Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.

Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm - for staged patterns - also uses a recurrence formula. We show that if the items are not so small compared to the dimensions of the bin, then these algorithms require polynomial time. Using these algorithms we solved all instances of the RK problem found at the OR-LIBRARY, including one for which no optimal solution was known. We also consider the Two-dimensional Cutting Stock problem. We present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We also investigate a variant of this problem where the bins have different sizes. At last, we study the Two-dimensional Strip Packing problem. We also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed. In this case we solve instances for two-, three- and four-staged patterns. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances. We give a detailed description (a pseudo-code) of all the algorithms presented here, so that the reader may easily implement these algorithms. (c) 2007 Elsevier B.V. All rights reserved.

Performance of the Equivalent Reservoir Modelling Technique for Multi-Reservoir Hydropower Systems

This paper investigates the validity of a simplified equivalent reservoir representation of a multi-reservoir hydroelectric system for modelling its optimal operation for power maximization. This simplification, proposed by Arvanitidis and Rosing (IEEE Trans Power Appar Syst 89(2):319-325, 1970), imputes a potential energy equivalent reservoir with energy inflows and outflows. The hydroelectric system is also modelled for power maximization considering individual reservoir characteristics without simplifications. Both optimization models employed MINOS package for solution of the non-linear programming problems. A comparison between total optimized power generation over the planning horizon by the two methods shows that the equivalent reservoir is capable of producing satisfactory power estimates with less than 6% underestimation. The generation and total reservoir storage trajectories along the planning horizon obtained by equivalent reservoir method, however, presented significant discrepancies as compared to those found in the detailed modelling. This study is motivated by the fact that Brazilian generation system operations are based on the equivalent reservoir method as part of the power dispatch procedures. The potential energy equivalent reservoir is an alternative which eliminates problems with the dimensionality of state variables in a dynamic programming model.

An effective recursive partitioning approach for the packing of identical rectangles in a rectangle

In this work, we deal with the problem of packing (orthogonally and without overlapping) identical rectangles in a rectangle. This problem appears in different logistics settings, such as the loading of boxes on pallets, the arrangements of pallets in trucks and the stowing of cargo in ships. We present a recursive partitioning approach combining improved versions of a recursive five-block heuristic and an L-approach for packing rectangles into larger rectangles and L-shaped pieces. The combined approach is able to rapidly find the optimal solutions of all instances of the pallet loading problem sets Cover I and II (more than 50 000 instances). It is also effective for solving the instances of problem set Cover III (almost 100 000 instances) and practical examples of a woodpulp stowage problem, if compared to other methods from the literature. Some theoretical results are also discussed and, based on them, efficient computer implementations are introduced. The computer implementation and the data sets are available for benchmarking purposes. Journal of the Operational Research Society (2010) 61, 306-320. doi: 10.1057/jors.2008.141 Published online 4 February 2009

Efficient solutions to factored MDPs with imprecise transition probabilities

When modeling real-world decision-theoretic planning problems in the Markov Decision Process (MDP) framework, it is often impossible to obtain a completely accurate estimate of transition probabilities. For example, natural uncertainty arises in the transition specification due to elicitation of MOP transition models from an expert or estimation from data, or non-stationary transition distributions arising from insufficient state knowledge. In the interest of obtaining the most robust policy under transition uncertainty, the Markov Decision Process with Imprecise Transition Probabilities (MDP-IPs) has been introduced to model such scenarios. Unfortunately, while various solution algorithms exist for MDP-IPs, they often require external calls to optimization routines and thus can be extremely time-consuming in practice. To address this deficiency, we introduce the factored MDP-IP and propose efficient dynamic programming methods to exploit its structure. Noting that the key computational bottleneck in the solution of factored MDP-IPs is the need to repeatedly solve nonlinear constrained optimization problems, we show how to target approximation techniques to drastically reduce the computational overhead of the nonlinear solver while producing bounded, approximately optimal solutions. Our results show up to two orders of magnitude speedup in comparison to traditional ""flat"" dynamic programming approaches and up to an order of magnitude speedup over the extension of factored MDP approximate value iteration techniques to MDP-IPs while producing the lowest error of any approximation algorithm evaluated. (C) 2011 Elsevier B.V. All rights reserved.

Multidisciplinary optimization of a catamaran's hydrofoil design with dynamic response surface and distributive processing

This paper presents a rational approach to the design of a catamaran's hydrofoil applied within a modern context of multidisciplinary optimization. The approach used includes the use of response surfaces represented by neural networks and a distributed programming environment that increases the optimization speed. A rational approach to the problem simplifies the complex optimization model; when combined with the distributed dynamic training used for the response surfaces, this model increases the efficiency of the process. The results achieved using this approach have justified this publication.

Dynamic Design of Piezoelectric Laminated Sensors and Actuators using Topology Optimization

Sensors and actuators based on piezoelectric plates have shown increasing demand in the field of smart structures, including the development of actuators for cooling and fluid-pumping applications and transducers for novel energy-harvesting devices. This project involves the development of a topology optimization formulation for dynamic design of piezoelectric laminated plates aiming at piezoelectric sensors, actuators and energy-harvesting applications. It distributes piezoelectric material over a metallic plate in order to achieve a desired dynamic behavior with specified resonance frequencies, modes, and enhanced electromechanical coupling factor (EMCC). The finite element employs a piezoelectric plate based on the MITC formulation, which is reliable, efficient and avoids the shear locking problem. The topology optimization formulation is based on the PEMAP-P model combined with the RAMP model, where the design variables are the pseudo-densities that describe the amount of piezoelectric material at each finite element and its polarization sign. The design problem formulated aims at designing simultaneously an eigenshape, i.e., maximizing and minimizing vibration amplitudes at certain points of the structure in a given eigenmode, while tuning the eigenvalue to a desired value and also maximizing its EMCC, so that the energy conversion is maximized for that mode. The optimization problem is solved by using sequential linear programming. Through this formulation, a design with enhancing energy conversion in the low-frequency spectrum is obtained, by minimizing a set of first eigenvalues, enhancing their corresponding eigenshapes while maximizing their EMCCs, which can be considered an approach to the design of energy-harvesting devices. The implementation of the topology optimization algorithm and some results are presented to illustrate the method.

Dynamic and steady: shear rheological properties of xanthan and guar gums dispersed in yellow passion fruit pulp (Passiflora edulis f. flavicarpa)

Yellow passion fruit pulp is unstable, presenting phase separation that can be avoided by the addition of hydrocolloids. For this purpose, xanthan and guar gum [0.3, 0.7 and 1.0% (w/w)] were added to yellow passion fruit pulp and the changes in the dynamic and steady - shear rheological behavior evaluated. Xanthan dispersions showed a more pronounced pseudoplasticity and the presence of yield stress, which was not observed in the guar gum dispersions. Cross model fitting to flow curves showed that the xanthan suspensions also had higher zero shear viscosity than the guar suspensions, and, for both gums, an increase in temperature led to lower values for this parameter. The gums showed different behavior as a function of temperature in the range of 5 - 35ºC. The activation energy of the apparent viscosity was dependent on the shear rate and gum concentration for guar, whereas for xanthan these values only varied with the concentration. The mechanical spectra were well described by the generalized Maxwell model and the xanthan dispersions showed a more elastic character than the guar dispersions, with higher values for the relaxation time. Xanthan was characterized as a weak gel, while guar presented a concentrated solution behavior. The simultaneous evaluation of temperature and concentration showed a stronger influence of the polysaccharide concentration on the apparent viscosity and the G' and G" moduli than the variation in temperature.

Spectroscopic characterization and investigation of the dynamic of charge compensation process of supramolecular films derived from tetra-2-pyridyl-1,4-pyrazine ligand

This work describes the infrared spectroscopy characterization and the charge compensation dynamics in supramolecular film FeTPPZFeCN derived from tetra-2-pyridyl-1,4-pyrazine (TPPZ) with hexacyanoferrate, as well as the hybrid film formed by FeTPPZFeCN and polypyrrole (PPy). For supramolecular film, it was found that anion flux is greater in a K+ containing solution than in Li+ solution, which seems to be due to the larger crystalline ionic radius of K+. The electroneutralization process is discussed in terms of electrostatic interactions between cations and metallic centers in the hosting matrix. The nature of the charge compensation process differs from others modified electrodes based on Prussian blue films, where only cations such as K+ participate in the electroneutralization process. In the case of FeTPPZFeCN/PPy hybrid film, the magnitude of the anions’s flux is also dependent on the identity of the anion of the supporting electrolyte.

FILTERING TECHNIQUES APPLIED ON RAW CARRIER PHASE FOR GPS DETECTING SMALL DYNAMIC DISPLACEMENTS

This work is part of a research under construction since 2000, in which the main objective is to measure small dynamic displacements by using L1 GPS receivers. A very sensible way to detect millimetric periodic displacements is based on the Phase Residual Method (PRM). This method is based on the frequency domain analysis of the phase residuals resulted from the L1 double difference static data processing of two satellites in almost orthogonal elevation angle. In this article, it is proposed to obtain the phase residuals directly from the raw phase observable collected in a short baseline during a limited time span, in lieu of obtaining the residual data file from regular GPS processing programs which not always allow the choice of the aimed satellites. In order to improve the ability to detect millimetric oscillations, two filtering techniques are introduced. One is auto-correlation which reduces the phase noise with random time behavior. The other is the running mean to separate low frequency from the high frequency phase sources. Two trials have been carried out to verify the proposed method and filtering techniques. One simulates a 2.5 millimeter vertical antenna displacement and the second uses the GPS data collected during a bridge load test. The results have shown a good consistency to detect millimetric oscillations.

Active Dendrites Enhance Neuronal Dynamic Range

Since the first experimental evidences of active conductances in dendrites, most neurons have been shown to exhibit dendritic excitability through the expression of a variety of voltage-gated ion channels. However, despite experimental and theoretical efforts undertaken in the past decades, the role of this excitability for some kind of dendritic computation has remained elusive. Here we show that, owing to very general properties of excitable media, the average output of a model of an active dendritic tree is a highly non-linear function of its afferent rate, attaining extremely large dynamic ranges (above 50 dB). Moreover, the model yields double-sigmoid response functions as experimentally observed in retinal ganglion cells. We claim that enhancement of dynamic range is the primary functional role of active dendritic conductances. We predict that neurons with larger dendritic trees should have larger dynamic range and that blocking of active conductances should lead to a decrease in dynamic range.

A Dynamic Analysis of Tuberculosis Dissemination to Improve Control and Surveillance

Background: Detailed analysis of the dynamic interactions among biological, environmental, social, and economic factors that favour the spread of certain diseases is extremely useful for designing effective control strategies. Diseases like tuberculosis that kills somebody every 15 seconds in the world, require methods that take into account the disease dynamics to design truly efficient control and surveillance strategies. The usual and well established statistical approaches provide insights into the cause-effect relationships that favour disease transmission but they only estimate risk areas, spatial or temporal trends. Here we introduce a novel approach that allows figuring out the dynamical behaviour of the disease spreading. This information can subsequently be used to validate mathematical models of the dissemination process from which the underlying mechanisms that are responsible for this spreading could be inferred. Methodology/Principal Findings: The method presented here is based on the analysis of the spread of tuberculosis in a Brazilian endemic city during five consecutive years. The detailed analysis of the spatio-temporal correlation of the yearly geo-referenced data, using different characteristic times of the disease evolution, allowed us to trace the temporal path of the aetiological agent, to locate the sources of infection, and to characterize the dynamics of disease spreading. Consequently, the method also allowed for the identification of socio-economic factors that influence the process. Conclusions/Significance: The information obtained can contribute to more effective budget allocation, drug distribution and recruitment of human skilled resources, as well as guiding the design of vaccination programs. We propose that this novel strategy can also be applied to the evaluation of other diseases as well as other social processes.

Diffusion anomaly and dynamic transitions in the Bell-Lavis water model

In this paper we investigate the dynamic properties of the minimal Bell-Lavis (BL) water model and their relation to the thermodynamic anomalies. The BL model is defined on a triangular lattice in which water molecules are represented by particles with three symmetric bonding arms interacting through van der Waals and hydrogen bonds. We have studied the model diffusivity in different regions of the phase diagram through Monte Carlo simulations. Our results show that the model displays a region of anomalous diffusion which lies inside the region of anomalous density, englobed by the line of temperatures of maximum density. Further, we have found that the diffusivity undergoes a dynamic transition which may be classified as fragile-to-strong transition at the critical line only at low pressures. At higher densities, no dynamic transition is seen on crossing the critical line. Thus evidence from this study is that relation of dynamic transitions to criticality may be discarded. (C) 2010 American Institute of Physics. [doi:10.1063/1.3479001]

Dynamic transitions in a three dimensional associating lattice gas model

The aggregation of interacting Brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in the concentration range considered. By generalizing Kramers' rate theory to the presence of shear and collective hydrodynamics, our model explains the significant increase in the shear-induced reaction-limited aggregation kinetics upon increasing the colloid concentration.