Credibilistic fuzzy clustering based on evolutionary method of crazy cats

The problem of fuzzy clustering of large datasets that are sent for processing in both batch and online modes, based on a credibilistic approach, is considered. To find the global extremum of the credibilistic fuzzy clustering goal function, the modification of the swarm algorithm of crazy cats swarms was introduced, that combined the advantages of evolutionary algorithms and a global random search. It is shown that different search modes are generated by a unified mathematical procedure, some cases of which are known algorithms for both local and global optimizations. The proposed approach is easy to implement and is characterized by the high speed and reliability in problems of multi-extreme fuzzy clustering.

Intelligent Prediction of Aeroengine Wear Based on the SVR Optimized by GMPSO

In order to predict aeroengine wear accurately and automatically, as a predictor, support vector regression (SVR) was optimized by means of particle swarm optimization (PSO). The guided mutation strategy of PSO (GMPSO) is presented herein to determine the proper structure parameters of an SVR, as well as the embedding dimensions of the training samples. The guided mutation strategy was able to increase the diversity of particles and improve the probability of finding the global extremum. Furthermore, single-step and multi-step prediction methods were designed to meet different accuracy requirements. A prediction comparison study on spectral analysis data was carried out, and the contrast experiments show that compared with SVR optimized by means of a traditional PSO, a neural network and an auto regressive moving average (ARMA) prediction model, the SVR optimized by means of the GMPSO approach produced prediction results not only with higher accuracy, but also with better consistency.

Machine learning for laser-induced electron diffraction imaging of molecular structures

Ultrafast diffraction imaging is a powerful tool to retrieve the geometric structure of gas-phase molecules with combined picometre spatial and attosecond temporal resolution. However, structural retrieval becomes progressively difficult with increasing structural complexity, given that a global extremum must be found in a multi-dimensional solution space. Worse, pre-calculating many thousands of molecular configurations for all orientations becomes simply intractable. As a remedy, here, we propose a machine learning algorithm with a convolutional neural network which can be trained with a limited set of molecular configurations. We demonstrate structural retrieval of a complex and large molecule, Fenchone (C10H16O), from laser-induced electron diffraction (LIED) data without fitting algorithms or ab initio calculations. Retrieval of such a large molecular structure is not possible with other variants of LIED or ultrafast electron diffraction. Combining electron diffraction with machine learning presents new opportunities to image complex and larger molecules in static and time-resolved studies.

APPLICATION OF THE ”WAVE“ METHOD TO SOLVE THE PROBLEMS OF OPTIMIZATION OF PASSENGER AND CARGO TRANSPORTATION IN MEGACITIES TO IMPROVE THEIR TRANSPORT NETWORK AND INFRASTRUCTURE. Conceptual basis, mathematical framework

The paper proposes a new approach to solving optimization problems arising in engineering and transport logistics in designing and construction of roads (in particular, in megacities, near large transport hubs, near state borders) for cargo and passenger transportation and implementation of international trade. The fundamental problems of modern engineering logistics - the problem of optimal location (transport hubs) and the problem of identification and segmentation of logistics, transport and logistics zones are considered. These problems are solved using methods of variational calculus, in particular, the so-called "wave" method based on the Fermat principle existing in physical optics, which is based on the analogy between finding the global extremum of the integral functional and the propagation of light in an optically heterogeneous medium. A numerical method for the above technique has been developed programatically. The idea of the "wave method/approach belongs to V.V. Bashurov, who proposed to use the methods of geometrical and physical optics to investigate applied safety problems and some related issues. The essence of the "wave method" is that initially the safety problem is reduced to the search for the global minimum of a nonlinear functional. In turn, the minimization problem is solved by constructing the trajectory of motion of the front of the "light wave" moving in an optically inhomogeneous medium. Finding the minimum of a functional is a classical problem of variational calculus, for the solution of which a significant mathematical apparatus has been developed. However, most of known methods effectively determine only local extrema. "Wave" method allows to solve the problem of finding a global extremum with greater efficiency. This paper proposes a conceptual framework and scientifically justified modification of this "wave" method for solving optimization problems arising in engineering and transport logistics, including the problem of optimal location of the transport hub, transport and logistics center (warehouse) and the problem of optimal identification and segmentation of logistical zones (metropolitan areas, large transport hubs).

Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning

This paper features the study of global optimization problems and numerical methods of their solution. Such problems are computationally expensive since the objective function can be multi-extremal, nondifferentiable, and, as a rule, given in the form of a “black box”. This study used a deterministic algorithm for finding the global extremum. This algorithm is based neither on the concept of multistart, nor nature-inspired algorithms. The article provides computational rules of the one-dimensional algorithm and the nested optimization scheme which could be applied for solving multidimensional problems. Please note that the solution complexity of global optimization problems essentially depends on the presence of multiple local extrema. In this paper, we apply machine learning methods to identify regions of attraction of local minima. The use of local optimization algorithms in the selected regions can significantly accelerate the convergence of global search as it could reduce the number of search trials in the vicinity of local minima. The results of computational experiments carried out on several hundred global optimization problems of different dimensionalities presented in the paper confirm the effect of accelerated convergence (in terms of the number of search trials required to solve a problem with a given accuracy).

Global optimization of default phases for parallel transmit coils for ultra-high-field cardiac MRI

The development of novel multiple-element transmit-receive arrays is an essential factor for improving B1+ field homogeneity in cardiac MRI at ultra-high magnetic field strength (B0 > = 7.0T). One of the key steps in the design and fine-tuning of such arrays during the development process is finding the default driving phases for individual coil elements providing the best possible homogeneity of the combined B1+-field that is achievable without (or before) subject-specific B1+-adjustment in the scanner. This task is often solved by time-consuming (brute-force) or by limited efficiency optimization methods. In this work, we propose a robust technique to find phase vectors providing optimization of the B1-homogeneity in the default setup of multiple-element transceiver arrays. The key point of the described method is the pre-selection of starting vectors for the iterative solver-based search to maximize the probability of finding a global extremum for a cost function optimizing the homogeneity of a shaped B1+-field. This strategy allows for (i) drastic reduction of the computation time in comparison to a brute-force method and (ii) finding phase vectors providing a combined B1+-field with homogeneity characteristics superior to the one provided by the random-multi-start optimization approach. The method was efficiently used for optimizing the default phase settings in the in-house-built 8Tx/16Rx arrays designed for cMRI in pigs at 7T.

A new method for global optimization

This paper presents a new method for global optimization. We use exact quadratic regularization for the transformation of the multimodal problems to a problem of a maximum norm vector on a convex set. Quadratic regularization often allows you to convert a multimodal problem into a unimodal problem. For this, we use the shift of the feasible region along the bisector of the positive orthant. We use only local search (primal-dual interior point method) and a dichotomy method for search of a global extremum in the multimodal problems. The comparative numerical experiments have shown that this method is very efficient and promising.

The sufficient condition to find an exact dual bound in a separable quadratic optimization problem

The paper considers nonconvex separable quadratic optimization problems subject to inequality constraints. A sufficient condition is given for finding the value and the point of the global extremum of a problem of this type by calculating the Lagrange dual bound. The peculiarity of this condition is that it is easily verified and requires from the Hessian matrix of the Lagrange function only that its region of positive definiteness is not empty. The result obtained for the dual bound also holds for the bound obtained using SDP relaxation.

Advanced supervised learning in multi-layer perceptrons to the recognition tasks based on correlation indicator

The article deals with the problem of recognition of handwritten digits using feedforward neural networks (perceptrons) using a correlation indicator. The proposed method is based on the mathematical model of the neural network as an oscillatory system similar to the information transmission system. The article uses theoretical developments of the authors to search for the global extremum of the error function in artificial neural networks. The handwritten digit image is considered as a one-dimensional input discrete signal representing a combination of "perfect digit writing" and noise, which describes the deviation of the input implementation from "perfect writing". The ideal observer criterion (Kotelnikov criterion), which is widely used in information transmission systems and describes the probability of correct recognition of the input signal, is used to form the loss function. In the article is carried out a comparative analysis of the convergence of learning and experimentally obtained sequences on the basis of the correlation indicator and widely used in the tasks of classification of the function CrossEntropyLoss with the use of the optimizer and without it. Based on the experiments carried out, it is concluded that the proposed correlation indicator has an advantage of 2-3 times.

Developing Software of Global Optimization Method Based on Grey Wolf Optimizer

This article discusses the development of software that allows to simulate the algorithm of the “Grey Wolf Optimizer” method. This algorithm belongs to the class of metaheuristic algorithms that allow finding a global extremum on a set of admissible solutions. This algorithm is being the most efficiently used in a situation where the cost function is specified in the form of a black box. The algorithm belongs to both bioinspired algorithms and to the class of algorithms of Particle Swarm Optimization. To analyze the efficiency of the algorithm, software was created that allows to vary the parameters of the method. The article contains examples of the program’s work on various test functions. The purpose of the program is to collect and analyze statistical results, making possible to evaluate the final result. The program provides to build graphs that make it possible to make a more thorough assessment of the results obtained. The program has a step-by-step function that allows one to analyze the specifics and features of the algorithm. Analysis of statistical data provides more detailed selection of the parameters of the algorithm.