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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 1457297, 12 pages
Research Article

Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

1Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China
2Faculty of Architecture and Built Environment, Delft University of Technology, Julianalaan 134, 2628 BL Delft, Netherlands
3Hangzhou Xiaoshan Urban Planning Institute, Hangzhou 311200, China
4Hangzhou Xiaoshan District Housing & Construction Bureau, Hangzhou 311200, China

Correspondence should be addressed to Qingpeng Li

Received 2 January 2017; Revised 14 March 2017; Accepted 23 April 2017; Published 4 June 2017

Academic Editor: Nantiwat Pholdee

Copyright © 2017 Yue Wu 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.


Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.