۱- Introduction

۲- Optimization problem formulation

۳- Nonlinear inelastic analysis of steel frames

۴- Improved DE algorithm

۵- Proposed optimization procedure of steel frames using nonlinear inelastic analysis

۶- Numerical examples

۷- Conclusion

References

Abstract

In this article, an efficient methodology is developed to optimize nonlinear steel frames under several load combinations. For that purpose, inelastic advanced analyses of steel frames are performed using plastic hinge beam–column elements to reduce computational efforts. An improved differential evolution (DE) algorithm is utilized as a global optimizer to refine the solution accuracy and enhance the convergence speed. Compared to the conventional DE algorithm, this newly developed method provides four major improvements such as: (1) a new mutation strategy based on the p-best method; (2) the multi-comparison technique (MCT) to decrease the number of unnecessary objective function evaluations; (3) a promising individual method (PIM) to choose trial individuals; and (4) a trial matrix containing all evaluated individuals to avoid objective function evaluations of duplicate individuals. Furthermore, panel zones are taken account of optimum design for the first time. Doubler plates are designed to prevent panel-zone shear deformations. Three mid- to large-size steel frames considering several load combinations required by AISC-LRFD are considered. Five new and efficient meta-heuristic algorithms are employed for comparison.

Introduction

Optimal solutions have been prioritized in design of steel frames since they save resources, money, materials, and time, while the structural performance is still guaranteed. Normally, design optimization of a steel frame is to minimize the total cost or weight of the structure subjected to various complex constraints including constructability, serviceability, and strength conditions and discrete design variables of the beam and column cross-sections (e.g., the W-shaped section list in AISC-LRFD [1]). Owing to these issues, design optimization of steel frames is highly nonlinear and multimodal. Finding optimal or even sub-optimal solutions is hence difficult. Normally, sufficiently good solutions, that are close to being optimal but not the “real” optimums, are acceptable. In light of this, meta-heuristic algorithms, which are also known as non-gradient-based ones, are preferable to gradient-based ones [2]. Indeed, these approaches use stochastic searching techniques to randomly choose potential solutions in a given search space, hence they are completely free from sensitivity analyses regarding derivatives of the objective function and constraints with respect to each of all design variable. Moreover, they require less mathematical knowledge. As a result, these methods are easy to implement and effective in finding global optimal solutions for optimization problems with highly nonlinear and non-convex properties. Nonetheless, since an optimum solution must be searched over the whole design domain without any directional information as that of derivative algorithms, their computational cost is often time-consuming and relatively expensive. Many improvements have been therefore proposed to deal with these shortcomings. The results of recent studies have confirmed that meta-heuristic algorithms work well for various structural optimization problems, including the sizing and topology optimization of truss structures [3–۶], optimization of rigid and semirigid steel frames [7–۱۱], reliability-based design optimization of structures [12–۱۵], and optimization of steel frames under seismic loading [16–۲۳]. In addition, many meta-heuristic algorithms have been developed, such as the harmony search (HS) [24], firefly algorithm (FA) [25], enhanced colliding bodies optimization (ECBO) [26], differential evolution (DE) [27], and big bang–big crunch (BB–BC) [28]. The reviews of several metaheuristic algorithms can be found in Refs. [29, 30].