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Exploiting Layout Optimization for Engineering
Layout Optimization (LayOpt) is a systematic and highly efficient numerical method used to identify optimum layouts of structural (or other) elements leading to e.g. the least-material design. The classical layout optimization method involves four steps (here illustrated with an example of material-efficient truss design):
Firstly, the design domain, loading and support conditions are specified.
Secondly, the design domain is discretized using a general or regular grid of nodes.
Thirdly, a ‘ground structure’ is created by interconnecting nodes with potential members (e.g., truss bars).
Finally, an optimum layout is identified by solving an optimization problem, that minimizes the weight of the structure while carrying the specified loads.
Wide range of applications
In addition to the structural elements depicted above, the lines of the 'ground structure' can represent a wide array of things. This allows the same underlying mathematical methods to be used in a selection of seemingly disconnected applications. To learn more about these applications, click on the relevant link below, or keep reading for more information on the underlying framework.
Member adding
Member adding
Solution of the optimization problem can be significantly sped up through the use of member adding, whereby instead of starting with a fully connected ground structure (shown on the left in the below figure), a sparser structure is initially adopted and critical members robustly identified and iteratively added (right hand three stages in the below figure). For large problems this can reduce the number of members that need to be considered by the optimizer by orders of magnitude, while still acheiving a robust and rigorous globally optimal solution.
Global vs local optimization
Heuristic and meta-heuristic optimisation methods such as genetic algorithms have proved popular in recent years, largely due to the ease with which a non-specialist user can include real-world constraints. However, these methods have severe drawbacks. For example, the starting points for these methods are usually randomly generated, or based on intuition, but will often influence the final output, likely leading to a sub-optimal design being obtained (i.e. corresponding to a “local hollow”, as shown in the left hand figure which may be much higher than the “valley bottom”). Additionally, with these methods there is no way of knowing how much further benefit is possible once a solution has been found. This may lead either to unnecessarily inefficient designs being accepted, or alternately to substantial effort being wasted attempting to improve on a design which is already optimal or near-optimal.
Our research typically adopts an alternative two step optimisation approach. In the first step the problem is simplified so that only the essential physics is modelled, for example meaning that only equilibrium and stress limit considerations remain. This allows a reference solution to be obtained, providing a lower bound on the optimal solution. The second step is to apply various methods to move through the design space to locate promising solutions, if possible in close proximity to the reference solution, as shown in the right hand figure.
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