Buildable Design in Optimisation of Steel Skeletal Structures: A Comparison of Existing and New Methods for Finding the Best Solution with Low Diversity

Abstract

In the design of steel structures, optimisation methods promise cheap, light and sustainable structures. However, the resulting designs tend to have a high diversity of profiles, making them unbuildable. Furthermore, the optimisation problem is mathematically complex, leading to a long and potentially unsolvable optimisation process. Grouping methods solve both issues by finding the optimum solution, for which the number of distinct profiles is limited. Multiple grouping methods exist in literature, and it is not known which is the best: the methods have not been applied on the same problems, and the computational effort has not been compared. This gap in literature leads to the following question: “Which method for grouping can find the lightest and cheapest steel structure with minimal computational effort?” To answer this question, a comparison of the existing grouping methods is made on their theoretical and numerical performance. The theoretical comparison comprises the size and properties of the search space, and the number of additional calculations. The numerical comparison consists of weight optimisation of eight benchmark problems. For each structure and method, the weight of the solution and corresponding computational effort is evaluated. Manually grouping of members, which is the most popular grouping method, relies on the engineer’s expertise and rules of thumb. This method requires no additional calculations but in general fails to find the optimum grouping for a light or cheap structure. Other existing methods include the geometry, axial force distribution or an ungrouped result in their grouping process, or adapt the optimisation problem. Of these methods, only the cardinality constraints method is guaranteed to potentially find the lightest grouped design, while reducing the search space for a small number of groups. However, it creates many local optima, which increases the complexity of the search space. In the aim of finding a grouping method which creates a simple and small search space and has low computational effort, the fully stressed combinatorial search method is proposed. In this method, the grouping is found by a combinatorial search, which evaluates the estimated weight or costs of a restricted set of groupings based on the weight per unit length of the members of a fully stressed design. Then, optimisation of a small and simple search space finds the corresponding optimum profiles. These steps are repeated, in which the fully stressed design uses the result of the previous optimisation as its reference design. The loop repeats until the grouping is unchanged, or the result diverges. In all numerical experiments, the new method gave results with a low weight, while it kept the computational effort to an acceptable level. It gave the lightest design for four out of eight problems and showed high certainty for converging to the lightest design in two problems. For the other two problems it performed second best. Conclusively, this method is the best available grouping method for steel structural optimisation. In case of cost optimisation, the new grouping method can efficiently find the optimum design including the optimum number of groups; the new method converges to cheaper design with less computations than in the case no grouping is applied. For a real-life case-study, the costs of a design were reduced with 7.3% compared to a manually grouped design and with 19.6% compared to the conventional design process. I suggest that further research focusses on further development of the new grouping method as proposed improvements can be made on the initial design, and the number of computations in the combinatorial search and fully stressed design. Moreover, the effectiveness of a suggested simplification of the new method should be investigated. This would allow application for engineers who are not able to apply a mathematical optimisation method. For practical application, incorporation of building codes and cost functions with a well-defined scope are desired. Finally, utilisation of the grouping methods in other applications is possible, but the performance of the methods should be evaluated per application.