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Interval analysis based robust truss optimization with continuous and discrete variables using mix-coded genetic algorithm

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2017年第2期56卷 353-370页

作者： Zhou, Pingzhang Du, Jianbin Lu, Zhenhua Tsinghua Univ Dept Automot Engn Beijing 100084 Peoples R China Tsinghua Univ Sch Aerosp Engn Beijing 100084 Peoples R China

The problem of optimizing truss structures in the presence of uncertain parameters considering both continuous and discrete design variables is studied. An interval analysis based robust optimization method combined with the improved genetic algorithm is proposed for solving the problem. Uncertain parameters are assumed to be bounded in specified intervals. The natural interval extensions are employed to obtain explicitly a conservative approximation of the upper and lower bounds of the structural response, and hereby the bounds of the objective function and the constraint function. This way the uncertainty design may be performed in a very efficient manner in comparison with the probabilistic analysis based method. A mix-coded genetic algorithm (GA), where the discrete variables are coded with binary numbers while the continuous variables are coded with real numbers, is developed to deal with simultaneously the continuous and discrete design variables of the optimization model. An improved differences control strategy is proposed to avoid the GA getting stuck in local optima. Several numerical examples concerning the optimization of plane and space truss structures with continuous, discrete or mixed design variables are presented to validate the method developed in the present paper. Monte Carlo simulation shows that the interval analysis based optimization method gives much more robust designs in comparison with the deterministic optimization method.

关键词： Interval analysis Robust truss optimization continuous and discrete variables Genetic algorithms Natural interval extensions

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Nondeterministic Kriging for Probabilistic Systems with Mixed continuous and discrete Input variables

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ASCE-ASME JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS PART A-CIVIL ENGINEERING 2024年第4期10卷

作者： Jayasekara, Jayasekara Kameshwar, Sabarethinam Louisiana State Univ Dept Civil & Environm Engn Baton Rouge LA 70803 USA

This paper presents a nondeterministic kriging (NDK) method to approximate the response of probabilistic systems with mixed continuous and discrete input variables. The proposed method approximates both epistemic (extrinsic) and aleatory (intrinsic) uncertainties in addition to the mean response of a system. Kriging is a popular metamodeling method for approximating the responses of computationally demanding systems along with prediction variances. However, conventional kriging fails to perform with nondeterministic data sets with replications. The recently developed NDK method addresses those challenges in the continuous input space. Currently, kriging is often used for approximations in probabilistic systems with mixed continuous and discrete input variables as well. Therefore, this study aims to fill the gap in the NDK method for probabilistic systems with mixed continuous and discrete input variables. Herein, the aleatory uncertainty is assessed using locally weighted regression (LWR). The proposed method uses a combination of continuous and discrete kernels to capture the effects of mixed inputs. The effectiveness of the newly proposed NDK method was demonstrated using a set of probabilistic analytical cases and engineering applications. The proposed method provides separable information about aleatory and epistemic uncertainties, which are beneficial in design optimizations and sequential explorations of probabilistic systems, especially with large-scale experiments and computer simulations with randomness.

关键词： Nondeterministic kriging (NDK) Mixed variables continuous and discrete variables Probabilistic systems Machine learning

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A VALUATION OF STATE OF OBJECT BASED ON WEIGHTED MAHALANOBIS DISTANCE

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PATTERN RECOGNITION 1987年第4期20卷 413-418页

作者： KRUSINSKA, E Wrocław Przesmyckiego 20 Poland

A method of valuation of the state of a multidimensional object is presented. The considered object may be described by continuous and discrete variables as well. The method consists in evaluating the weighted Mahalanobis distance between the object and a multidimensional norm estimate. This distance can be standardized to take the values from the interval [0, 1].

关键词： Weighted Mahalanobis distance continuous and discrete variables Linguistic variables Norm estimate Difference degree

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Minimum volume design of structures with constraints on ductility and stability

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ENGINEERING STRUCTURES 2014年 68卷 47-56页

作者： Palizzolo, Luigi Caffarelli, Alessandra Tabbuso, Pietro Univ Palermo Dept Civil DICAM I-90128 Palermo Italy

A minimum volume design problem of elastic perfectly plastic frame structures subjected to different combinations of fixed and seismic loads is presented, in which the design variables are considered as appertaining alternatively to a continuous assigned range as well as to appropriate discrete sets. The structure is designed so as to behave elastically for the applied fixed loads, to shakedown in presence of serviceability seismic conditions and to prevent the instantaneous collapse for suitably chosen combinations affixed and high seismic loadings. In order to avoid further undesired collapse modes, the P-Delta effects are considered and the structure is also constrained to prevent element budding. Furthermore, some suitable constraint on the structure ductility is imposed referring to the plastic strains generated during the transient phase structural response. The dynamic structural response is obtained by utilizing an appropriate modal technique referring to the response spectrum defined by the Italian code. The proposed minimum volume design problem is formulated, according to the required structural behaviour, on the ground of a statical approach. Different numerical applications related to steel frames conclude the paper. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： continuous and discrete variables Optimal design Seismic loading Limited ductility Element slenderness

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Multi-strategy enhanced snake optimizer for quantitative structure-activity relationship modeling

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APPLIED MATHEMATICAL MODELLING 2024年 132卷 531-560页

作者： Wang, Jiayin Wang, Yukun Univ Sci & Technol Liaoning Sch Elect & Informat Engn Anshan 114051 Peoples R China

Quantitative structure -activity relationship modeling techniques are widely employed in diverse areas of chemistry, including environmental risk assessment of compounds and virtual screening of drugs. The modeling process entails optimizing the hyper parameters of the model and selecting appropriate molecular descriptors. It is a typical optimization problem with high -dimensional, nonlinear, continuous and discrete variables coexisting. To address this challenge, this paper proposes an enhanced snake optimizer with multiple strategies. First, new food emergence and temperature change mechanisms are introduced to balance the exploration and exploitation. Second, a death and regeneration mechanism is employed to enhance the algorithm's ability to escape from local optima. Third, new formulas for food searching, fighting, mating and eating are designed to simplify the complexity of the algorithm and improve its search efficiency and accuracy. Fourth, the performance of the proposed algorithm is evaluated using the CEC2017 benchmark functions, eight engineering cases with continuous variables, and six feature selection cases with discrete variables. Experimental results demonstrate that the algorithm significantly outperforms comparison algorithms. Finally, the algorithm was applied to quantitative structureactivity relationship modeling for environmental toxicity prediction. Compared with other algorithms, the algorithm can better configure hyper -parameters and select fewer and more effective features for environmental toxicity prediction model. It will be an effective tool to improve the performance of quantitative structure -activity relationship models.

关键词： Enhanced snake optimizer Multiple strategies Quantitative structure-activity relationship continuous and discrete variables Toxicity Prediction

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Scoring Bayesian networks of mixed variables

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INTERNATIONAL JOURNAL OF DATA SCIENCE AND ANALYTICS 2018年第1期6卷 3-18页

作者： Andrews, Bryan Ramsey, Joseph Cooper, Gregory F. Univ Pittsburgh Pittsburgh PA 15260 USA Carnegie Mellon Univ Pittsburgh PA 15213 USA

In this paper we outline two novel scoring methods for learning Bayesian networks in the presence of both continuous and discrete variables, that is, mixed variables. While much work has been done in the domain of automated Bayesian network learning, few studies have investigated this task in the presence of both continuous and discrete variables while focusing on scalability. Our goal is to provide two novel and scalable scoring functions capable of handling mixed variables. The first method, the Conditional Gaussian (CG) score, provides a highly efficient option. The second method, the Mixed Variable Polynomial (MVP) score, allows for a wider range of modeled relationships, including nonlinearity, but it is slower than CG. Both methods calculate log likelihood and degrees of freedom terms, which are incorporated into a Bayesian Information Criterion (BIC) score. Additionally, we introduce a structure prior for efficient learning of large networks and a simplification in scoring the discrete case which performs well empirically. While the core of this work focuses on applications in the search and score paradigm, we also show how the introduced scoring functions may be readily adapted as conditional independence tests for constraint-based Bayesian network learning algorithms. Lastly, we describe ways to simulate networks of mixed variable types and evaluate our proposed methods on such simulations.

关键词： Bayesian network structure learning Mixed variables continuous and discrete variables

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Surrogate Model for continuous and discrete Genetic Optimization Based on RBF Networks

Surrogate Model for Continuous and Discrete Genetic Optimiza...

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11th International Conference on Intelligent Data Engineering and Automated Learning

作者： Bajer, Lukas Holena, Martin Charles Univ Prague Fac Math & Phys Prague 1 Czech Republic Acad Sci Czech Republ Inst Comp Sci Prague 8 Czech Republic

ISBN: (纸本)9783642153808

Surrogate modelling has become a successful method improving the optimization of costly objective functions. It brings less accurate, but much faster means of evaluating candidate solutions. This paper describes a model based on radial basis function networks which takes into account both continuous and discrete variables. It shows the applicability of our surrogate model to the optimization of empirical objective functions for which mixing of discrete and continuous dimensions is typical. Results of testing with a genetic algorithm confirm considerably faster convergence in terms of the number of the original empirical fitness evaluations.

关键词： surrogate modelling RBF networks genetic algorithms continuous and discrete variables

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Surrogate Model for Mixed-variables Evolutionary Optimization Based on GLM and RBF Networks

Surrogate Model for Mixed-Variables Evolutionary Optimizatio...

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39th Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM)

作者： Bajer, Lukas Holena, Martin Charles Univ Prague Fac Math & Phys Malostranske Nam 25 Prague 1 Czech Republic Acad Sci Czech Republ Inst Comp Sci Prague 8 Czech Republic

ISBN: (纸本)9783642358432

Approximation of costly objective functions by surrogate models is an increasingly popular method in many engineering optimization tasks. Surrogate models can substantially decrease the number of expensive experiments or simulations needed to achieve an optimal or near-optimal solution. In this paper, a novel surrogate model is presented. Compared to the most of the surrogate models reported in the literature, it has an advantage of explicitly dealing with mixed continuous and discrete variables. The model use radial basis function networks for continuous and clustering and a generalized linear model for the discrete covariates. The applicability of the model is shown on a benchmark problem, and the model's regression performance is further measured on a dataset from a real-world application.

关键词： surrogate modelling RBF networks genetic algorithms mixed-variables optimization continuous and discrete variables

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variables PROCESSING IN EXPERT SYSTEM BUILDING - APPLICATION TO THE ETIOLOGIC DIAGNOSIS OF INFANTILE MENINGITIS

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MEDICAL INFORMATICS 1990年第2期15卷 115-124页

作者： FRANCOIS, P ROBERT, C CREMILLEUX, B BUCHARLES, C DEMONGEOT, J Clinique Médicale Infantile C.H.U. de Grenoble La Tronche France.

We describe a method for the analysis and quantitative synthesis of information in a clinical data file using as an example the aetiological diagnosis of infantile meningitis. The results obtained together with the qualitative knowledge of experts in the field have enabled an experimental system to be constructed. This is performing sufficiently well to be introduced into a hospital environment to assist young doctors facing an emergency situation.

关键词： continuous and discrete variables Knowledge base Multivariate descriptive analysis ROC curves Validation

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