Evolutionary Structural Optimisation

This project aims to develop a simple but versatile technique for finding structurally efficient designs.

Professors Mike Xie and Grant Steven proposed the (ESO) in the 1990s.

ESO is based on the simple concept of slowly removing inefficient material from a structure so that the residual shape evolves towards the optimum.

In the example above, we try to find the optimal shape for an object hanging in the air under gravity. By gradually removing the least stressed material from the surface, we obtain a final shape with a uniform stress on the surface. The result reminds us of certain fruits such as apple or cherry.

Another classical example of ESO is the design of tension- or compression-only structures. By using the compressive stress as the removal criterion, a tension-only catenary structure can be easily achieved as shown above.

The original ESO method did not allow deleted elements to be restored. To improve the robustness and efficiency of the optimisation process, a bi-directional ESO (BESO) method was developed in the late 1990s in which material can be added and deleted simultaneously. In more recent years, we have further improved the algorithms and extended the BESO technique to a wide range of optimisation problems of structural and material designs. Please see our other projects and publications for more details.

Key people

  • Dist. Professor Mike Xie
  • Dr Xiaodong Huang
  • Dr Zhihao Zuo
  • Dr Jiwu Tang
  • Dr Xiaoying Yang


  • Y.M. Xie and G.P. Steven, ’A simple evolutionary procedure for structural optimization’, Computers & Structures, 49, pp 885-886, 1993.
  • Y.M. Xie and G.P. Steven, Evolutionary Structural Optimization, Springer, London, 1997.
  • O.M. Querin, G.P. Steven and Y.M. Xie, ’Evolutionary structural optimization (ESO) using a bidirectional algorithm’, Engineering Computations, 15, pp 1031-1048, 1998.
  • X. Huang and Y.M. Xie, ’Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method’, Finite Elements in Analysis and Design, 43, pp 1039–1049, 2007.
  • X. Huang and Y.M Xie, 'Evolutionary Topology Optimization of Continuum Structures: Methods and Applications', Chichester, England, John Wiley & Sons, 2010.
  • Y.M. Xie, Z.H. Zuo, X. Huang, J.W. Tang, B. Zhao and P. Felicetti, ’Architecture and urban design through evolutionary structural optimisation algorithms’, Keynote Lecture of International Symposium on Algorithmic Design for Architecture and Urban Design, Tokyo, Japan, 14-16 March, 2011
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Acknowledgement of country

RMIT University acknowledges the people of the Woi wurrung and Boon wurrung language groups of the eastern Kulin Nation on whose unceded lands we conduct the business of the University. RMIT University respectfully acknowledges their Ancestors and Elders, past and present. RMIT also acknowledges the Traditional Custodians and their Ancestors of the lands and waters across Australia where we conduct our business. - Artwork created by Louisa Bloomer