scholarly journals Global Optimization Algorithm Based on Kriging Using Multi-Point Infill Sampling Criterion and Its Application in Transportation System

2021 ◽  
Vol 13 (19) ◽  
pp. 10645
Author(s):  
Xiaodong Song ◽  
Mingyang Li ◽  
Zhitao Li ◽  
Fang Liu
Keyword(s):  
Global Optimization ◽  
Single Point ◽  
Great Influence ◽  
Kriging Model ◽  
Expected Improvement ◽  
Particle Swarm Algorithm ◽  
Beijing City ◽  
Public Traffic ◽  
Low Dimensional ◽  
Infill Sampling

Public traffic has a great influence, especially with the background of COVID-19. Solving simulation-based optimization (SO) problem is efficient to study how to improve the performance of public traffic. Global optimization based on Kriging (KGO) is an efficient method for SO; to this end, this paper proposes a Kriging-based global optimization using multi-point infill sampling criterion. This method uses an infill sampling criterion which obtains multiple new design points to update the Kriging model through solving the constructed multi-objective optimization problem in each iteration. Then, the typical low-dimensional and high-dimensional nonlinear functions, and a SO based on 445 bus line in Beijing city, are employed to test the performance of our algorithm. Moreover, compared with the KGO based on the famous single-point expected improvement (EI) criterion and the particle swarm algorithm (PSO), our method can obtain better solutions in the same amount or less time. Therefore, the proposed algorithm expresses better optimization performance, and may be more suitable for solving the tricky and expensive simulation problems in real-world traffic problems.

Global Optimization Based on Weighting-Integral Expected Improvement

2012 ◽  
Vol 630 ◽  
pp. 383-388
Author(s):  
Zheng Li ◽  
Xi Cheng Wang
Keyword(s):  
Global Optimization ◽  
Numerical Experiments ◽  
Kriging Model ◽  
Global Optimum ◽  
Engineering Problem ◽  
Expected Improvement ◽  
Iteration Step ◽  
Global Optimization Algorithm ◽  
Mathematical Functions ◽  
High Flexibility

Balancing the global exploration and the local exploitation has received particular attention in global optimization algorithm. In this paper, based on Kriging model an infill sample criteria named weighting-integral expected improvement is proposed, which provides a high flexibility to balance the scope of search. Coupled with this infill sample criteria, a strategy is proposed that on each iteration step, the infill sample point was selected by the urgency of each search scope. Two mathematical functions and one engineering problem are used to test this method. The numerical experiments show that this method has excellent efficiency in finding global optimum solutions.

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 Expected improvement in efficient global optimization through bootstrapped kriging

2011 ◽  
Vol 54 (1) ◽  
pp. 59-73 ◽  
Author(s):  
Jack P. C. Kleijnen ◽  
Wim van Beers ◽  
Inneke van Nieuwenhuyse
Keyword(s):  
Global Optimization ◽  
Expected Improvement ◽  
Efficient Global Optimization

Handling of Constraints in Efficient Global Optimization

2020 ◽  
pp. 2050033
Author(s):  
Hu Wang ◽  
Wei Hu ◽  
Enying Li
Keyword(s):  
Global Optimization ◽  
Variable Stiffness ◽  
Kriging Model ◽  
Superior Performance ◽  
Efficient Global Optimization ◽  
Feasible Region ◽  
Support Vector ◽  
Multiple Constraint ◽  
Fiber Path ◽  
Feasible Points

Although the Efficient Global Optimization (EGO) algorithm has been widely used in multi-disciplinary optimization, it is still difficult to handle multiple constraint problems. In this study, to increase the accuracy of approximation, the Least Squares Support Vector Regression (LSSVR) is suggested to replace the kriging model for approximating both objective and constrained functions while the variances of these surrogate models are still obtained by kriging. To enhance the ability to search the feasible region, two criteria are suggested. First, a Maximize Probability of Feasibility (MPF) strategy to handle the infeasible initial sample points is suggested to generate feasible points. Second, a Multi-Constraint Parallel (MCP) criterion is suggested for multiple constraints handling, parallel computation and validation, respectively. To illustrate the efficiency of the suggested EGO-based method, several deterministic benchmarks are tested and the suggested methods demonstrate a superior performance compared with two other constrained algorithms. Finally, the suggested algorithm is successfully utilized to optimize the fiber path of variable-stiffness beam and lightweight B-pillar to demonstrate the performance for engineering applications.

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