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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: B.H.V. Topping
Chapter 7

Searching for Good Topological Solutions using Evolutionary Algorithms

J.C. Miles, A.S.K. Kwan, K. Wang and Y. Zhang

Cardiff School of Engineering, Cardiff University, United Kingdom

Full Bibliographic Reference for this chapter
J.C. Miles, A.S.K. Kwan, K. Wang, Y. Zhang, "Searching for Good Topological Solutions using Evolutionary Algorithms", in B.H.V. Topping, (Editor), "Civil Engineering Computations: Tools and Techniques", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 7, pp 149-172, 2007. doi:10.4203/csets.16.7
Keywords: design, topology, evolutionary algorithm.

Design is typically undertaken by multi-disciplinary teams who come together to create whatever is required. Also design has in the last two decades moved from the "over the wall" model,where each discipline made its contribution in sequence, to being a parallel process where the designers collaborate. This has made the design process more demanding in that it increases the complexity of the decision making. It can be shown that, for the design of a typical multi-storey building, the number of feasible options is of the order of 200 million. Given this level of complexity, there is no way, other than by chance, that a design team will ever find a "good" solution (the word optimise is deliberately avoided for reasons that are explained in the full paper) and that really their only hope is to find solutions that satisfy the imposed constraints. Therefore, if the design process is to be improved, by helping designers to find "good" solutions, some form of search engine is required.

The search engine will have to be able to cope with the complexity of modern design problems which are multi-objective and highly constrained as well as being multi-disciplinary. The search spaces are likely to be highly complex, involving non-linearities, discontinuities and discrete variables. In places even gradient information may be absent. Traditional optimisation techniques are unable to cope with such problems and the only methods that have sufficient functionality are those that are collectively called evolutionary computation. Of these, the most commonly used are genetic algorithms and the paper focuses on these.

Most design problems involve objects with complex and very mixed topologies. For instance in a building, there are spaces, beams and columns, slabs, pipes, ducting, etc. At the moment there is no topological reasoning tool that can cope with such a variety of shapes. If the form of the solution is know a priori, and it is not too complex, then it is possible to find a suitable topological reasoning technique but to impose such a process is to guess the answer and therefore limit the search. Therefore what is needed is a new way of dealing with topological reasoning which can cope with complex, multi-form objects.

At the moment, no such method exists. Two possible candidates are discussed, these being generative representations and generative geometries. In both cases, the description is of work in progress rather than final results. For the generative representation, the method involves using rewriting rules coupled to Turtle graphics. These are then coupled to an evolutionary computation search engine. The method has some significant differences from traditional evolutionary computation methods which means that it has to be applied with more thought than is normally required.

For the generative geometry, the work is in its early stages but the basis of the theory is presented and its practical application is then discussed. The method seems to have the ability to cope with complex topologies but until it is fully tested, it is not possible to be sure and there will almost certainly be unexpected difficulties.

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