Fuzzy clustering of univariate and multivariate time series by genetic multiobjective optimization

Given a set of time series, it is of interest to discover subsets that share similar properties. For instance, this may be useful for identifying and estimating a single model that may fit conveniently several time series, instead of performing the usual identification and estimation steps for each one. On the other hand time series in the same cluster are related with respect to the measures assumed for cluster analysis and are suitable for building multivariate time series models. Though many approaches to clustering time series exist, in this view the most effective method seems to have to rely on choosing some features relevant for the problem at hand and seeking for clusters according to their measurements, for instance the autoregressive coe±cients, spectral measures or the eigenvectors of the covariance matrix. Some new indexes based on goodnessof-fit criteria will be proposed in this paper for fuzzy clustering of multivariate time series. A general purpose fuzzy clustering algorithm may be used to estimate the proper cluster structure according to some internal criteria of cluster validity. Such indexes are known to measure actually definite often conflicting cluster properties, compactness or connectedness, for instance, or distribution, orientation, size and shape. It is argued that the multiobjective optimization supported by genetic algorithms is a most effective choice in such a di±cult context. In this paper we use the Xie-Beni index and the C-means functional as objective functions to evaluate the cluster validity in a multiobjective optimization framework. The concept of Pareto optimality in multiobjective genetic algorithms is used to evolve a set of potential solutions towards a set of optimal non-dominated solutions. Genetic algorithms are well suited for implementing di±cult optimization problems where objective functions do not usually have good mathematical properties such as continuity, differentiability or convexity. In addition the genetic algorithms, as population based methods, may yield a complete Pareto front at each step of the iterative evolutionary procedure. The method is illustrated by means of a set of real data and an artificial multivariate time series data set.Fuzzy clustering, Internal criteria of cluster validity, Genetic algorithms, Multiobjective optimization, Time series, Pareto optimality

Optimization. An attempt at describing the State of the Art

This paper is an attempt at describing the State of the Art of the vast field of continuous optimization. We will survey deterministic and stochastic methods as well as hybrid approaches in their application to single objective and multiobjective optimization. We study the parameters of optimization algorithms and possibilities for tuning them. Finally, we discuss several methods for using approximate models for computationally expensive problems

Fuzzy clustering of univariate and multivariate time series by genetic multiobjective optimization

COMISEF Working Papers Series WPS-028 08/02/2010 URL: http://comisef.eu/files/wps028.pd

Explicit Building Block Multiobjective Evolutionary Computation: Methods and Applications

This dissertation presents principles, techniques, and performance of evolutionary computation optimization methods. Concentration is on concepts, design formulation, and prescription for multiobjective problem solving and explicit building block (BB) multiobjective evolutionary algorithms (MOEAs). Current state-of-the-art explicit BB MOEAs are addressed in the innovative design, execution, and testing of a new multiobjective explicit BB MOEA. Evolutionary computation concepts examined are algorithm convergence, population diversity and sizing, genotype and phenotype partitioning, archiving, BB concepts, parallel evolutionary algorithm (EA) models, robustness, visualization of evolutionary process, and performance in terms of effectiveness and efficiency. The main result of this research is the development of a more robust algorithm where MOEA concepts are implicitly employed. Testing shows that the new MOEA can be more effective and efficient than previous state-of-the-art explicit BB MOEAs for selected test suite multiobjective optimization problems (MOPs) and U.S. Air Force applications. Other contributions include the extension of explicit BB definitions to clarify the meanings for good single and multiobjective BBs. A new visualization technique is developed for viewing genotype, phenotype, and the evolutionary process in finding Pareto front vectors while tracking the size of the BBs. The visualization technique is the result of a BB tracing mechanism integrated into the new MOEA that enables one to determine the required BB sizes and assign an approximation epistasis level for solving a particular problem. The culmination of this research is explicit BB state-of-the-art MOEA technology based on the MOEA design, BB classifier type assessment, solution evolution visualization, and insight into MOEA test metric validation and usage as applied to test suite, deception, bioinformatics, unmanned vehicle flight pattern, and digital symbol set design MOPs

Adaptive algorithms for history matching and uncertainty quantification

Numerical reservoir simulation models are the basis for many decisions in regard to predicting, optimising, and improving production performance of oil and gas reservoirs. History matching is required to calibrate models to the dynamic behaviour of the reservoir, due to the existence of uncertainty in model parameters. Finally a set of history matched models are used for reservoir performance prediction and economic and risk assessment of different development scenarios. Various algorithms are employed to search and sample parameter space in history matching and uncertainty quantification problems. The algorithm choice and implementation, as done through a number of control parameters, have a significant impact on effectiveness and efficiency of the algorithm and thus, the quality of results and the speed of the process. This thesis is concerned with investigation, development, and implementation of improved and adaptive algorithms for reservoir history matching and uncertainty quantification problems. A set of evolutionary algorithms are considered and applied to history matching. The shared characteristic of applied algorithms is adaptation by balancing exploration and exploitation of the search space, which can lead to improved convergence and diversity. This includes the use of estimation of distribution algorithms, which implicitly adapt their search mechanism to the characteristics of the problem. Hybridising them with genetic algorithms, multiobjective sorting algorithms, and real-coded, multi-model and multivariate Gaussian-based models can help these algorithms to adapt even more and improve their performance. Finally diversity measures are used to develop an explicit, adaptive algorithm and control the algorithm’s performance, based on the structure of the problem. Uncertainty quantification in a Bayesian framework can be carried out by resampling of the search space using Markov chain Monte-Carlo sampling algorithms. Common critiques of these are low efficiency and their need for control parameter tuning. A Metropolis-Hastings sampling algorithm with an adaptive multivariate Gaussian proposal distribution and a K-nearest neighbour approximation has been developed and applied

Efficient Learning Machines

Computer scienc

Several fitness functions and entanglement gates in quantum kernel generation

Quantum machine learning (QML) represents a promising frontier in the realm of quantum technologies. In this pursuit of quantum advantage, the quantum kernel method for support vector machine has emerged as a powerful approach. Entanglement, a fundamental concept in quantum mechanics, assumes a central role in quantum computing. In this paper, we study the necessities of entanglement gates in the quantum kernel methods. We present several fitness functions for a multi-objective genetic algorithm that simultaneously maximizes classification accuracy while minimizing both the local and non-local gate costs of the quantum feature map's circuit. We conduct comparisons with classical classifiers to gain insights into the benefits of employing entanglement gates. Surprisingly, our experiments reveal that the optimal configuration of quantum circuits for the quantum kernel method incorporates a proportional number of non-local gates for entanglement, contrary to previous literature where non-local gates were largely suppressed. Furthermore, we demonstrate that the separability indexes of data can be effectively leveraged to determine the number of non-local gates required for the quantum support vector machine's feature maps. This insight can significantly aid in selecting appropriate parameters, such as the entanglement parameter, in various quantum programming packages like https://qiskit.org/ based on data analysis. Our findings offer valuable guidance for enhancing the efficiency and accuracy of quantum machine learning algorith

A Bayesian Approach to Computer Model Calibration and Model-Assisted Design

Computer models of phenomena that are difficult or impossible to study directly are critical for enabling research and assisting design in many areas. In order to be effective, computer models must be calibrated so that they accurately represent the modeled phenomena. There exists a rich variety of methods for computer model calibration that have been developed in recent decades. Among the desiderata of such methods is a means of quantifying remaining uncertainty after calibration regarding both the values of the calibrated model inputs and the model outputs. Bayesian approaches to calibration have met this need in recent decades. However, limitations remain. Whereas in model calibration one finds point estimates or distributions of calibration inputs in order to induce the model to reflect reality accurately, interest in a computer model often centers primarily on its use for model-assisted design, in which the goal is to find values for design inputs to induce the modeled system to approximate some target outcome. Existing Bayesian approaches are limited to the first of these two tasks. The present work develops an approach adapting Bayesian methods for model calibration for application in model-assisted design. The approach retains the benefits of Bayesian calibration in accounting for and quantifying all sources of uncertainty. It is capable of generating a comprehensive assessment of the Pareto optimal inputs for a multi-objective optimization problem. The present work shows that this approach can apply as a method for model-assisted design using a previously calibrated system, and can also serve as a method for model-assisted design using a model that still requires calibration, accomplishing both ends simultaneously

Advances in Evolutionary Algorithms

With the recent trends towards massive data sets and significant computational power, combined with evolutionary algorithmic advances evolutionary computation is becoming much more relevant to practice. Aim of the book is to present recent improvements, innovative ideas and concepts in a part of a huge EA field