DESIGN OPTIMIZATION OF PLATE GIRDER USING GENERALIZED REDUCED GRADIENT AND ARTIFICIAL BEE COLONY ALGORITHMS

Abstract

The Generalized Reduced Gradient (GRG) algorithm available in Excel Solver, and the Artificial Bee Colony (ABC) algorithm modified for constrained optimization were utilized to optimize the design of plate girder for minimum weight, given the span and grade of the material of the girder. The cross sectional areas of the girder and stiffeners were minimized subject to the provisions of the Code of Practice BS 5950: 2000, as well as the Steel Designers’ manual provisions. A typical example in the Steel Designers’ manual was used to test the design models (excel spreadsheet model for GRG and a Delphi program for ABC). The results obtained included curves of optimal pairs of web depth and web thickness, web depth and flange thickness, and flange width and flange thickness. A curve was also obtained which for a given web depth, gives the optimal cross sectional dimensions of the girder and the stiffener. Although the results obtained using the GRG and the ABC algorithms were very close, the GRG algorithm was slightly superior, giving a 7.44% reduction in girder’s cross-sectional area compared to the initial design