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Mathematical Problems in Engineering
Volume 2015, Article ID 932029, 13 pages
Research Article

An Efficient Hybrid Algorithm for Multiobjective Optimization Problems with Upper and Lower Bounds in Engineering

1School of Mechanical Science and Engineering, Jilin University, Changchun 130022, China
2State Key Laboratory of Automotive Simulation and Control, Changchun 130022, China

Received 12 March 2015; Revised 8 June 2015; Accepted 17 June 2015

Academic Editor: Farhang Daneshmand

Copyright © 2015 Guang Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Generally, the inconvenience of establishing the mathematical optimization models directly and the conflicts of preventing simultaneous optimization among several objectives lead to the difficulty of obtaining the optimal solution of a practical engineering problem with several objectives. So in this paper, a generate-first-choose-later method is proposed to solve the multiobjective engineering optimization problems, which can set the number of Pareto solutions and optimize repeatedly until the satisfactory results are obtained. Based on Frisch’s method, Newton method, and weighed sum method, an efficient hybrid algorithm for multiobjective optimization models with upper and lower bounds and inequality constraints has been proposed, which is especially suitable for the practical engineering problems based on surrogate models. The generate-first-choose-later method with this hybrid algorithm can calculate the Pareto optimal set, show the Pareto front, and provide multiple designs for multiobjective engineering problems fast and accurately. Numerical examples demonstrate the effectiveness and high efficiency of the hybrid algorithm. In order to prove that the generate-first-choose-later method is rapid and suitable for solving practical engineering problems, an optimization problem for crash box of vehicle has been handled well.