Search

• Optimal foraging algorithm with direction prediction & Gaussian oscillation is built. • New algorithm includes two update methods: prediction model and random model. • Prediction model mends exploitation ability by predicting the evolutionary direction. • Random model mends exploration by exploring the space with Gaussian distribution. • The superiority of algorithm is verified on benchmark set and engineering problems. Optimal foraging algorithm (OFA) is a newly stochastic optimization technique and is famous for its computational accuracy. However, the high computational accuracy leads to slow convergence speed. Experimental results demonstrate that OFA is good at unimodal functions but poor at multimodal functions. To improve these drawbacks, in this paper a novel modified OFA with direction prediction and Gaussian oscillation, named OFA/P&G is introduced. In OFA/P&G, a transition matrix is constructed when a new global optimum is found to generate the candidate individuals. If the current global optimum does not change, the Gaussian oscillation is employed in a low probability and OFA update method is used in a high probability to generate the candidate individuals. The superior performance of OFA/P&G is verified on the 12 CEC2017 benchmark functions, 13 constrained benchmark functions and 5 engineering problems. Experimental results demonstrate that OFA/P&G outperforms other comparative algorithms. Finally, a real-world problem, drilling path optimization, is solved by OFA/P&G. [ABSTRACT FROM AUTHOR]

Abstract: The Gaussian kernel function implicitly defines the feature space of an algorithm and plays an essential role in the application of kernel methods. The parameter of Gaussian kernel function is a scalar that has significant influences on final results. However, until now, it is still unclear how to choose an optimal kernel parameter. In this paper, we propose a novel data-driven method to optimize the Gaussian kernel parameter, which only depends on the original dataset distribution and yields a simple solution to this complex problem. The proposed method is task irrelevant and can be used in any Gaussian kernel-based approach, including supervised and unsupervised machine learning. Simulation experiments demonstrate the efficacy of the obtained results. A user-friendly online calculator is implemented at: www.csbio.sjtu.edu.cn/bioinf/kernel/ for public use. [Copyright &y& Elsevier]

Abstract: This paper deals with the convergence of the expected improvement algorithm, a popular global optimization algorithm based on a Gaussian process model of the function to be optimized. The first result is that under some mild hypotheses on the covariance function k of the Gaussian process, the expected improvement algorithm produces a dense sequence of evaluation points in the search domain, when the function to be optimized is in the reproducing kernel Hilbert space generated by k. The second result states that the density property also holds for all continuous functions, where P is the (prior) probability distribution induced by the Gaussian process. [Copyright &y& Elsevier]

Abstract: This paper develops a new understanding of mean shift algorithms from an information theoretic perspective. We show that the Gaussian blurring mean shift (GBMS) directly minimizes the Renyi’s quadratic entropy of the dataset and hence is unstable by definition. Further, its stable counterpart, the Gaussian mean shift (GMS), minimizes the Renyi’s “cross” entropy where the local stationary solutions are modes of the dataset. By doing so, we aptly answer the question “What does mean shift algorithms optimize?”, thus highlighting naturally the properties of these algorithms. A consequence of this new understanding is the superior performance of GMS over GBMS which we show in a wide variety of applications ranging from mode finding to clustering and image segmentation. [Copyright &y& Elsevier]

Abstract: In this paper, an efficient approach to search for the global threshold of image using Gaussian mixture model is proposed. Firstly, a gray-level histogram of an image is represented as a function of the frequencies of gray-level. Then to fit the Gaussian mixtures to the histogram of image, the expectation maximization (EM) algorithm is developed to estimate the number of Gaussian mixture of such histograms and their corresponding parameterization. Finally, the optimal threshold which is the average of these Gaussian mixture means is chosen. And the experimental results show that the new algorithm performs better. [Copyright &y& Elsevier]

Abstract: The most commonly used parameters selection method for support vector machines (SVM) is cross-validation, which needs a long-time complicated calculation. In this paper, a novel regularization parameter and a kernel parameter tuning approach of SVM are presented based on quantum-inspired evolutionary algorithm (QEA). QEA with quantum chromosome and quantum mutation has better global search capacity. The parameters of least squares support vector machines (LS-SVM) can be adjusted using quantum-inspired evolutionary optimization. Classification and function estimation are studied using LS-SVM with wavelet kernel and Gaussian kernel. The simulation results show that the proposed approach can effectively tune the parameters of LS-SVM, and the improved LS-SVM with wavelet kernel can provide better precision. [Copyright &y& Elsevier]

Abstract: Gaussian process (GP) regression is a Bayesian non-parametric regression model, showing good performance in various applications. However, it is quite rare to see research results on log-likelihood maximization algorithms. Instead of the commonly used conjugate gradient method, the Hessian matrix is first derived/simplified in this paper and the trust-region optimization method is then presented to estimate GP hyperparameters. Numerical experiments verify the theoretical analysis, showing the advantages of using Hessian matrix and trust-region algorithms. In the GP context, the trust-region optimization method is a robust alternative to conjugate gradient method, also in view of future researches on approximate and/or parallel GP-implementation. [Copyright &y& Elsevier]

This paper introduces a new and simple criterion for rigid registration based on Gaussian fields. The criterion is always differentiable and convex in a large neighborhood of the alignment parameters; allowing for the use of well-proven optimization techniques. Using this method we can extend the size of the region of convergence so that no close initialization is needed, thus overcoming local convergence problems of Iterative Closest Point algorithms. Furthermore, the Gaussian energy function can be evaluated with linear complexity using the fast Gauss transform, which permits efficient implementation of the registration algorithm. Experimental analysis on real-world data sets shows the usefulness and points the limits of the approach. [Copyright &y& Elsevier]

This paper explores the use of Gradient-enhanced Kriging for optimization of expensive black-box design problems, which is not completely limited by the conventional Efficient Global Optimization algorithm framework. Specifically, we give the best linear unbiased predictor and mean squared prediction error of the partial derivatives of Gradient-enhanced Kriging and then propose a measure named "Approximate Probability of Stationary Point" to estimate the approximate probability of a candidate infill point be a stationary point of the underlying function. When it comes to the selection of infill point, we not only maximize the well-known Expected Improvement but also evaluate the Approximate Probability of Stationary Point as a "double-check" step. Then the infill decision is made according to the extent of consistency between these two quantities. Furthermore, to examine whether the optimization process will gain from sparing more costs for response evaluation, we investigate also the cases that the gradient evaluation step is conditionally skipped in some iterations. Three new infill criteria are proposed and experimented with three analytical test functions and an airfoil optimal shape design. Results show that the optimization performance can be improved by exploiting the auxiliary gradient information in the proposed way. [ABSTRACT FROM AUTHOR]