Pre-tensioned concrete beams optimized with a unified function of objective (UFO) using ANN-based Hong-Lagrange method

Abstract

ABSTRACT The present study simultaneously optimizes the three objective functions of pre-tensioned concrete (PT) beams, such as construction and material cost, beam weights, and beam depth, where multiple objectives optimizations (MOO) conflicting with each other are performed. MOO is performed based on 21 input parameters including tendon parameters and the 21 output parameters. Preassigned input parameters are defined by 16 equalities and design requirements are also implemented during the optimization through 19 code-based inequalities. Finally, the five-step ANN-based algorithms are presented to find optimized design parameters subject to external loads within ranges prescribed by inequalities. A Pareto frontier is presented based on the combinations of weight fractions representing contributions made by the three objective functions. ANN-based optimizations are capable of quantifying tendon ratios and rebar areas when concrete sections crack under service loads while optimizing multi-design targets and objective functions at the same time. The ANN-based optimized designs are verified with a structural mechanics-based software, AutoPT. Reductions of 9.1%, 30.1%, and 10.4% in beam depths, costs, and weights, respectively, obtained based on a Pareto frontier which simultaneously optimizes multi-objective functions are compared with probable designs by human engineers, demonstrating a design efficiency for a pre-tensioned concrete (PT) beam.