An efficient multi-objective optimization method based on the adaptive approximation model of the radial basis function
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RESEARCH PAPER
An efficient multi-objective optimization method based on the adaptive approximation model of the radial basis function Xin Liu 1,2 & Xiang Liu 2 & Zhenhua Zhou 2 & Lin Hu 2 Received: 18 May 2020 / Revised: 21 September 2020 / Accepted: 9 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Considering the high computational cost caused by solving multi-objective optimization (MOO) problems, an efficient multiobjective optimization method based on the adaptive approximation model is developed. Firstly, the Latin hypercube design (LHD) is employed for obtaining the initial sample points. Secondly, initial approximation models of objective functions and constraints are established by using the radial basis function (RBF). For ensuring the accuracy of the approximation models, the reverse shape parameter analysis method (RSPAM) is proposed to obtain improved approximation models. Thirdly, the micro multi-objective genetic algorithm (μMOGA) is adopted to solve the Pareto optimal set and the local-densifying approximation method is also applied to strengthen the ability of solving accurate Pareto optimal sets. Finally, the effectiveness and practicability of the proposed method is demonstrated by two numerical examples and two engineering examples. Keywords Multi-objective optimization . Reverse shape parameter analysis method . Local-densifying approximation method . Adaptive approximation model
1 Introduction The multi-objective optimization (MOO) problems widely exist in engineering design (Zarchi and Attaran 2019; Tian et al. 2018; Wang et al. 2011; Jaouadi et al. 2020), and a large number of optimization schemes have been provided by different MOO methods. A series of prominent work in this filed has been carried out and reported. Omkar et al. (2011) proposed a vector evaluated artificial bee colony (VEABC) algorithm to deal with the multi-objective design optimization of the laminated composite components. Bui et al. (2019) suggested a multi-objective optimization method based on the mixed integer linear programming (MILP) to determine Responsible Editor: Ren-Jye Yang * Zhenhua Zhou [email protected] 1
Engineering Research Center of Catastrophic Prophylaxis and Treatment of Road & Traffic Safety of Ministry of Education, Changsha University of Science & Technology, Changsha 410114, China
2
Hunan Province Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle, Changsha University of Science and Technology, Changsha 410114, China
trade-off between conflicting operation objectives of wind farm systems. Posteljnik et al. (2016) proposed a multiobjective optimization method for the wind turbine structure by adopting the particle swarm (PSO) algorithm. In the abovementioned works, the multi-objective optimization problems are mostly formulated by explicit mathematical expressions. However, the objective functions and constraints are usually black-box functions for most MOO problems, which are evaluated by complex simulation model with hi
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