Tabu efficient global optimization with applications in additive manufacturing

AbstractMethods based on Gaussian stochastic process (GSP) models and expected improvement (EI) functions have been promising for box-constrained expensive optimization problems. These include robust design problems with environmental variables having set-type constraints. However, the methods that combine GSP and EI sub-optimizations suffer from the following problem, which limits their computational performance. Efficient global optimization (EGO) methods often repeat the same or nearly the same experimental points. We present a novel EGO-type constraint-handling method that maintains a so-called tabu list to avoid past points. Our method includes two types of penalties for the key “infill” optimization, which selects the next test runs. We benchmark our tabu EGO algorithm with five alternative approaches, including DIRECT methods using nine test problems and two engineering examples. The engineering examples are based on additive manufacturing process parameter optimization informed using point-based thermal simulations and robust-type quality constraints. Our test problems span unconstrained, simply constrained, and robust constrained problems. The comparative results imply that tabu EGO offers very promising computational performance for all types of black-box optimization in terms of convergence speed and the quality of the final solution.

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Uncertainty Based Optimization Strategy for the Gappy-POD Multi-Fidelity Method

Volume 2D: Turbomachinery ◽

10.1115/gt2020-15166 ◽

2020 ◽

Author(s):

Bernhard Poethke ◽

Stefan Völker ◽

Konrad Vogeler

Keyword(s):

Global Optimization ◽

Uncertainty Quantification ◽

Industrial Test ◽

Expected Improvement ◽

Efficient Global Optimization ◽

Test Case ◽

Optimization Strategy ◽

Constrained Problems ◽

Design Variables ◽

Gappy Pod

Abstract In the surrogate model-based optimization of turbine airfoils, often only the prediction values for objective and constraints are employed, without considering uncertainties in the prediction. This is also the case for multi-fidelity optimization strategies based on e.g. the Gappy-POD approach, in which results from analyses of different fidelities are incorporated. However, the consideration of uncertainties in global optimization has the advantage that a balanced coverage of the design space between unexplored regions and regions close to the current optimum takes place. This means that on the one hand regions are covered in which so far only a few sample points are present and thus a high degree of uncertainty exists (global exploration), and on the other hand regions with promising objective and constraint values are investigated (local exploitation). The genuine new contribution in this work is the quantification of the uncertainty of the multi-fidelity Gappy-POD method and an adapted optimization strategy based on it. The uncertainty quantification is based on the error of linear fitting of low-fidelity values to the POD basis and subsequent forward propagation to the high-fidelity values. The uncertainty quantification is validated for random airfoil designs in a design of experiment. Based on this, a global optimization strategy for constrained problems is presented, which is based on the well-known Efficient Global Optimization (EGO) strategy and the Feasible Expected Improvement criterion. This means that Kriging models are created for both the objective and the constraint values depending on the design variables that consider both the predictions and the uncertainties. This approach offers the advantage that existing and widely used programs or libraries can be used for multi-fidelity optimization that support the (single-fidelity) EGO algorithm. Finally, the method is demonstrated for an industrial test case. A comparison between a single-fidelity optimization and a multi-fidelity optimization is made, each with the EGO strategy. A coupling of 2D/3D simulations is used for multi-fidelity analyses. The proposed method achieves faster feasible members in the optimization, resulting in faster turn-around compared to the single-fidelity strategy.

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Trust Region Based Mode Pursuing Sampling Method for Global Optimization of High Dimensional Design Problems

Journal of Mechanical Design ◽

10.1115/1.4029219 ◽

2015 ◽

Vol 137 (2) ◽

Cited By ~ 24

Author(s):

George H. Cheng ◽

Adel Younis ◽

Kambiz Haji Hajikolaei ◽

G. Gary Wang

Keyword(s):

Global Optimization ◽

Optimization Problems ◽

Trust Region ◽

Standard Test ◽

Black Box ◽

High Dimensional ◽

Efficient Global Optimization ◽

Test Problems ◽

Design Problems ◽

Design Variables

Mode pursuing sampling (MPS) was developed as a global optimization algorithm for design optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for design problems of low dimensionality, i.e., the number of design variables is less than 10. This work integrates the concept of trust regions into the MPS framework to create a new algorithm, trust region based mode pursuing sampling (TRMPS2), with the aim of dramatically improving performance and efficiency for high dimensional problems. TRMPS2 is benchmarked against genetic algorithm (GA), dividing rectangles (DIRECT), efficient global optimization (EGO), and MPS using a suite of standard test problems and an engineering design problem. The results show that TRMPS2 performs better on average than GA, DIRECT, EGO, and MPS for high dimensional, expensive, and black box (HEB) problems.

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An exploitation-enhanced multi-objective efficient global optimization algorithm for expensive aerodynamic shape optimizations

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/09544100211032432 ◽

2021 ◽

pp. 095441002110324

Author(s):

Feng Deng ◽

Ning Qin

Keyword(s):

Global Optimization ◽

Shape Optimization ◽

Optimization Algorithm ◽

Optimization Problems ◽

Efficient Global Optimization ◽

Test Problems ◽

Aerodynamic Shape Optimization ◽

Aerodynamic Shape ◽

Multi Objective ◽

Complex Landscape

The traditional multi-objective efficient global optimization (EGO) algorithms have been hybridized and adapted to solving the expensive aerodynamic shape optimization problems based on high-fidelity numerical simulations. Although the traditional EGO algorithms are highly efficient in solving some of the optimization problems with very complex landscape, it is not preferred to solve most of the aerodynamic shape optimization problems with relatively low-degree multi-modal design spaces. A new infill criterion encouraging more local exploitation has been proposed by hybridizing two traditional multi-objective expected improvements (EIs), namely, statistical multi-objective EI and expected hypervolume improvement, in order to improve their robustness and efficiency in aerodynamic shape optimization. Different analytical test problems and aerodynamic shape optimization problems have been investigated. In comparison with traditional multi-objective EI algorithms and a standard evolutionary multi-objective optimization algorithm, the proposed method is shown to be more robust and efficient in the tests due to its hybrid characteristics, easier handling of sub-optimization problems, and enhanced exploitation capability.

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Comparison of parallel infill sampling criteria based on Kriging surrogate model

Scientific Reports ◽

10.1038/s41598-021-04553-5 ◽

2022 ◽

Vol 12 (1) ◽

Author(s):

Cong Chen ◽

Jiaxin Liu ◽

Pingfei Xu

Keyword(s):

Optimization Problems ◽

Expected Improvement ◽

Efficient Global Optimization ◽

Test Problems ◽

Local Optimum ◽

Concentration Problem ◽

Key Issues ◽

The Common ◽

Optimization Efficiency ◽

Infill Sampling

AbstractOne of the key issues that affect the optimization effect of the efficient global optimization (EGO) algorithm is to determine the infill sampling criterion. Therefore, this paper compares the common efficient parallel infill sampling criterion. In addition, the pseudo-expected improvement (EI) criterion is introduced to minimizing the predicted (MP) criterion and the probability of improvement (PI) criterion, which helps to improve the problem of MP criterion that is easy to fall into local optimum. An adaptive distance function is proposed, which is used to avoid the concentration problem of update points and also improves the global search ability of the infill sampling criterion. Seven test problems were used to evaluate these criteria to verify the effectiveness of these methods. The results show that the pseudo method is also applicable to PI and MP criteria. The DMP and PEI criteria are the most efficient and robust. The actual engineering optimization problems can more directly show the effects of these methods. So these criteria are applied to the inverse design of RAE2822 airfoil. The results show the criterion including the MP has higher optimization efficiency.

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