scholarly journals A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 149
Author(s):  
Yaohui Li ◽  
Jingfang Shen ◽  
Ziliang Cai ◽  
Yizhong Wu ◽  
Shuting Wang
Keyword(s):  
Global Optimization ◽  
Pareto Frontier ◽  
Kriging Model ◽  
Optimization Method ◽  
Function Evaluation ◽  
Sampling Point ◽  
Constrained Global Optimization ◽  
Multi Objective ◽  
Sample Data ◽  
Sampling Points

The kriging optimization method that can only obtain one sampling point per cycle has encountered a bottleneck in practical engineering applications. How to find a suitable optimization method to generate multiple sampling points at a time while improving the accuracy of convergence and reducing the number of expensive evaluations has been a wide concern. For this reason, a kriging-assisted multi-objective constrained global optimization (KMCGO) method has been proposed. The sample data obtained from the expensive function evaluation is first used to construct or update the kriging model in each cycle. Then, kriging-based estimated target, RMSE (root mean square error), and feasibility probability are used to form three objectives, which are optimized to generate the Pareto frontier set through multi-objective optimization. Finally, the sample data from the Pareto frontier set is further screened to obtain more promising and valuable sampling points. The test results of five benchmark functions, four design problems, and a fuel economy simulation optimization prove the effectiveness of the proposed algorithm.

scholarly journals Optimizing the 3D Distributed Climate inside Greenhouses Using Multi-Objective Optimization Algorithms and Computer Fluid Dynamics

Energies ◽  
2019 ◽  
Vol 12 (15) ◽  
pp. 2873 ◽  
Author(s):  
Kangji Li ◽  
Wenping Xue ◽  
Hanping Mao ◽  
Xu Chen ◽  
Hui Jiang ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Field Experiments ◽  
Climate Model ◽  
Pareto Frontier ◽  
Environmental Parameters ◽  
Optimization Method ◽  
Crop Growth ◽  
Control Variables ◽  
Greenhouse Production ◽  
Multi Objective

As one of the major production facilities in agriculture, a greenhouse has many spatial distributed factors influencing crop growth and energy consumption, such as temperature field, air flow pattern, CO 2 concentration distribution, etc. By introducing a hybrid computational fluid dynamics–evolutionary algorithm (CFD-EA) method, this paper constructs a micro-climate model of greenhouse with main environmental parameters optimized. Considering environmental factors’ spatial influences together with energy usage simultaneously, the optimal solutions of control variables for crop growth are calculated. A commercial greenhouse located in east China is chosen for the method validation. Field experiments using temperature/velocity sensor matrix are carried out for CFD accuracy investigation. On this basis, the proposed optimization method is employed to search for the optimal control variables and parameters corresponding to the environmental Pareto frontier. By the proposed multi-objective scheme, we believe the method can provide set point basis for the design and regulation of large/medium-sized greenhouse production with high spatial resolution.

Multi-Objective Design Optimization of Cooling Turbine Blade Based on Kriging Model

2012 ◽  
Vol 184-185 ◽  
pp. 316-319
Author(s):  
Liang Bo Ao ◽  
Lei Li ◽  
Yuan Sheng Li ◽  
Zhi Xun Wen ◽  
Zhu Feng Yue
Keyword(s):  
Design Optimization ◽  
Turbine Blade ◽  
Optimization Model ◽  
Sampling Technique ◽  
Latin Hypercube Sampling ◽  
Kriging Model ◽  
Optimization Method ◽  
Approximate Model ◽  
Multi Objective ◽  
Pin Fin

The multi-objective design optimization of cooling turbine blade is studied using Kriging model. The optimization model is created, with the diameter of pin fin at the trailing edge of cooling turbine blade and the location, width, height of rib as design variable, the blade body temperature, flow resistance loss and aerodynamic efficiency as optimization object. The sample points are selected using Latin hypercube sampling technique, and the approximate model is created using Kriging method, the set of Pareto-optimal solutions of optimization objects is obtained by the multi-object optimization model using elitist non-dominated sorting genetic algorithm (NSGA-Ⅱ) based on the approximate model. The result shows that the conflict among all optimization objects is solved effectively and the feasibility of the optimization method is improved.

Hybrid and Adaptive Metamodel Based Global Optimization

2009 ◽  
Author(s):  
J. Gu ◽  
G. Y. Li ◽  
Z. Dong
Keyword(s):  
Global Optimization ◽  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Method ◽  
Global Optimum ◽  
Superior Performance ◽  
Automatic Identification ◽  
Design Problems ◽  
Sample Data ◽  
Data Points

Metamodeling techniques are increasingly used in solving computation intensive design optimization problems today. In this work, the issue of automatic identification of appropriate metamodeling techniques in global optimization is addressed. A generic, new hybrid metamodel based global optimization method, particularly suitable for design problems involving computation intensive, black-box analyses and simulations, is introduced. The method employs three representative metamodels concurrently in the search process and selects sample data points adaptively according to the values calculated using the three metamodels to improve the accuracy of modeling. The global optimum is identified when the metamodels become reasonably accurate. The new method is tested using various benchmark global optimization problems and applied to a real industrial design optimization problem involving vehicle crash simulation, to demonstrate the superior performance of the new algorithm over existing search methods. Present limitations of the proposed method are also discussed.

scholarly journals New multiobjective optimization algorithm using NBI-SASP approaches for mechanical structural problems

2022 ◽  
Vol 13 ◽  
pp. 4
Author(s):  
Samira El Moumen ◽  
Siham Ouhimmou
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Pareto Frontier ◽  
Optimization Method ◽  
Multi Objective Optimization ◽  
Design Problems ◽  
Multi Objective ◽  
Structural Problems ◽  
Engineering Design Problems ◽  
Set Of Points

Various engineering design problems are formulated as constrained multi-objective optimization problems. One of the relevant and popular methods that deals with these problems is the weighted method. However, the major inconvenience with its application is that it does not yield a well distributed set. In this study, the use of the Normal Boundary Intersection approach (NBI) is proposed, which is effective in obtaining an evenly distributed set of points in the Pareto set. Given an evenly distributed set of weights, it can be strictly shown that this approach is absolutely independent of the relative scales of the functions. Moreover, in order to ensure the convergence to the Global Pareto frontier, NBI approach has to be aligned with a global optimization method. Thus, the following paper suggests NBI-Simulated Annealing Simultaneous Perturbation method (NBI-SASP) as a new method for multiobjective optimization problems. The study shall test also the applicability of the NBI-SASP approach using different engineering multi-objective optimization problems and the findings shall be compared to a method of reference (NSGA). Results clearly demonstrate that the suggested method is more efficient when it comes to search ability and it provides a well distributed global Pareto Front.

scholarly journals Parameter Analysis and Optimization of Annular Jet Pump Based on Kriging Model

2020 ◽  
Vol 10 (21) ◽  
pp. 7860
Author(s):  
Kai Xu ◽  
Gang Wang ◽  
Liquan Wang ◽  
Feihong Yun ◽  
Wenhao Sun ◽  
...  
Keyword(s):  
Global Optimization ◽  
Kriging Model ◽  
Optimization Method ◽  
Area Ratio ◽  
Pump Efficiency ◽  
Jet Pump ◽  
Pump Design ◽  
Annular Jet ◽  
Design Variables ◽  
Annular Jet Pump

Jet pump efficiency heavily relies on the geometrical parameters of the pump design and parameter global optimization in the full variable space is still a big challenge. This paper proposed a global optimization method for annular jet pump design combining computational fluid dynamics (CFD) simulation, the Kriging approximate model and experimental data. The suction angle, the flow ratio, the diffusion angle, and the area ratio are selected as the design variables for optimization. The optimal space filling design (OSF) method is used to generate sampling points from the design space of the four design variables. The optimization method solves the constrained optimization problem with a given head ratio by building the functional relationship established by the Kriging model between efficiency and design parameters, which makes the method more applicable. The design result shows that the annular jet pump efficiency is predicted well by the Kriging model; m is a key variable affecting the annular jet pump efficiency. As the area ratio m decreases, the mixing effect at the suction chamber outlet can be improved, but the frictional resistance increases.

A Methodology for Trading-Off Performance and Robustness Under Uncertainty

2005 ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Jinghong Liang
Keyword(s):  
Design Optimization ◽  
Pareto Frontier ◽  
Mathematical Optimization ◽  
Optimization Method ◽  
Mean Value ◽  
Preference Aggregation ◽  
Efficient Design ◽  
Multi Objective ◽  
Reliability Based Design ◽  
Reliability And Robustness

Mathematical optimization plays an important role in engineering design, leading to greatly improved performance. Deterministic optimization however, may result in undesired choices because it neglects uncertainty. Reliability-based design optimization (RBDO) and robust design can improve optimization by considering uncertainty. This paper proposes an efficient design optimization method under uncertainty, which simultaneously considers reliability and robustness. A mean performance is traded-off against robustness for a given reliability level of all performance targets. This results in a probabilistic multi-objective optimization problem. Variation is expressed in terms of a percentile difference, which is efficiently computed using the Advanced Mean Value (AMV) method. A preference aggregation method converts the multi-objective problem to a single-objective problem, which is then solved using an RBDO approach. Indifference points are used to select the best solution without calculating the entire Pareto frontier. Examples illustrate the concepts and demonstrate their applicability.

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