Updating Kriging Surrogate Models Based on the Hypervolume Indicator in Multi-Objective Optimization

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Koji Shimoyama ◽  
Koma Sato ◽  
Shinkyu Jeong ◽  
Shigeru Obayashi
Keyword(s):  
Objective Function ◽  
Objective Function Value ◽  
Kriging Model ◽  
Surrogate Models ◽  
Expected Improvement ◽  
Multi Objective Optimization ◽  
Nondominated Solutions ◽  
Multi Objective ◽  
Beam Design ◽  
Hypervolume Indicator

This paper presents a comparison of the criteria for updating the Kriging surrogate models in multi-objective optimization: expected improvement (EI), expected hypervolume improvement (EHVI), estimation (EST), and those in combination (EHVI + EST). EI has been conventionally used as the criterion considering the stochastic improvement of each objective function value individually, while EHVI has recently been proposed as the criterion considering the stochastic improvement of the front of nondominated solutions in multi-objective optimization. EST is the value of each objective function estimated nonstochastically by the Kriging model without considering its uncertainties. Numerical experiments were implemented in the welded beam design problem, and empirically showed that, in an unconstrained case, EHVI maintains a balance between accuracy, spread, and uniformity in nondominated solutions for Kriging-model-based multiobjective optimization. In addition, the present experiments suggested future investigation into techniques for handling constraints with uncertainties to enhance the capability of EHVI in constrained cases.

scholarly journals Optimal Design of IPMSM for EV Using Subdivided Kriging Multi-Objective Optimization

Processes ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1490
Author(s):  
Jong-Min Ahn ◽  
Myung-Ki Baek ◽  
Sang-Hun Park ◽  
Dong-Kuk Lim
Keyword(s):  
Optimal Design ◽  
Objective Function ◽  
Pareto Front ◽  
Permanent Magnet Synchronous Motor ◽  
Kriging Model ◽  
Superior Performance ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Design Variables ◽  
Interior Permanent Magnet

In this paper, subdivided kriging multi-objective optimization (SKMOO) is proposed for the optimal design of interior permanent magnet synchronous motor (IPMSM). The SKMOO with surrogate kriging model can obtain a uniform and accurate pareto front set with a reduced computation cost compared to conventional algorithms which directly adds the solution in the objective function area. In other words, the proposed algorithm uses a kriging surrogate model, so it is possible to know which design variables have the value of the objective function on the blank space. Therefore, the solution can be added directly in the objective function area. In the SKMOO algorithm, a non-dominated sorting method is used to find the pareto front set and the fill blank method is applied to prevent premature convergence. In addition, the subdivided kriging grid is proposed to make a well-distributed and more precise pareto front set. Superior performance of the SKMOO is confirmed by compared conventional multi objective optimization (MOO) algorithms with test functions and are applied to the optimal design of IPMSM for electric vehicle.

Multi-objective optimization of squirrel cage fan for range hood based on Kriging model

2021 ◽  
pp. 095440622199586
Author(s):  
Qianhao Xiao ◽  
Jun Wang ◽  
Boyan Jiang ◽  
Weigang Yang ◽  
Xiaopei Yang
Keyword(s):  
Flow Rate ◽  
Optimization Design ◽  
Volume Flow Rate ◽  
Kriging Model ◽  
Volume Flow ◽  
Design Parameters ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Squirrel Cage

In view of the multi-objective optimization design of the squirrel cage fan for the range hood, a blade parameterization method based on the quadratic non-uniform B-spline (NUBS) determined by four control points was proposed to control the outlet angle, chord length and maximum camber of the blade. Morris-Mitchell criteria were used to obtain the optimal Latin hypercube sample based on the evolutionary operation, and different subsets of sample numbers were created to study the influence of sample numbers on the multi-objective optimization results. The Kriging model, which can accurately reflect the response relationship between design variables and optimization objectives, was established. The second-generation Non-dominated Sorting Genetic algorithm (NSGA-II) was used to optimize the volume flow rate at the best efficiency point (BEP) and the maximum volume flow rate point (MVP). The results show that the design parameters corresponding to the optimization results under different sample numbers are not the same, and the fluctuation range of the optimal design parameters is related to the influence of the design parameters on the optimization objectives. Compared with the prototype, the optimized impeller increases the radial velocity of the impeller outlet, reduces the flow loss in the volute, and increases the diffusion capacity, which improves the volume flow rate, and efficiency of the range hood system under multiple working conditions.

Multi-objective optimization of weld geometry in hybrid fiber laser-arc butt welding using Kriging model and NSGA-II

2016 ◽  
Vol 122 (6) ◽  
Author(s):  
Zhongmei Gao ◽  
Xinyu Shao ◽  
Ping Jiang ◽  
Chunming Wang ◽  
Qi Zhou ◽  
...  
Keyword(s):  
Fiber Laser ◽  
Kriging Model ◽  
Multi Objective Optimization ◽  
Hybrid Fiber ◽  
Nsga Ii ◽  
Butt Welding ◽  
Multi Objective ◽  
Weld Geometry

A multi-objective optimization model for logistic planning in the crisis response phase

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammad Mahdi Ershadi ◽  
Hossein Shams Shemirani
Keyword(s):  
Objective Function ◽  
Optimization Model ◽  
Crisis Response ◽  
Multi Objective Optimization ◽  
Content Type ◽  
Multi Objective ◽  
Proposed Model ◽  
Different Types ◽  
Response Phase ◽  
Logistic Planning

PurposeProper planning for the response phase of humanitarian relief can significantly prevent many financial and human losses. To this aim, a multi-objective optimization model is proposed in this paper that considers different types of injured people, different vehicles with determining capacities and multi-period logistic planning. This model can be updated based on new information about resources and newly identified injured people.Design/methodology/approachThe main objective function of the proposed model in this paper is minimizing the unsatisfied prioritized injured people in the network. Besides, the total transportation activities of different types of vehicles are considered as another objective function. Therefore, these objectives are optimized hierarchically in the proposed model using the Lexicographic method. This method finds the best value for the first objective function. Then, it tries to optimize transportation activities as the second objective function while maintaining the optimality of the first objective function.FindingsThe performances of the proposed model were analyzed in different cases and its robust approach for different problems was shown within the framework of a case study. Besides, the sensitivity analysis of results shows the logical behavior of the proposed model against various factors.Practical implicationsThe proposed methodology can be applied to find the best response plan for all crises.Originality/valueIn this paper, we have tried to use a multi-objective optimization model to guide and correct response programs to deal with the occurred crisis. This is important because it can help emergency managers to improve their plans.

Extreme Learning Surrogate Models in Multi-objective Optimization based on Decomposition

2016 ◽  
Vol 180 ◽  
pp. 55-67 ◽  
Author(s):  
Lucas M. Pavelski ◽  
Myriam R. Delgado ◽  
Carolina P. Almeida ◽  
Richard A. Gonçalves ◽  
Sandra M. Venske
Keyword(s):  
Surrogate Models ◽  
Multi Objective Optimization ◽  
Multi Objective

scholarly journals Optimizing the Water Treatment Design and Management of the Artificial Lake with Water Quality Modeling and Surrogate-Based Approach

Water ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 391 ◽  
Author(s):  
Chuankun Liu ◽  
Yue Hu ◽  
Ting Yu ◽  
Qiang Xu ◽  
Chaoqing Liu ◽  
...  
Keyword(s):  
Water Quality ◽  
Water Treatment ◽  
Surrogate Models ◽  
Water Quality Modeling ◽  
Support Vector ◽  
Practical Case ◽  
Multi Objective Optimization ◽  
Artificial Lake ◽  
Multi Objective ◽  
Engineering Costs

The tradeoff between engineering costs and water treatment of the artificial lake system has a significant effect on engineering decision-making. However, decision-makers have little access to scientific tools to balance engineering costs against corresponding water treatment. In this study, a framework integrating numerical modeling, surrogate models and multi-objective optimization is proposed. This framework was applied to a practical case in Chengdu, China. A water quality model (MIKE21) was developed, providing training datasets for surrogate modeling. The Artificial Neural Network (ANN) and Support Vector Machine (SVM) were utilized for training surrogate models. Both surrogate models were validated with the coefficient of determinations (R2) greater than 0.98. SVM performed more stably with limited training data sizes while ANN demonstrated higher accuracies with more training samples. The multi-objective optimization model was developed using the genetic algorithm, with targets of reducing both engineering costs and target aquatic pollutant concentrations. An optimal target concentration after treatment was identified, characterized by the ammonia concentration (1.3 mg/L) in the artificial lake. Furthermore, scenarios with varying water quality in the upstream river were evaluated. Given the assumption of deteriorated upstream water quality in the future, the optimal proportion of pre-treatment in the total costs is increasing.

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