Least Squares Approach to Inverse Problems in Musculoskeletal Biomechanics

Inverse simulations of musculoskeletal models computes the internal forces such as muscle and joint reaction forces, which are hard to measure, using the more easily measured motion and external forces as input data. Because of the difficulties of measuring muscle forces and joint reactions, simulations are hard to validate. One way of reducing errors for the simulations is to ensure that the mathematical problem is well-posed. This paper presents a study of regularity aspects for an inverse simulation method, often called forward dynamics or dynamical optimization, that takes into account both measurement errors and muscle dynamics. The simulation method is explained in detail. Regularity is examined for a test problem around the optimum using the approximated quadratic problem. The results shows improved rank by including a regularization term in the objective that handles the mechanical over-determinancy. Using the 3-element Hill muscle model the chosen regularization term is the norm of the activation. To make the problem full-rank only the excitation bounds should be included in the constraints. However, this results in small negative values of the activation which indicates that muscles are pushing and not pulling. Despite this unrealistic behavior the error maybe small enough to be accepted for specific applications. These results is a starting point start for achieving better results of inverse musculoskeletal simulations from a numerical point of view.

Optimization models and methods for real-time transportation planning in forestry

Lors du transport du bois de la forêt vers les usines, de nombreux événements imprévus peuvent se produire, événements qui perturbent les trajets prévus (par exemple, en raison des conditions météo, des feux de forêt, de la présence de nouveaux chargements, etc.). Lorsque de tels événements ne sont connus que durant un trajet, le camion qui accomplit ce trajet doit être détourné vers un chemin alternatif. En l’absence d’informations sur un tel chemin, le chauffeur du camion est susceptible de choisir un chemin alternatif inutilement long ou pire, qui est lui-même "fermé" suite à un événement imprévu. Il est donc essentiel de fournir aux chauffeurs des informations en temps réel, en particulier des suggestions de chemins alternatifs lorsqu’une route prévue s’avère impraticable. Les possibilités de recours en cas d’imprévus dépendent des caractéristiques de la chaîne logistique étudiée comme la présence de camions auto-chargeurs et la politique de gestion du transport. Nous présentons trois articles traitant de contextes d’application différents ainsi que des modèles et des méthodes de résolution adaptés à chacun des contextes. Dans le premier article, les chauffeurs de camion disposent de l’ensemble du plan hebdomadaire de la semaine en cours. Dans ce contexte, tous les efforts doivent être faits pour minimiser les changements apportés au plan initial. Bien que la flotte de camions soit homogène, il y a un ordre de priorité des chauffeurs. Les plus prioritaires obtiennent les volumes de travail les plus importants. Minimiser les changements dans leurs plans est également une priorité. Étant donné que les conséquences des événements imprévus sur le plan de transport sont essentiellement des annulations et/ou des retards de certains voyages, l’approche proposée traite d’abord l’annulation et le retard d’un seul voyage, puis elle est généralisée pour traiter des événements plus complexes. Dans cette ap- proche, nous essayons de re-planifier les voyages impactés durant la même semaine de telle sorte qu’une chargeuse soit libre au moment de l’arrivée du camion à la fois au site forestier et à l’usine. De cette façon, les voyages des autres camions ne seront pas mo- difiés. Cette approche fournit aux répartiteurs des plans alternatifs en quelques secondes. De meilleures solutions pourraient être obtenues si le répartiteur était autorisé à apporter plus de modifications au plan initial. Dans le second article, nous considérons un contexte où un seul voyage à la fois est communiqué aux chauffeurs. Le répartiteur attend jusqu’à ce que le chauffeur termine son voyage avant de lui révéler le prochain voyage. Ce contexte est plus souple et offre plus de possibilités de recours en cas d’imprévus. En plus, le problème hebdomadaire peut être divisé en des problèmes quotidiens, puisque la demande est quotidienne et les usines sont ouvertes pendant des périodes limitées durant la journée. Nous utilisons un modèle de programmation mathématique basé sur un réseau espace-temps pour réagir aux perturbations. Bien que ces dernières puissent avoir des effets différents sur le plan de transport initial, une caractéristique clé du modèle proposé est qu’il reste valable pour traiter tous les imprévus, quelle que soit leur nature. En effet, l’impact de ces événements est capturé dans le réseau espace-temps et dans les paramètres d’entrée plutôt que dans le modèle lui-même. Le modèle est résolu pour la journée en cours chaque fois qu’un événement imprévu est révélé. Dans le dernier article, la flotte de camions est hétérogène, comprenant des camions avec des chargeuses à bord. La configuration des routes de ces camions est différente de celle des camions réguliers, car ils ne doivent pas être synchronisés avec les chargeuses. Nous utilisons un modèle mathématique où les colonnes peuvent être facilement et naturellement interprétées comme des itinéraires de camions. Nous résolvons ce modèle en utilisant la génération de colonnes. Dans un premier temps, nous relaxons l’intégralité des variables de décision et nous considérons seulement un sous-ensemble des itinéraires réalisables. Les itinéraires avec un potentiel d’amélioration de la solution courante sont ajoutés au modèle de manière itérative. Un réseau espace-temps est utilisé à la fois pour représenter les impacts des événements imprévus et pour générer ces itinéraires. La solution obtenue est généralement fractionnaire et un algorithme de branch-and-price est utilisé pour trouver des solutions entières. Plusieurs scénarios de perturbation ont été développés pour tester l’approche proposée sur des études de cas provenant de l’industrie forestière canadienne et les résultats numériques sont présentés pour les trois contextes.

GRASP and statistical bounds for heuristic solutions to combinatorial problems

The quality of a heuristic solution to a NP-hard combinatorial problem is hard to assess. A few studies have advocated and tested statistical bounds as a method for assessment. These studies indicate that statistical bounds are superior to the more widely known and used deterministic bounds. However, the previous studies have been limited to a few metaheuristics and combinatorial problems and, hence, the general performance of statistical bounds in combinatorial optimization remains an open question. This work complements the existing literature on statistical bounds by testing them on the metaheuristic Greedy Randomized Adaptive Search Procedures (GRASP) and four combinatorial problems. Our findings confirm previous results that statistical bounds are reliable for the p-median problem, while we note that they also seem reliable for the set covering problem. For the quadratic assignment problem, the statistical bounds has previously been found reliable when obtained from the Genetic algorithm whereas in this work they found less reliable. Finally, we provide statistical bounds to four 2-path network design problem instances for which the optimum is currently unknown.

Convex Optimization Algorithms and Statistical Bounds for Learning Structured Models

Thesis (Ph.D.)--University of Washington, 2016-08

Discrete-event Simulation and Optimization to Improve the Performance of a Healthcare System

Thesis (Ph.D.)--University of Washington, 2016-08

Problems in Algebraic Vision

Thesis (Ph.D.)--University of Washington, 2016-08

Ant Colony Optimization for Requirement selection in Incremental Software development

This proposal shows that ACO systems can be applied to problems of requirements selection in software incremental development, with the idea of obtaining better results of those produced by expert judgment alone. The evaluation of the ACO systems should be done through a compared analysis with greedy and simulated annealing algorithms, performing experiments with some problems instances

'The application of Bayesian Optimization and Classifier Systems in Nurse Scheduling'

Abstract. Two ideas taken from Bayesian optimization and classifier systems are presented for personnel scheduling based on choosing a suitable scheduling rule from a set for each person's assignment. Unlike our previous work of using genetic algorithms whose learning is implicit, the learning in both approaches is explicit, i.e. we are able to identify building blocks directly. To achieve this target, the Bayesian optimization algorithm builds a Bayesian network of the joint probability distribution of the rules used to construct solutions, while the adapted classifier system assigns each rule a strength value that is constantly updated according to its usefulness in the current situation. Computational results from 52 real data instances of nurse scheduling demonstrate the success of both approaches. It is also suggested that the learning mechanism in the proposed approaches might be suitable for other scheduling problems.

Hybrid Graph Heuristics within a Hyper-heuristic Approach to Exam Timetabling Problems

This paper is concerned with the hybridization of two graph coloring heuristics (Saturation Degree and Largest Degree), and their application within a hyperheuristic for exam timetabling problems. Hyper-heuristics can be seen as algorithms which intelligently select appropriate algorithms/heuristics for solving a problem. We developed a Tabu Search based hyper-heuristic to search for heuristic lists (of graph heuristics) for solving problems and investigated the heuristic lists found by employing knowledge discovery techniques. Two hybrid approaches (involving Saturation Degree and Largest Degree) including one which employs Case Based Reasoning are presented and discussed. Both the Tabu Search based hyper-heuristic and the hybrid approaches are tested on random and real-world exam timetabling problems. Experimental results are comparable with the best state-of-the-art approaches (as measured against established benchmark problems). The results also demonstrate an increased level of generality in our approach.

A Multi-Objective Approach for VNE: Problems using multiple ILP formulations

Network Virtualization is a key technology for the Future Internet, allowing the deployment of multiple independent virtual networks that use resources of the same basic infrastructure. An important challenge in the dynamic provision of virtual networks resides in the optimal allocation of physical resources (nodes and links) to requirements of virtual networks. This problem is known as Virtual Network Embedding (VNE). For the resolution of this problem, previous research has focused on designing algorithms based on the optimization of a single objective. On the contrary, in this work we present a multi-objective algorithm, called VNE-MO-ILP, for solving dynamic VNE problem, which calculates an approximation of the Pareto Front considering simultaneously resource utilization and load balancing. Experimental results show evidences that the proposed algorithm is better or at least comparable to a state-of-the-art algorithm. Two performance metrics were simultaneously evaluated: (i) Virtual Network Request Acceptance Ratio and (ii) Revenue/Cost Relation. The size of test networks used in the experiments shows that the proposed algorithm scales well in execution times, for networks of 84 nodes

Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Thermal Tracking and Estimation for Microprocessors

Due to increasing integration density and operating frequency of today's high performance processors, the temperature of a typical chip can easily exceed 100 degrees Celsius. However, the runtime thermal state of a chip is very hard to predict and manage due to the random nature in computing workloads, as well as the process, voltage and ambient temperature variability (together called PVT variability). The uneven nature (both in time and space) of the heat dissipation of the chip could lead to severe reliability issues and error-prone chip behavior (e.g. timing errors). Many dynamic power/thermal management techniques have been proposed to address this issue such as dynamic voltage and frequency scaling (DVFS), clock gating and etc. However, most of such techniques require accurate knowledge of the runtime thermal state of the chip to make efficient and effective control decisions. In this work we address the problem of tracking and managing the temperature of microprocessors which include the following sub-problems: (1) how to design an efficient sensor-based thermal tracking system on a given design that could provide accurate real-time temperature feedback; (2) what statistical techniques could be used to estimate the full-chip thermal profile based on very limited (and possibly noise-corrupted) sensor observations; (3) how do we adapt to changes in the underlying system's behavior, since such changes could impact the accuracy of our thermal estimation. The thermal tracking methodology proposed in this work is enabled by on-chip sensors which are already implemented in many modern processors. We first investigate the underlying relationship between heat distribution and power consumption, then we introduce an accurate thermal model for the chip system. Based on this model, we characterize the temperature correlation that exists among different chip modules and explore statistical approaches (such as those based on Kalman filter) that could utilize such correlation to estimate the accurate chip-level thermal profiles in real time. Such estimation is performed based on limited sensor information because sensors are usually resource constrained and noise-corrupted. We also took a further step to extend the standard Kalman filter approach to account for (1) nonlinear effects such as leakage-temperature interdependency and (2) varying statistical characteristics in the underlying system model. The proposed thermal tracking infrastructure and estimation algorithms could consistently generate accurate thermal estimates even when the system is switching among workloads that have very distinct characteristics. Through experiments, our approaches have demonstrated promising results with much higher accuracy compared to existing approaches. Such results can be used to ensure thermal reliability and improve the effectiveness of dynamic thermal management techniques.

Bayesian Optimisation Algorithm for Nurse Scheduling, Scalable Optimization via Probabilistic Modeling

Our research has shown that schedules can be built mimicking a human scheduler by using a set of rules that involve domain knowledge. This chapter presents a Bayesian Optimization Algorithm (BOA) for the nurse scheduling problem that chooses such suitable scheduling rules from a set for each nurse’s assignment. Based on the idea of using probabilistic models, the BOA builds a Bayesian network for the set of promising solutions and samples these networks to generate new candidate solutions. Computational results from 52 real data instances demonstrate the success of this approach. It is also suggested that the learning mechanism in the proposed algorithm may be suitable for other scheduling problems.

'The application of Bayesian Optimization and Classifier Systems in Nurse Scheduling'

Abstract. Two ideas taken from Bayesian optimization and classifier systems are presented for personnel scheduling based on choosing a suitable scheduling rule from a set for each person's assignment. Unlike our previous work of using genetic algorithms whose learning is implicit, the learning in both approaches is explicit, i.e. we are able to identify building blocks directly. To achieve this target, the Bayesian optimization algorithm builds a Bayesian network of the joint probability distribution of the rules used to construct solutions, while the adapted classifier system assigns each rule a strength value that is constantly updated according to its usefulness in the current situation. Computational results from 52 real data instances of nurse scheduling demonstrate the success of both approaches. It is also suggested that the learning mechanism in the proposed approaches might be suitable for other scheduling problems.

Optimization of flocculation process and continuous filtration for sea water primary treatment filtration to reduce SDI for entree to reverse osmosis system

Today , Providing drinking water and process water is one of the major problems in most countries ; the surface water often need to be treated to achieve necessary quality, and in this way, technological and also financial difficulties cause great restrictions in operating the treatment units. Although water supply by simple and cheap systems has been one of the important objectives in most scientific and research centers in the world, still a great percent of population in developing countries, especially in rural areas, don't benefit well quality water. One of the big and available sources for providing acceptable water is sea water. There are two ways to treat sea water first evaporation and second reverse osmosis system. Nowadays R.O system has been used for desalination because of low budget price and easily to operate and maintenance. The sea water should be pretreated before R.O plants, because there is some difficulties in raw sea water that can decrease yield point of membranes in R.O system. The subject of this research may be useful in this way, and we hope to be able to achieve complete success in design and construction of useful pretreatment systems for R.O plant. One of the most important units in the sea water pretreatment plant is filtration, the conventional method for filtration is pressurized sand filters, and the subject of this research is about new filtration which is called continuous back wash sand filtration (CBWSF). The CBWSF designed and tested in this research may be used more economically with less difficulty. It consists two main parts first shell body and second central part comprising of airlift pump, raw water feeding pipe, air supply hose, backwash chamber and sand washer as well as inlet and outlet connections. The CBWSF is a continuously operating filter, i.e. the filter does not have to be taken out of operation for backwashing or cleaning. Inlet water is fed through the sand bed while the sand bed is moving downwards. The water gets filtered while the sand becomes dirty. Simultaneously, the dirty sand is cleaned in the sand washer and the suspended solids are discharged in backwash water. We analyze the behavior of CBWSF in pretreatment of sea water instead of pressurized sand filter. There is one important factor which is not suitable for R.O membranes, it is bio-fouling. This factor is defined by Silt Density Index (SDI).measured by SDI. In this research has been focused on decreasing of SDI and NTU. Based on this goal, the prototype of pretreatment had been designed and manufactured to test. The system design was done mainly by using the design fundamentals of CBWSF. The automatic backwash sand filter can be used in small and also big water supply schemes. In big water treatment plants, the units of filters perform the filtration and backwash stages separately, and in small treatment plants, the unit is usually compacted to achieve less energy consumption. The analysis of the system showed that it may be used feasibly for water treating, especially for limited population. The construction is rapid, simple and economic, and its performance is high enough because no mobile mechanical part is used in it, so it may be proposed as an effective method to improve the water quality and consequently the hygiene level in the remote places of the country.