Cost-based optimization of steel frame member sizing and connection type using dimension increasing search

This paper describes a novel method to select the optimal member sizes and connection types for steel frame structures to minimize total installed cost. The proposed dimension increasing search (DIS) method addresses geometric constraints associated with connection, safety, and serviceability constraints. Solving this optimization problem requires addressing a non-convex objective function of total installed cost, a large number of constraints, the time-consuming structural analysis for evaluation of the constraints, and intractability resulting from high-dimensional variables. The DIS method involves initial grouping of design variables to reduce the search dimension from the original dimension. Random search coupled with forward checking and branch-and-bound techniques are then employed to optimize the configuration of the steel frame. This approach eliminates designs that are more expensive or do not satisfy geometric constraints without performing structural analysis. The variable groups are then split into subgroups to increase the search dimension, and the increased dimensional design variables are optimized until the original search dimension is achieved. We benchmarked the DIS method against leading methods using three numerical examples with increasing problem scales. The DIS method was more computationally efficient compared to other leading methods by an order of magnitude, and the solutions found by the method have a 9% lower total installed cost on average. The DIS method also showed scalability; the computational time increased only slightly as the problem scale increased. The scalability of the DIS method demonstrates the potential for its successful industrial application to large-scale building projects.