Modular steel frames are prefabricated structures with slender elements, mostly under compressive forces. The analysis includes different non-linearities, e.g. the geometric non-linearities, global and local stability effects, in particular the local buckling of thin-walled elements, slippage and non-linear behaviour of joints.

The objective of the optimization is the minimal cost-design, which can be approximated by the weighted sum of the volume of the individual elements. The weighting factors and the objective function are adjustable. The optimization of modular systems requires the most advanced solution techniques but also a systematic pre-processing, sophisticated non-linear structural analysis within a three-dimensional model, an automated handling of stress- and displacement-constraints and other side-constraints.

The Optimization of these structures involves continuous and discrete variables mixed. The problem could be solved by decomposition into two subproblems: The first one is related to the discrete variables and solved by evolutionary strategies (ES). To solve this subproblem special accommodations of the ES regarding the discontinuous behaviour of the discrete variables has to be done. The second subproblem with continuous variables is solved by mathematical programming. The ES are used as upstream strategies, which calls the gradient-based solver iterative. The decomposition of the optimization problem is well suited for parallelization on multi-processors.

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