Decomposition-Based Multiobjective Evolutionary Optimization with Adaptive Multiple Gaussian Process Models

In recent years, a number of recombination operators have been proposed for multiobjective evolutionary algorithms (MOEAs). One kind of recombination operators is designed based on the Gaussian process model. However, this approach only uses one standard Gaussian process model with fixed variance, which may not work well for solving various multiobjective optimization problems (MOPs). To alleviate this problem, this paper introduces a decomposition-based multiobjective evolutionary optimization with adaptive multiple Gaussian process models, aiming to provide a more effective heuristic search for various MOPs. For selecting a more suitable Gaussian process model, an adaptive selection strategy is designed by using the performance enhancements on a number of decomposed subproblems. In this way, our proposed algorithm owns more search patterns and is able to produce more diversified solutions. The performance of our algorithm is validated when solving some well-known F, UF, and WFG test instances, and the experiments confirm that our algorithm shows some superiorities over six competitive MOEAs.

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On Nonstationary Gaussian Process Model for Solving Data-Driven Optimization Problems

IEEE Transactions on Cybernetics ◽

10.1109/tcyb.2021.3120188 ◽

2021 ◽

pp. 1-14

Author(s):

Caie Hu ◽

Sanyou Zeng ◽

Changhe Li ◽

Fei Zhao

Keyword(s):

Gaussian Process ◽

Process Model ◽

Optimization Problems ◽

Data Driven ◽

Gaussian Process Model

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A Gaussian Process Model-Guided Surface Polishing Process in Additive Manufacturing

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4045334 ◽

2019 ◽

Vol 142 (1) ◽

Author(s):

Shilan Jin ◽

Ashif Iquebal ◽

Satish Bukkapatnam ◽

Andrew Gaynor ◽

Yu Ding

Keyword(s):

Titanium Alloy ◽

Gaussian Process ◽

Process Model ◽

Surface Defects ◽

Sample Surface ◽

Process Models ◽

Polishing Process ◽

Surface Polishing ◽

Multi Stage ◽

Gaussian Process Models

Abstract Polishing of additively manufactured products is a multi-stage process, and a different combination of polishing pad and process parameters is employed at each stage. Pad change decisions and endpoint determination currently rely on practitioners’ experience and subjective visual inspection of surface quality. An automated and objective decision process is more desired for delivering consistency and reducing variability. Toward that objective, a model-guided decision-making scheme is developed in this article for the polishing process of a titanium alloy workpiece. The model used is a series of Gaussian process models, each established for a polishing stage at which surface data are gathered. The series of Gaussian process models appear capable of capturing surface changes and variation over the polishing process, resulting in a decision protocol informed by the correlation characteristics over the sample surface. It is found that low correlations reveal the existence of extreme roughness that may be deemed surface defects. Making judicious use of the change pattern in surface correlation provides insights enabling timely actions. Physical polishing of titanium alloy samples and a simulation of this process are used together to demonstrate the merit of the proposed method.

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Fuzzy clustering based Gaussian Process Model for large training set and its application in expensive evolutionary optimization

2009 IEEE Congress on Evolutionary Computation ◽

10.1109/cec.2009.4983242 ◽

2009 ◽

Cited By ~ 2

Author(s):

Wudong Liu ◽

Qingfu Zhang ◽

Edward Tsang ◽

Botond Virginas

Keyword(s):

Gaussian Process ◽

Fuzzy Clustering ◽

Process Model ◽

Evolutionary Optimization ◽

Training Set ◽

Gaussian Process Model

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Deterministic global optimization with Gaussian processes embedded

Mathematical Programming Computation ◽

10.1007/s12532-021-00204-y ◽

2021 ◽

Author(s):

Artur M. Schweidtmann ◽

Dominik Bongartz ◽

Daniel Grothe ◽

Tim Kerkenhoff ◽

Xiaopeng Lin ◽

...

Keyword(s):

Global Optimization ◽

Gaussian Process ◽

Gaussian Processes ◽

Optimization Problems ◽

Process Models ◽

Bayesian Optimization ◽

Computational Time ◽

Chance Constrained Programming ◽

Deterministic Global Optimization ◽

Gaussian Process Models

AbstractGaussian processes (Kriging) are interpolating data-driven models that are frequently applied in various disciplines. Often, Gaussian processes are trained on datasets and are subsequently embedded as surrogate models in optimization problems. These optimization problems are nonconvex and global optimization is desired. However, previous literature observed computational burdens limiting deterministic global optimization to Gaussian processes trained on few data points. We propose a reduced-space formulation for deterministic global optimization with trained Gaussian processes embedded. For optimization, the branch-and-bound solver branches only on the free variables and McCormick relaxations are propagated through explicit Gaussian process models. The approach also leads to significantly smaller and computationally cheaper subproblems for lower and upper bounding. To further accelerate convergence, we derive envelopes of common covariance functions for GPs and tight relaxations of acquisition functions used in Bayesian optimization including expected improvement, probability of improvement, and lower confidence bound. In total, we reduce computational time by orders of magnitude compared to state-of-the-art methods, thus overcoming previous computational burdens. We demonstrate the performance and scaling of the proposed method and apply it to Bayesian optimization with global optimization of the acquisition function and chance-constrained programming. The Gaussian process models, acquisition functions, and training scripts are available open-source within the “MeLOn—MachineLearning Models for Optimization” toolbox (https://git.rwth-aachen.de/avt.svt/public/MeLOn).

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