A grouping method for optimization of steel skeletal structures by applying a combinatorial search algorithm based on a fully stressed design

In the design of steel structures, optimization methods can find minimum weight solutions. However, the solutions tend to have a high diversity of profiles, thereby raising costs. Grouping methods provide a solution by limiting the number of unique profiles, while still providing an optimal solution. This study proposes a new grouping method and compares its performance to that of existing methods in eight benchmark problems. In current practice, the grouping is mostly performed manually, relying on an engineer’s expertise. This technique requires no additional calculations but fails in finding a light or cheap structure. In general, all other grouping methods perform better than manual grouping. Out of the compared methods, the cardinality constraints method finds the lightest solutions. However, this method requires solving a big optimization problem, thereby increasing computational costs and the variance in the outcome. The new method, ‘the fully stressed combinatorial search’, groups members by a combinatorial search, which evaluates the estimated weight of a restricted set of groupings based on the weight per unit length of the members of a fully stressed design. Subsequently, optimization of a small search space finds the corresponding optimum profiles. These steps are repeated, in which the fully stressed design uses the result of the previous optimization as its reference design. The loop repeats until the grouping is unchanged, or the result becomes less optimal. This new method finds similar results as the cardinality constraints with less finite element evaluations and higher consistency in the results upon repetition of the analysis.