A comparison of mixed-variables Bayesian optimization approaches

Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation. General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more easily harvested by classical Bayesian optimization techniques than a mixed space would. Discrete variables are recovered either subsequently to the continuous optimization, or simultaneously with an additional continuous-discrete compatibility constraint that is handled with augmented Lagrangians. Several possible implementations of such Bayesian mixed optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with searches working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, a particular attention is devoted to the Lagrange multipliers for which a local and a global estimation techniques are studied. The comparisons are based on the repeated optimization of three analytical functions and a beam design problem.

Guidelines for the Measurement of Rein Tension in Equestrian Sport

Rein tension is relatively easy to measure, and the resulting data are useful for evaluating the interaction between horse and rider. To date, there have been a number of studies using different transducers, calibration methods and analytical techniques. The purpose of this paper is to make recommendations regarding the collection, analysis and reporting of rein tension data. The goal is to assist users in selecting appropriate equipment, choosing verified methods of calibration, data collection and analysis, and reporting their results consistently to facilitate comparisons between different studies. Sensors should have a suitable range and resolution together with a fast enough dynamic response, according to the gait, speed and type of riding for which they will be used. An appropriate calibration procedure is necessary before each recording session. A recording frequency of 50 Hz is adequate for most rein tension studies. The data may be analyzed using time-series methods or by extracting and analyzing discrete variables chosen in accordance with the study objectives. Consistent reporting facilitates comparisons between studies.

PROPOSTA DE AUTOMAÇÃO DO PROCESSO DE ENFARDAMENTO DE UMA PERFILADEIRA DRYWALL DE UMA INDÚSTRIA METALÚRGICA

The fundamentals of industrial automation are based on communication and data monitoring, on realtime control of industrial processes without human interference, with that providing opportunities improvements in various ways in the equipment of industries. This article seeks to propose an advance to the final process of a Drywall Roll Forming Machine through an automated baling system to improve the production process of a Metallurgical Industry. That way, a system was built with conveyor and lift tables by rollers and chains with support of sensors and electrical and pneumatic actuators for its operation. The proposal was carried out and successful through computational simulations, using engineering software based on discrete variables of components and communication of a Virtual PLC (Programmable Logic Controller) and a Supervisory System.

Method of Moments for Topic Models with Mixed Discrete and Continuous Features

Topic models are characterized by a latent class variable that represents the different topics. Traditionally, their observable variables are modeled as discrete variables like, for instance, in the prototypical latent Dirichlet allocation (LDA) topic model. In LDA, words in text documents are encoded by discrete count vectors with respect to some dictionary. The classical approach for learning topic models optimizes a likelihood function that is non-concave due to the presence of the latent variable. Hence, this approach mostly boils down to using search heuristics like the EM algorithm for parameter estimation. Recently, it was shown that topic models can be learned with strong algorithmic and statistical guarantees through Pearson's method of moments. Here, we extend this line of work to topic models that feature discrete as well as continuous observable variables (features). Moving beyond discrete variables as in LDA allows for more sophisticated features and a natural extension of topic models to other modalities than text, like, for instance, images. We provide algorithmic and statistical guarantees for the method of moments applied to the extended topic model that we corroborate experimentally on synthetic data. We also demonstrate the applicability of our model on real-world document data with embedded images that we preprocess into continuous state-of-the-art feature vectors.

Harris Hawks Optimization for Optimum Design of Truss Structures with Discrete Variables

This article investigates the use of Harris Hawks Optimization (HHO) to solve planar and spatial trusses with design variables that are discrete. The original HHO has been used to solve continuous design variables problems. However, HHO is formulated to solve optimization problems with discrete variables in this research. HHO is a population-based metaheuristic algorithm that simulates the chasing style and the collaborative behavior of predatory birds Harris hawks. The mathematical model of HHO uses a straightforward formulation and does not require tuning of algorithmic parameters and it is a robust algorithm in exploitation. The performance of HHO is evaluated using five benchmark structural problems and the final designs are compared with ten state-of-the-art algorithms. The statistical outcomes (average and standard deviation of final designs) show that HHO is quite consistent and robust in solving truss structure optimization problems. This is an important characteristic that leads to better confidence in the final solution from a single run of the algorithm for an optimization problem.

ANALYSIS OF FERTILITY FACTORS IN RUSSIA

The article presents an algorithm for modeling fertility factors, which are discrete variables, taking into account endogeneity. Cross-sectional data for individuals is used. The main factors influencing the probability of having a child within the next year and the number of children a woman has are described.