitin Sulphate Multilayers for Cartilage Tissue Engineering

Nanostructured three-dimensional constructs combining layer-by-layer technology (LbL) and template leaching were processed and evaluated as possible support structures for cartilage tissue engineering. Multilayered constructs were formed by depositing the polyelectrolytes chitosan (CHT) and chondroitin sulphate (CS) on either bidimensional glass surfaces or 3D packet of paraffin spheres. 2D CHT/CS multi-layered constructs proved to support the attachment and proliferation of bovine chondrocytes (BCH). The technology was transposed to 3D level and CHT/CS multi-layered hierarchical scaffolds were retrieved after paraffin leaching. The obtained nanostructured 3D constructs had a high porosity and water uptake capacity of about 300%. Dynamical mechanical analysis (DMA) showed the viscoelastic nature of the scaffolds. Cellular tests were performed with the culture of BCH and multipotent bone marrow derived stromal cells (hMSCs) up to 21 days in chondrogenic differentiation media. Together with scanning electronic microscopy analysis, viability tests and DNA quantification, our results clearly showed that cells attached, proliferated and were metabolically active over the entire scaffold. Cartilaginous extracellular matrix (ECM) formation was further assessed and results showed that GAG secretion occurred indicating the maintenance of the chondrogenic phenotype and the chondrogenic differentiation of hMSCs

Multiplicity dependence of jet-like two-particle correlations in p-Pb collisions at sNN\sqrt{s_{NN}} = 5.02 TeV

Two-particle angular correlations between unidentified charged trigger and associated particles are measured by the ALICE detector in p-Pb collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV. The transverse-momentum range 0.7 $< p_{\rm{T}, assoc} < p_{\rm{T}, trig} <$ 5.0 GeV/$c$ is examined, to include correlations induced by jets originating from low momen\-tum-transfer scatterings (minijets). The correlations expressed as associated yield per trigger particle are obtained in the pseudorapidity range $|\eta|<0.9$. The near-side long-range pseudorapidity correlations observed in high-multiplicity p-Pb collisions are subtracted from both near-side short-range and away-side correlations in order to remove the non-jet-like components. The yields in the jet-like peaks are found to be invariant with event multiplicity with the exception of events with low multiplicity. This invariance is consistent with the particles being produced via the incoherent fragmentation of multiple parton--parton scatterings, while the yield related to the previously observed ridge structures is not jet-related. The number of uncorrelated sources of particle production is found to increase linearly with multiplicity, suggesting no saturation of the number of multi-parton interactions even in the highest multiplicity p-Pb collisions. Further, the number scales in the intermediate multiplicity region with the number of binary nucleon-nucleon collisions estimated with a Glauber Monte-Carlo simulation.Comment: 23 pages, 6 captioned figures, 1 table, authors from page 17, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/161

Multi-particle azimuthal correlations in p-Pb and Pb-Pb collisions at the CERN Large Hadron Collider

Measurements of multi-particle azimuthal correlations (cumulants) for charged particles in p-Pb and Pb-Pb collisions are presented. They help address the question of whether there is evidence for global, flow-like, azimuthal correlations in the p-Pb system. Comparisons are made to measurements from the larger Pb-Pb system, where such evidence is established. In particular, the second harmonic two-particle cumulants are found to decrease with multiplicity, characteristic of a dominance of few-particle correlations in p-Pb collisions. However, when a $|\Delta \eta|$ gap is placed to suppress such correlations, the two-particle cumulants begin to rise at high-multiplicity, indicating the presence of global azimuthal correlations. The Pb-Pb values are higher than the p-Pb values at similar multiplicities. In both systems, the second harmonic four-particle cumulants exhibit a transition from positive to negative values when the multiplicity increases. The negative values allow for a measurement of $v_{2}\{4\}$ to be made, which is found to be higher in Pb-Pb collisions at similar multiplicities. The second harmonic six-particle cumulants are also found to be higher in Pb-Pb collisions. In Pb-Pb collisions, we generally find $v_{2}\{4\} \simeq v_{2}\{6\}\neq 0$ which is indicative of a Bessel-Gaussian function for the $v_{2}$ distribution. For very high-multiplicity Pb-Pb collisions, we observe that the four- and six-particle cumulants become consistent with 0. Finally, third harmonic two-particle cumulants in p-Pb and Pb-Pb are measured. These are found to be similar for overlapping multiplicities, when a $|\Delta\eta| > 1.4$ gap is placed.Comment: 25 pages, 11 captioned figures, 3 tables, authors from page 20, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/87