Structural and Multidisciplinary Optimization

, Volume 57, Issue 3, pp 1047–1060 | Cite as

An intelligent sampling approach for metamodel-based multi-objective optimization with guidance of the adaptive weighted-sum method

  • Cheng Lin
  • Fengling Gao
  • Yingchun Bai


In order to reduce the computational cost of multi-objective optimization (MOO) with expensive black-box simulation models, an intelligent sampling approach (ISA) is proposed with the guidance of the adaptive weighted-sum method (AWS) to construct a metamodel for MOO gradually. The initial metamodel is built by using radial basis function (RBF) with Latin Hypercube Sampling (LHS) to distribute samples over the design space. An adaptive weighted-sum method is then employed to obtain the Pareto Frontier (POF) efficiently based on the metamodel constructed. The design variables related to extreme points on the frontier and an extra point interpolated between the maximal-minimal-distance point along the frontier and the nearest boundary point are selected as the concerned points to update the metamodel, which could improve the metamodel accuracy gradually. This iterative updating strategy is performed until the optimization problem is converged. A series of representative mathematical examples are systematically investigated to demonstrate the effectiveness of the proposed method, and finally it is employed for the design of a bus body frame.


Multi-objective optimization Intelligent sampling technique Adaptive weighted-sum method Radial basis function 



This work is supported by the National Natural Science Foundation of China (NO. 51575044), the Science and Technology Planning Project of Beijing City (NO. Z161100001416007) and the National Key R&D Program of China (NO. 2017YFB0103801).


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.National Engineering Laboratory for Electric Vehicles, School of Mechanical EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.Collaborative Innovation Center of Electric Vehicles in BeijingBeijing Institute of TechnologyBeijingChina

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