Features of using a two-point crossover for solving an inhomogeneous minimax problem modified by the Goldberg model

The relevance of the topic of this work is the strong growth of multiprocessor systems, for which it is important to solve a large volume of tasks in a minimum time. There are various algorithms for solving such a problem, which can be divided into classes of exact and approximate. The representative of approximate algorithms is the algorithm of the Goldberg model, which gives acceptable results, the modifications of the crossovers of which are studied in this paper.

Predictive Maintenance: An Autoencoder Anomaly-Based Approach for a 3 DoF Delta Robot

Performing predictive maintenance (PdM) is challenging for many reasons. Dealing with large datasets which may not contain run-to-failure data (R2F) complicates PdM even more. When no R2F data are available, identifying condition indicators (CIs), estimating the health index (HI), and thereafter, calculating a degradation model for predicting the remaining useful lifetime (RUL) are merely impossible using supervised learning. In this paper, a 3 DoF delta robot used for pick and place task is studied. In the proposed method, autoencoders (AEs) are used to predict when maintenance is required based on the signal sequence distribution and anomaly detection, which is vital when no R2F data are available. Due to the sequential nature of the data, nonlinearity of the system, and correlations between parameter time-series, convolutional layers are used for feature extraction. Thereafter, a sigmoid function is used to predict the probability of having an anomaly given CIs acquired from AEs. This function can be manually tuned given the sensitivity of the system or optimized by solving a minimax problem. Moreover, the proposed architecture can be used for fault localization for the specified system. Additionally, the proposed method can calculate RUL using Gaussian process (GP), as a degradation model, given HI values as its input.

Minimax Design of 2D FIR Half-Band Filters Using an Efficient Matrix-Based IRLS Algorithm

This paper considers the minimax design of two-dimensional (2D) finite impulse response (FIR) half-band filters. First, the design problem is formulated in a matrix form, where the half-band constraints are expressed as a pair of matrix equations. By matrix transformations, the constrained minimax problem is transformed into an unconstrained one. Then, we propose an efficient iterative reweighted least squares (IRLS) algorithm to solve this problem. The weighted least squares (WLS) subproblems arising from the IRLS algorithm are solved using a generalized conjugate gradient (GCG) algorithm. Moreover, the GCG algorithm is guaranteed to converge in a finite number of iterations. In the proposed algorithm, the design coefficients of filters are solved in their matrix form, leading to a great saving in computations and memory space. Design examples and comparisons with existing methods are provided to demonstrate the effectiveness and efficiency of the proposed algorithm.

Predictive Maintenance: An Autoencoder Anomaly-based Approach for a 3 DoF Delta Robot

Performing predictive maintenance (PdM) is challenging for many reasons. Dealing with large datasets which may not contain run-to-failure data (R2F) complicates PdM even more. When no R2F data are available, identifying condition indicators (CIs), estimating the health index (HI), and thereafter, calculating a degradation model for predicting the remaining useful lifetime (RUL) are merely impossible using supervised learning. In this paper, a 3 dof delta robot used for pick and place task is studied. In the proposed method, autoencoders (AEs) are used to predict when maintenance is required based on the signal sequence distribution and anomaly detection, which is vital when no R2F data is available. Due to the sequential nature of the data, non-linearity of the system, and correlations between parameter time series, convolutional layers are used for feature extraction. Thereafter, a sigmoid function is used to predict the probability of having an anomaly given CIs acquired from AEs. This function can be manually tuned given the sensitivity of the system or optimized by solving a minimax problem. Moreover, the proposed architecture can be used for fault localization for the specified system. Additionally, the proposed method is capable of calculating RUL using Gaussian process (GP), as a degradation model, given HI values as its input.

On the Convergence of Stochastic Compositional Gradient Descent Ascent Method

The compositional minimax problem covers plenty of machine learning models such as the distributionally robust compositional optimization problem. However, it is yet another understudied problem to optimize the compositional minimax problem. In this paper, we develop a novel efficient stochastic compositional gradient descent ascent method for optimizing the compositional minimax problem. Moreover, we establish the theoretical convergence rate of our proposed method. To the best of our knowledge, this is the first work achieving such a convergence rate for the compositional minimax problem. Finally, we conduct extensive experiments to demonstrate the effectiveness of our proposed method.

Aspects of a Phase Transition in High-Dimensional Random Geometry

A phase transition in high-dimensional random geometry is analyzed as it arises in a variety of problems. A prominent example is the feasibility of a minimax problem that represents the extremal case of a class of financial risk measures, among them the current regulatory market risk measure Expected Shortfall. Others include portfolio optimization with a ban on short-selling, the storage capacity of the perceptron, the solvability of a set of linear equations with random coefficients, and competition for resources in an ecological system. These examples shed light on various aspects of the underlying geometric phase transition, create links between problems belonging to seemingly distant fields, and offer the possibility for further ramifications.

Minimax Estimation in Regression under Sample Conformity Constraints

The paper is devoted to the guaranteeing estimation of parameters in the uncertain stochastic nonlinear regression. The loss function is the conditional mean square of the estimation error given the available observations. The distribution of regression parameters is partially unknown, and the uncertainty is described by a subset of probability distributions with a known compact domain. The essential feature is the usage of some additional constraints describing the conformity of the uncertain distribution to the realized observation sample. The paper contains various examples of the conformity indices. The estimation task is formulated as the minimax optimization problem, which, in turn, is solved in terms of saddle points. The paper presents the characterization of both the optimal estimator and the set of least favorable distributions. The saddle points are found via the solution to a dual finite-dimensional optimization problem, which is simpler than the initial minimax problem. The paper proposes a numerical mesh procedure of the solution to the dual optimization problem. The interconnection between the least favorable distributions under the conformity constraint, and their Pareto efficiency in the sense of a vector criterion is also indicated. The influence of various conformity constraints on the estimation performance is demonstrated by the illustrative numerical examples.