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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 521482, 11 pages
Research Article

Improved Genetic Algorithm with Two-Level Approximation for Truss Optimization by Using Discrete Shape Variables

School of Astronautics, Beihang University, XueYuan Road No. 37, HaiDian District, Beijing 100191, China

Received 25 September 2014; Revised 10 April 2015; Accepted 17 April 2015

Academic Editor: P. Beckers

Copyright © 2015 Shen-yan Chen 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.


This paper presents an Improved Genetic Algorithm with Two-Level Approximation (IGATA) to minimize truss weight by simultaneously optimizing size, shape, and topology variables. On the basis of a previously presented truss sizing/topology optimization method based on two-level approximation and genetic algorithm (GA), a new method for adding shape variables is presented, in which the nodal positions are corresponding to a set of coordinate lists. A uniform optimization model including size/shape/topology variables is established. First, a first-level approximate problem is constructed to transform the original implicit problem to an explicit problem. To solve this explicit problem which involves size/shape/topology variables, GA is used to optimize individuals which include discrete topology variables and shape variables. When calculating the fitness value of each member in the current generation, a second-level approximation method is used to optimize the continuous size variables. With the introduction of shape variables, the original optimization algorithm was improved in individual coding strategy as well as GA execution techniques. Meanwhile, the update strategy of the first-level approximation problem was also improved. The results of numerical examples show that the proposed method is effective in dealing with the three kinds of design variables simultaneously, and the required computational cost for structural analysis is quite small.