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ItemOnline time series approximation and predictionXu, Zhenghua ( 2012)In recent years, there are rapidly increasing research interests in the management of time series data due to its importance in a variety of applications such as network traffic management, telecommunications, finance, sensor network and location based services. In this thesis, we focus on two important problems of the management of time series data: the online time series approximation problem and the online time series prediction problem. The time series approximation can reduce the space and the computational cost of storing and transmitting time series data, and also reduce the workload of the data processing. Segmentation is one of the most commonly used methods to meet this requirement. However, while most of the current segmentation methods aim to minimize the holistic error between the approximation and the original time series, few works try to represent time series as compact as possible with an error bound guarantee on each data point. Moreover, in many real world situations, the patterns of the time series do not follow a constant rule such that using only one type of functions may not yield the best compaction. Motivated by these observations, we propose an online segmentation algorithm which approximates time series by a set of different types of candidate functions (poly nomials of different orders, exponential functions, etc.) and adaptively chooses the most compact one as the pattern of the time series changes. A challenge in this approach is to determine the approximation function on the fly (“online”). Thereby, we further present a novel method to efficiently generate the compact approximation of a time series in an online fashion for several types of candidate functions. This method incrementally narrows the feasible coefficient spaces of candidate functions in coefficient coordinate systems such that it can make each segment as long as possible given an error bound on each data point. Extensive experimental results show that our algorithm generates more compact approximations of the time series with lower average errors than the state-of-the-art algorithm. The time series prediction aims to predict future values of the time series according to their previously observed values. In this thesis, we focus our work on a specific branch of the time series prediction: the online locational time series prediction problem, i.e, predicting the final locations of the locational time series according to their current observed locational time series values on the fly. This problem is also called the destination prediction problem and the systems used to solve this problem are the called destination prediction systems. However, most of current destination prediction systems are based on the traveling histories of specific users so they are too ad hoc to accurately predict other users’ destination. In our work, we propose the first generic destination prediction solution to provide the accurate destination prediction services to all users based on the given user queries (i.e., the users’ current partial traveling trajectories) without knowing any traveling histories of the users. Extensive experiments validate that the prediction result of our method is more accurate than that of the competing method.
ItemOn the Pareto-Following Variation Operator for fast converging Multiobjective Evolutionary AlgorithmsTalukder, A. K. M. K. A. ( 2008)The focus of this research is to provide an efficient approach to deal with computationally expensive Multiobjective Optimization Problems (MOP’s). Typically, approximation or surrogate based techniques are adopted to reduce the computational cost. In such cases, the original expensive objective function is replaced by a cheaper mathematical model, where this model mimics the behavior/input-output (i.e. design variable – objective value) relationship. However, it is difficult to model an exact substitute of the targeted objective function. Furthermore, if this kind of approach is used in an evolutionary search, literally, the number of function evaluations does not reduce (i.e. The number of original function evaluation is replaced by the number of surrogate/approximate function evaluation). However, if a large number of individuals are considered, the surrogate model fails to offer smaller computational cost. To tackle this problem, we have reformulated the concept of surrogate modeling in a different way, which is more suitable for the Multiobjective Evolutionary Algorithm(MOEA) paradigm. In our approach, we do not approximate the objective function; rather we model the input-output behavior of the underlying MOEA itself. The model attempts to identify the search path (in both design-variable and objective spaces) and from this trajectory the model is guaranteed to generate non-dominated solutions (especially, during the initial iterations of the underlying MOEA – with respect to the current solutions) for the next iterations of the MOEA. Therefore, the MOEA can avoid re-evaluating the dominated solutions and thus can save large amount of computational cost due to expensive function evaluations. We have designed our approximation model as a variation operator – that follows the trajectory of the fronts and can be “plugged-in” to any kind of MOEA where non-domination based selection is used. Hence it is termed– the “Pareto-Following Variation Operator (PFVO)”. This approach also provides some added advantage that we can still use the original objective function and thus the search procedure becomes robust and suitable, especially for dynamic problems. We have integrated the model into three base-line MOEA’s: “Non-dominated Sorting Genetic Algorithm - II (NSGA-II)”, “Strength Pareto Evolutionary Algorithm - II (SPEAII)”and the recently proposed “Regularity Model Based Estimation of Distribution Algorithm (RM-MEDA)”. We have also conducted an exhaustive simulation study using several benchmark MOP’s. Detailed performance and statistical analysis reveals promising results. As an extension, we have implemented our idea for dynamic MOP’s. We have also integrated PFVO into diffusion based/cellular MOEA in a distributed/Grid environment. Most experimental results and analysis reveal that PFVO can be used as a performance enhancement tool for any kind of MOEA.