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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 838102, 9 pages
Research Article

Simultaneous Topology, Shape, and Sizing Optimisation of Plane Trusses with Adaptive Ground Finite Elements Using MOEAs

1Department of Engineering Management, Faculty of Science and Technology, Rajabhat Maha Sarakham University, Maha Sarakham 44000, Thailand
2Department of Mechanical Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen 40002, Thailand

Received 4 October 2012; Revised 7 January 2013; Accepted 8 January 2013

Academic Editor: Sheng-yong Chen

Copyright © 2013 Norapat Noilublao and Sujin Bureerat. 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 proposes a novel integrated design strategy to accomplish simultaneous topology shape and sizing optimisation of a two-dimensional (2D) truss. An optimisation problem is posed to find a structural topology, shape, and element sizes of the truss such that two objective functions, mass and compliance, are minimised. Design constraints include stress, buckling, and compliance. The procedure for an adaptive ground elements approach is proposed and its encoding/decoding process is detailed. Two sets of design variables defining truss layout, shape, and element sizes at the same time are applied. A number of multiobjective evolutionary algorithms (MOEAs) are implemented to solve the design problem. Comparative performance based on a hypervolume indicator shows that multiobjective population-based incremental learning (PBIL) is the best performer. Optimising three design variable types simultaneously is more efficient and effective.