205 research outputs found

    The development of a weighted directed graph model for dynamic systems and application of Dijkstra’s algorithm to solve optimal control problems.

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    Master of Science (Chemical Engineering). University of KwaZulu-Natal. Durban, 2017.Optimal control problems are frequently encountered in chemical engineering process control applications as a result of the drive for more regulatory compliant, efficient and economical operation of chemical processes. Despite the significant advancements that have been made in Optimal Control Theory and the development of methods to solve this class of optimization problems, limitations in their applicability to non-linear systems inherent in chemical process unit operations still remains a challenge, particularly in determining a globally optimal solution and solutions to systems that contain state constraints. The objective of this thesis was to develop a method for modelling a chemical process based dynamic system as a graph so that an optimal control problem based on the system can be solved as a shortest path graph search problem by applying Dijkstra’s Algorithm. Dijkstra’s algorithm was selected as it is proven to be a robust and global optimal solution based algorithm for solving the shortest path graph search problem in various applications. In the developed approach, the chemical process dynamic system was modelled as a weighted directed graph and the continuous optimal control problem was reformulated as graph search problem by applying appropriate finite discretization and graph theoretic modelling techniques. The objective functional and constraints of an optimal control problem were successfully incorporated into the developed weighted directed graph model and the graph was optimized to represent the optimal transitions between the states of the dynamic system, resulting in an Optimal State Transition Graph (OST Graph). The optimal control solution for shifting the system from an initial state to every other achievable state for the dynamic system was determined by applying Dijkstra’s Algorithm to the OST Graph. The developed OST Graph-Dijkstra’s Algorithm optimal control solution approach successfully solved optimal control problems for a linear nuclear reactor system, a non-linear jacketed continuous stirred tank reactor system and a non-linear non-adiabatic batch reactor system. The optimal control solutions obtained by the developed approach were compared with solutions obtained by the variational calculus, Iterative Dynamic Programming and the globally optimal value-iteration based Dynamic Programming optimal control solution approaches. Results revealed that the developed OST Graph-Dijkstra’s Algorithm approach provided a 14.74% improvement in the optimality of the optimal control solution compared to the variational calculus solution approach, a 0.39% improvement compared to the Iterative Dynamic Programming approach and the exact same solution as the value–iteration Dynamic Programming approach. The computational runtimes for optimal control solutions determined by the OST Graph-Dijkstra’s Algorithm approach were 1 hr 58 min 33.19 s for the nuclear reactor system, 2 min 25.81s for the jacketed reactor system and 8.91s for the batch reactor system. It was concluded from this work that the proposed method is a promising approach for solving optimal control problems for chemical process-based dynamic systems

    A Finite Domain Constraint Approach for Placement and Routing of Coarse-Grained Reconfigurable Architectures

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    Scheduling, placement, and routing are important steps in Very Large Scale Integration (VLSI) design. Researchers have developed numerous techniques to solve placement and routing problems. As the complexity of Application Specific Integrated Circuits (ASICs) increased over the past decades, so did the demand for improved place and route techniques. The primary objective of these place and route approaches has typically been wirelength minimization due to its impact on signal delay and design performance. With the advent of Field Programmable Gate Arrays (FPGAs), the same place and route techniques were applied to FPGA-based design. However, traditional place and route techniques may not work for Coarse-Grained Reconfigurable Architectures (CGRAs), which are reconfigurable devices offering wider path widths than FPGAs and more flexibility than ASICs, due to the differences in architecture and routing network. Further, the routing network of several types of CGRAs, including the Field Programmable Object Array (FPOA), has deterministic timing as compared to the routing fabric of most ASICs and FPGAs reported in the literature. This necessitates a fresh look at alternative approaches to place and route designs. This dissertation presents a finite domain constraint-based, delay-aware placement and routing methodology targeting an FPOA. The proposed methodology takes advantage of the deterministic routing network of CGRAs to perform a delay aware placement

    A new ant colony optimization model for complex graph-based problems

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    Tesis doctoral inédita leída en la Universidad Autónoma de Madrid. Escuela Politécnica Superior, Departamento de Ingeniería Informática. Fecha de lectura: julio de 2014Nowadays, there is a huge number of problems that due to their complexity have employed heuristic-based algorithms to search for near-to-optimal (or even optimal) solutions. These problems are usually NP-complete, so classical algorithms are not the best candidates to address these problems because they need a large amount of computational resources, or they simply cannot find any solution when the problem grows. Some classical examples of these kind of problems are the Travelling Salesman Problem (TSP) or the N-Queens problem. It is also possible to find examples in real and industrial domains related to the optimization of complex problems, like planning, scheduling, Vehicle Routing Problems (VRP), WiFi network Design Problem (WiFiDP) or behavioural pattern identification, among others. Regarding to heuristic-based algorithms, two well-known paradigms are Swarm Intelligence and Evolutionary Computation. Both paradigms belongs to a subfield from Artificial Intelligence, named Computational Intelligence that also contains Fuzzy Systems, Artificial Neural Networks and Artificial Immune Systems areas. Swarm Intelligence (SI) algorithms are focused on the collective behaviour of selforganizing systems. These algorithms are characterized by the generation of collective intelligence from non-complex individual behaviour and the communication schemes amongst them. Some examples of SI algorithms are particle swarm optimization, ant colony optimization (ACO), bee colony optimization o bird flocking. Ant Colony Optimization (ACO) are based on the foraging behaviour of these insects. In these kind of algorithms, the ants take different decisions during their execution that allows them to build their own solution to the problem. Once any ant has finished its execution, the ant goes back through the followed path and it deposits, in the environment, pheromones that contains information about the built solution. These pheromones will influence the decision of future ants, so there is an indirect communication through the environment called stigmergy. When an ACO algorithm is applied to any of the optimization problems just described, the problem is usually modelled into a graph. Nevertheless, the classical graph-based representation is not the best one for the execution of ACO algorithms because it presents some important pitfalls. The first one is related to the polynomial, or even exponential, growth of the resulting graph. The second pitfall is related to those problems that needs from real variables because these problems cannot be modelled using the classical graph-based representation. On the other hand, Evolutionary Computation (EC) are a set of population-based algorithms based in the Darwinian evolutionary process. In this kind of algorithms there is one (or more) population composed by different individuals that represent a possible solution to the problem. For each iteration, the population evolves by the use of evolutionary procedures which means that better individuals (i.e. better solutions) are generated along the execution of the algorithm. Both kind of algorithms, EC and SI, have been traditionally applied in previous NP-hard problems. Different population-based strategies have been developed, compared and even combined to design hybrid algorithms. This thesis has been focused on the analysis of classical graph-based representations and its application in ACO algorithms into complex problems, and the development of a new ACO model that tries to take a step forward in this kind of algorithms. In this new model, the problem is represented using a reduced graph that affects to the ants behaviour, which becomes more complex. Also, this size reduction generates a fast growth in the number of pheromones created. For this reason, a new metaheuristic (called Oblivion Rate) has been designed to control the number of pheromones stored in the graph. In this thesis different metaheuristics have been designed for the proposed system and their performance have been compared. One of these metaheuristics is the Oblivion Rate, based on an exponential function that takes into account the number of pheromones created in the system. Other Oblivion Rate function is based on a bioinspired swarm algorithm that uses some concepts extracted from the evolutionary algorithms. This bio-inspired swarm algorithm is called Coral Reef Opmization (CRO) algorithm and it is based on the behaviour of the corals in a reef. Finally, to test and validate the proposed model, different domains have been used such as the N-Queens Problem, the Resource-Constraint Project Scheduling Problem, the Path Finding problem in Video Games, or the Behavioural Pattern Identification in users. In some of these domains, the performance of the proposed model has been compared against a classical Genetic Algorithm to provide a comparative study and perform an analytical comparison between both approaches.En la actualidad, existen un gran número de problemas que debido a su complejidad necesitan algoritmos basados en heurísticas para la búsqueda de solucionas subóptimas (o incluso óptimas). Normalmente, estos problemas presentan una complejidad NP-completa, por lo que los algoritmos clásicos de búsqueda de soluciones no son apropiados ya que necesitan una gran cantidad de recursos computacionales, o simplemente, no son capaces de encontrar alguna solución cuando el problema crece. Ejemplos clásicos de este tipo de problemas son el problema del vendedor viajero (o TSP del inglés Travelling Salesman Problem) o el problema de las N-reinas. También se pueden encontrar ejemplos en dominios reales o industriales que generalmente están ligados a temas de optimización de sistemas complejos, como pueden ser problemas de planificación, scheduling, problemas de enrutamiento de vehículos (o VRP del inglés Vehicle Routing Problem), el diseño de redes Wifi abiertas (o WiFiDP del inglés WiFi network Design Problem), o la identificación de patrones de comportamiento, entre otros. En lo referente a los algoritmos basados en heuristicas, dos paradigmas muy conocidos son los algoritmos de enjambre (Swarm Intelligence) y la computación evolutiva (Evolutionary Computation). Ambos paradigmas pertencen al subárea de la Inteligencia Artificial denominada Inteligencia Computacional, que además contiene los sistemas difusos, redes neuronales y sistemas inmunológicos artificiales. Los algoritmos de inteligencia de enjambre, o Swarm Intelligence, se centran en el comportamiento colectivo de sistemas auto-organizativos. Estos algoritmos se caracterizan por la generación de inteligencia colectiva a partir del comportamiento, no muy complejo, de los individuos y los esquemas de comunicación entre ellos. Algunos ejemplos son particle swarm optimization, ant colony optimization (ACO), bee colony optimization o bird flocking. Los algoritmos de colonias de hormigas (o ACO del inglés Ant Colony Optimization) se basan en el comportamiento de estos insectos en el proceso de recolección de comida. En este tipo de algoritmos, las hormigas van tomando decisiones a lo largo de la simulación que les permiten construir su propia solución al problema. Una vez que una hormiga termina su ejecución, deshace el camino andado depositando en el entorno feronomas que contienen información sobre la solución construida. Estas feromonas influirán en las decisiones de futuras hormigas, por lo que produce una comunicación indirecta utilizando el entorno. A este proceso se le llama estigmergia. Cuando un algoritmo de hormigas se aplica a alguno de los problemas de optimización descritos anteriormente, se suele modelar el problema como un grafo sobre el cual se ejecutarán las hormigas. Sin embargo, la representación basada en grafos clásica no parece ser la mejor para la ejecución de algoritmos de hormigas porque presenta algunos problemas importantes. El primer problema está relacionado con el crecimiento polinómico, o incluso expnomencial, del grafo resultante. El segundo problema tiene que ver con los problemas que necesitan de variables reales, o de coma flotante, porque estos problemas, con la representación tradicional basada en grafos, no pueden ser modelados. Por otro lado, los algoritmos evolutivos (o EC del inglés Evolutionary Computation) son un tipo de algoritmos basados en población que están inspirados en el proceso evolutivo propuesto por Darwin. En este tipo de algoritmos, hay una, o varias, poblaciones compuestas por individuos diferentes que representan problems solutiones al problema modelado. Por cada iteración, la población evoluciona mediante el uso de procedimientos evolutivos, lo que significa que mejores individuos (mejores soluciones) son creados a lo largo de la ejecución del algoritmo. Ambos tipos de algorithmos, EC y SI, han sido tradicionalmente aplicados a los problemas NPcompletos descritos anteriormente. Diferentes estrategias basadas en población han sido desarrolladas, comparadas e incluso combinadas para el diseño de algoritmos híbridos. Esta tesis se ha centrado en el análisis de los modelos clásicos de representación basada en grafos de problemas complejos para la posterior ejecución de algoritmos de colonias de hormigas y el desarrollo de un nuevo modelo de hormigas que pretende suponer un avance en este tipo de algoritmos. En este nuevo modelo, los problemas son representados en un grafo más compacto que afecta al comportamiento de las hormigas, el cual se vuelve más complejo. Además, esta reducción en el tamaño del grafo genera un rápido crecimiento en el número de feronomas creadas. Por esta razón, una nueva metaheurística (llamada Oblivion Rate) ha sido diseñada para controlar el número de feromonas almacenadas en el grafo. En esta tesis, varias metaheuristicas han sido diseñadas para el sistema propuesto y sus rendimientos han sido comparados. Una de estas metaheurísticas es la Oblivion Rate basada en una función exponencial que tiene en cuenta el número de feromonas creadas en el sistema. Otra Oblivion Rate está basada en un algoritmo de enjambre bio-inspirado que usa algunos conceptos extraídos de la computación evolutiva. Este algoritmo de enjambre bio-inspirado se llama Optimización de arrecifes de corales (o CRO del inglés Coral Reef Optimization) y está basado en el comportamiento de los corales en el arrecife. Finalmente, para validar y testear el modelo propuesto, se han utilizado diversos dominios de aplicación como son el problema de las N-reinas, problemas de planificación de proyectos con restricciones de recursos, problemas de búsqueda de caminos en entornos de videojuegos y la identificación de patrones de comportamiento de usuarios. En algunos de estos dominios, el rendimiento del modelo propuesto ha sido comparado contra un algoritmo genético clásico para realizar un estudio comparativo, y analítico, entre ambos enfoques

    Conflict-Free Routing of Mobile Robots

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    The recent advances in perception have enabled the development of more autonomous mobile robots in the sense that they can operate in a more dynamic environment where obstacles surrounding the robot emerge, disappear, and move. The increased perception of Autonomous Mobile Robots (AMRs) allows them to plan detailed on-line trajectories in order to avoid previously unforeseen obstacles, making AMRs useful in dynamic environments where humans, traditional fork-lifts, and also other mobile robots operate. These abilities contributed to increase automation in logistic applications. This thesis discusses how to efficiently operate a fleet of AMRs and make sure that all tasks are successfully completed.Assigning robots to specific delivery tasks and deciding the routes they have to travel can be modelled as a variant of the classical Vehicle Routing Problem (VRP), the combinatorial optimization problem of designing routes for vehicles. In related research it has been extended to scheduling routes for vehicles to serve customers according to predetermined specifications, such as arrival time at a customer, amount of goods to deliver, etc.In this thesis we consider to schedule a fleet of robots such that areas avoid being congested, delivery time-windows are met, the need for robots to recharge is considered, while at the same time the robots have freedom to use alternative paths to handle changes in the environment. This particular version of the VRP, called CF-EVRP (Conflict-free Electrical Vehicle Routing Problem) is motivated by an industrial need. In this work we consider using optimizing general purpose solvers, in particular, MILP and SMT solvers are investigated. We run extensive computational analysis over well-known combinatorial optimization problems, such as job shop scheduling and bin-packing problems, to evaluate modeling techniques and the relative performance of state-of-the-art MILP and SMT solvers.We propose a monolithic model for the CF-EVRP as well as a compositional approach that decomposes the problem into sub-problems and formulate them as either MILP or SMT problems depending on what fits each particular problem best. The performance of the two approaches is evaluated on a set of CF-EVRP benchmark problems, showing the feasibility of using a compositional approach for solving practical fleet scheduling problems

    An extensive English language bibliography on graph theory and its applications

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    Bibliography on graph theory and its application

    Placement and routing for cross-referencing digital microfluidic biochips.

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    Xiao, Zigang."October 2010."Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (leaves 62-66).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.viChapter 1 --- Introduction --- p.1Chapter 1.1 --- Microfluidic Technology --- p.2Chapter 1.1.1 --- Continuous Flow Microfluidic System --- p.2Chapter 1.1.2 --- Digital Microfluidic System --- p.2Chapter 1.2 --- Pin-Constrained Biochips --- p.4Chapter 1.2.1 --- Droplet-Trace-Based Array Partitioning Method --- p.5Chapter 1.2.2 --- Broadcast-addressing Method --- p.5Chapter 1.2.3 --- Cross-Referencing Method --- p.6Chapter 1.2.3.1 --- Electrode Interference in Cross-Referencing Biochips --- p.7Chapter 1.3 --- Computer-Aided Design Techniques for Biochip --- p.8Chapter 1.4 --- Placement Problem in Biochips --- p.8Chapter 1.5 --- Droplet Routing Problem in Cross-Referencing Biochips --- p.11Chapter 1.6 --- Our Contributions --- p.14Chapter 1.7 --- Thesis Organization --- p.15Chapter 2 --- Literature Review --- p.16Chapter 2.1 --- Introduction --- p.16Chapter 2.2 --- Previous Works on Placement --- p.17Chapter 2.2.1 --- Basic Simulated Annealing --- p.17Chapter 2.2.2 --- Unified Synthesis Approach --- p.18Chapter 2.2.3 --- Droplet-Routing-Aware Unified Synthesis Approach --- p.19Chapter 2.2.4 --- Simulated Annealing Using T-tree Representation --- p.20Chapter 2.3 --- Previous Works on Routing --- p.21Chapter 2.3.1 --- Direct-Addressing Droplet Routing --- p.22Chapter 2.3.1.1 --- A* Search Method --- p.22Chapter 2.3.1.2 --- Open Shortest Path First Method --- p.23Chapter 2.3.1.3 --- A Two Phase Algorithm --- p.24Chapter 2.3.1.4 --- Network-Flow Based Method --- p.25Chapter 2.3.1.5 --- Bypassibility and Concession Method --- p.26Chapter 2.3.2 --- Cross-Referencing Droplet Routing --- p.28Chapter 2.3.2.1 --- Graph Coloring Method --- p.28Chapter 2.3.2.2 --- Clique Partitioning Method --- p.30Chapter 2.3.2.3 --- Progressive-ILP Method --- p.31Chapter 2.4 --- Conclusion --- p.32Chapter 3 --- CrossRouter for Cross-Referencing Biochip --- p.33Chapter 3.1 --- Introduction --- p.33Chapter 3.2 --- Problem Formulation --- p.34Chapter 3.3 --- Overview of Our Method --- p.35Chapter 3.4 --- Net Order Computation --- p.35Chapter 3.5 --- Propagation Stage --- p.36Chapter 3.5.1 --- Fluidic Constraint Check --- p.38Chapter 3.5.2 --- Electrode Constraint Check --- p.38Chapter 3.5.3 --- Handling 3-pin net --- p.44Chapter 3.5.4 --- Waste Reservoir --- p.45Chapter 3.6 --- Backtracking Stage --- p.45Chapter 3.7 --- Rip-up and Re-route Nets --- p.45Chapter 3.8 --- Experimental Results --- p.46Chapter 3.9 --- Conclusion --- p.47Chapter 4 --- Placement in Cross-Referencing Biochip --- p.49Chapter 4.1 --- Introduction --- p.49Chapter 4.2 --- Problem Formulation --- p.50Chapter 4.3 --- Overview of the method --- p.50Chapter 4.4 --- Dispenser and Reservoir Location Generation --- p.51Chapter 4.5 --- Solving Placement Problem Using ILP --- p.51Chapter 4.5.1 --- Constraints --- p.53Chapter 4.5.1.1 --- Validity of modules --- p.53Chapter 4.5.1.2 --- Non-overlapping and separation of Modules --- p.53Chapter 4.5.1.3 --- Droplet-Routing length constraint --- p.54Chapter 4.5.1.4 --- Optical detector resource constraint --- p.55Chapter 4.5.2 --- Objective --- p.55Chapter 4.5.3 --- Problem Partition --- p.56Chapter 4.6 --- Pin Assignment --- p.56Chapter 4.7 --- Experimental Results --- p.57Chapter 4.8 --- Conclusion --- p.59Chapter 5 --- Conclusion --- p.60Bibliography --- p.6

    Acta Cybernetica : Volume 17. Number 2.

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    Strategic Optimization Techniques For FRTU Deployment and Chip Physical Design

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    Combinatorial optimization is a complex engineering subject. Although formulation often depends on the nature of problems that differs from their setup, design, constraints, and implications, establishing a unifying framework is essential. This dissertation investigates the unique features of three important optimization problems that can span from small-scale design automation to large-scale power system planning: (1) Feeder remote terminal unit (FRTU) planning strategy by considering the cybersecurity of secondary distribution network in electrical distribution grid, (2) physical-level synthesis for microfluidic lab-on-a-chip, and (3) discrete gate sizing in very-large-scale integration (VLSI) circuit. First, an optimization technique by cross entropy is proposed to handle FRTU deployment in primary network considering cybersecurity of secondary distribution network. While it is constrained by monetary budget on the number of deployed FRTUs, the proposed algorithm identi?es pivotal locations of a distribution feeder to install the FRTUs in different time horizons. Then, multi-scale optimization techniques are proposed for digital micro?uidic lab-on-a-chip physical level synthesis. The proposed techniques handle the variation-aware lab-on-a-chip placement and routing co-design while satisfying all constraints, and considering contamination and defect. Last, the first fully polynomial time approximation scheme (FPTAS) is proposed for the delay driven discrete gate sizing problem, which explores the theoretical view since the existing works are heuristics with no performance guarantee. The intellectual contribution of the proposed methods establishes a novel paradigm bridging the gaps between professional communities

    Optimization of Robot Motion Planning using Ant Colony Optimization

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    Motion planning in robotics is a process to compute a collision free path between the initial and final configuration among obstacles. To plan a collision free path in the workspace, it would need to plan the motion of every point of its shaping according its degree of freedom. The motion of robot between obstacles is represented by a path in configuration space. It is an imaginary concept. Motion planning is aimed at enabling robots with capabilities of automatically deciding and executing a sequence motion in order to achieve a task without ollision with other objects in a given environment. Motion planning in a robot workspace for robotic assembly depends on sequence of parts or the order they are arranged to produce a robotic assembly product obeying all the constraints and instability of base assembly movement. If the number of parts increases the sequencing becomes difficult and hence the path planning. As multiple no. of paths are possible, the path is considered to be optimal when it minimizes the travelling time while satisfying the process constraint. For this purpose, it is necessary to select appropriate optimization technique for optimization of paths. Such types of problem can be solved by metaheuristic methods.The present work utilizes ACO for the generation of optimal motion planning sequence. The present algorithm is based on ant's behavior, pheromone update & pheromone evaporation and is used to enhance the local search. This procedure is applied to a grinder assembly, driver assembly and car alternator assembly. Two robots like adept-one and puma-762 are selected for picking and placing operation of parts in their workspace

    Learning bounded optimal behavior using Markov decision processes

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.Includes bibliographical references (p. 171-175).Creating agents that behave rationally in the real-world is one goal of Artificial Intelligence. A rational agent is one that takes, at each point in time, the optimal action such that its expected utility is maximized. However, to determine the optimal action the agent may need to engage in lengthy deliberations or computations. The effect of computation is generally not explicitly considered when performing deliberations. In reality, spending too much time in deliberation may yield high quality plans that do not satisfy the natural timing constraints of a problem, making them effectively useless. Enforcing shortened deliberation times may yield timely plans, but these may be of diminished utility. These two cases suggest the possibility of optimizing an agent's deliberation process. This thesis proposes a framework for generating meta level controllers that select computational actions to perform by optimally trading off their benefit against their costs. The metalevel optimization problem is posed within a Markov Decision Process framework and is solved off-line to determine a policy for carrying out computations. Once the optimal policy is determined, it serves efficiently as an online metalevel controller that selects computational actions conditioned upon the current state of computation. Solving for the exact policy of the metalevel optimization problem becomes computationally intractable with problem size. A learning approach that takes advantage of the problem structure is proposed to generate approximate policies that are shown to perform relatively well in comparison to optimal policies. Metalevel policies are generated for two types of problem scenarios, distinguished by the representation of the cost of computation. In the first case, the cost of computation is explicitly defined as part of the problem description. In the second case, it is implicit in the timing constraints of problem. Results are presented to validate the beneficial effects of metalevel planning over traditional methods when the cost of computation has a significant effect on the utility of a plan.by Hon Fai Vuong.Ph.D
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