Discrete sizing optimization method based on dividing rectangles algorithm and local response surface for steel frame structures

Abstract

It has always been the goal of structural engineers to construct safe and stable buildings using the least amount of materials. Utilizing a quick and effective way to optimize the cross-section size is crucial because conventional building design methods are impacted by the designers' knowledge, and it is challenging to prevent material waste. Due to its implicit optimization function, discrete design variables, and expensive individual evaluation, sizing optimization of high-rise buildings is very challenging to achieve. In order to effectively handle this optimization problem, a two-stage discrete sizing optimization method for high-rise buildings based on the DIviding RECTangles (DIRECT) algorithm and local response surface is proposed in this paper. The optimization method suggested in this research consists of two key stages: the global search stage and the local search stage. In the global search stage, the entire design domain is divided using a modified DIRECT algorithm to swiftly identify potentially optimal subregions that may contain the best points. In the local search stage, the local response surface model is constructed to approximate the objective and constraint functions using the sampling points from the previous stage, and the discrete optimal solution is rapidly found through mathematical iterative solving. A sizing optimization calculation program for high-rise buildings was developed in Microsoft Visual Studio 2015 on the basis of C++ to achieve automatic optimization. The new method was applied to optimize three high-rise steel frame buildings with different heights and plan shapes. The results showed that the material cost could be successfully saved compared with the conventional design, and the over-limit constraints could be adjusted automatically, which demonstrated the viability and efficacy of the two-stage optimization method.