A comparison of mixed-variables Bayesian optimization approaches

Jhouben Cuesta-Ramirez, R. Riche, O. Roustant, G. Perrin, Cédric Durantin, A. Glière
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引用次数: 7

Abstract

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.
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混合变量贝叶斯优化方法的比较
大多数实际的优化问题都是在混合搜索空间上定义的,其中变量既离散又连续。在工程应用中,目标函数通常使用数值昂贵的黑盒模拟进行计算。因此,一般的混合和昂贵的优化问题具有很大的实际意义,但它们的解决在很大程度上仍然是一个开放的科学问题。在本文中,通过高斯过程来处理代价高昂的混合问题,其中离散变量被松弛为连续的潜在变量。与混合空间相比,经典贝叶斯优化技术更容易获得连续空间。离散变量要么在连续优化之后恢复,要么与用增广拉格朗日算子处理的附加连续离散兼容性约束同时恢复。比较了这种贝叶斯混合优化器的几种可能的实现方式。特别是,具有连续潜变量的问题的重新表述与直接在混合空间中进行的搜索相竞争。在涉及潜在变量和增广拉格朗日量的算法中,特别关注拉格朗日乘子,研究了其局部和全局估计技术。比较是基于三个分析函数的重复优化和一个梁设计问题。
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来源期刊
Advanced Modeling and Simulation in Engineering Sciences
Advanced Modeling and Simulation in Engineering Sciences Engineering-Engineering (miscellaneous)
CiteScore
6.80
自引率
0.00%
发文量
22
审稿时长
30 weeks
期刊介绍: The research topics addressed by Advanced Modeling and Simulation in Engineering Sciences (AMSES) cover the vast domain of the advanced modeling and simulation of materials, processes and structures governed by the laws of mechanics. The emphasis is on advanced and innovative modeling approaches and numerical strategies. The main objective is to describe the actual physics of large mechanical systems with complicated geometries as accurately as possible using complex, highly nonlinear and coupled multiphysics and multiscale models, and then to carry out simulations with these complex models as rapidly as possible. In other words, this research revolves around efficient numerical modeling along with model verification and validation. Therefore, the corresponding papers deal with advanced modeling and simulation, efficient optimization, inverse analysis, data-driven computation and simulation-based control. These challenging issues require multidisciplinary efforts – particularly in modeling, numerical analysis and computer science – which are treated in this journal.
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