Contents lists available at ScienceDirect
Engineering Structures
journal homepage: www.elsevier.com/locate/engstruct
School based optimization algorithm for design of steel frames
Mohammad Farshchin, Mohsen Maniat, Charles V. Camp
⁎
, Shahram Pezeshk
Department of Civil Engineering, University of Memphis, Memphis, TN 38152, United States
ARTICLE INFO
Keywords:
Structural design optimization
School-based optimization algorithm
Steel frames
Discrete optimization
Metaheuristic algorithms
ABSTRACT
In this paper, a school-based optimization (SBO) algorithm is applied to the design of steel frames. The objective
is to minimize total weight of steel frames subjected to both strength and displacement requirements specified by
the American Institute of Steel Construction (AISC) Load Resistance Factor Design (LRFD). SBO is a meta-
heuristic optimization algorithm inspired by the traditional educational process that operates within a multi-
classroom school. SBO is a collaborative optimization strategy, which allows for extensive exploration of the
search space and results in high-quality solutions. To investigate the efficiency of SBO algorithm, several popular
benchmark frame examples are optimized and the designs are compared to other optimization methods in the
literature. Results indicate that SBO can develop superior low-weight frame designs when compared to other
optimization methods and improves computational efficiency in solving discrete variable structural optimization
problems.
1. Introduction
During the last decades, many optimization techniques have been
developed for structural design problems. Among them, metaheuristic
algorithms have been proven quite effective. Genetic algorithms (GA)
[1–3], ant colony optimization (ACO) [4–8], particle swarm optimiza-
tion (PSO) [9–12], harmony search (HS) [13,14], charged system
search (CSS) [15–17], and colliding bodies optimization (CBO) [18–20]
are some of the most popular techniques in structural optimization.
Many optimization algorithms have been developed to solve steel frame
optimization problems: Camp et al. used ACO [21]; Degertekin em-
ployed HS [22]; Kaveh and Talatahari employed imperialist competi-
tive algorithm [23]; Hasancebi and Azad utilized Big Bang–Big Crunch
[24]; Kaveh and Talatahari utilized CSS [25]; Togan used teaching-
learning-based optimization (TLBO) [26] ; Kaveh and Farhoudi pro-
posed dolphin echolocation [27] ; Maheri and Narimani used an en-
hanced HS [28]; Hasançebi and Carbas employed a bat-inspired algo-
rithm [29]; Talatahari et al. utilized an eagle strategy [30]; Carraro
et al. employed a search group algorithm [31]; Afzali et al. proposed
modified honey bee mating optimization [32]; and Kaveh and Ilchi
employed enhanced whale optimization [33].
A common approach in metaheuristic optimization is to randomly
generate an initial population of potential solutions and gradually im-
prove the overall fitness of the population in a systematic process.
Standard metaheuristic optimization algorithms typically allow only
intra-population collaboration; however, a more sophisticated ap-
proach is to utilize sets of independent parallel populations that
collaborate – extending the explorative capabilities of the algorithm
and improving the overall efficiency. An example of this approach is a
two-stage optimization algorithm that employs a series of independent
metaheuristics to explore different regions of the search space (first
stage) and then focus the search on the sub-region with the most pro-
mising solutions (second stage) such as eagle strategy [34] and multi-
class teaching-learning-based optimization (MC-TLBO) [35]. One of the
challenges in the application of two-stage algorithms is the selection
and implementation of the fi
rst stage termination criterion. The ter-
mination
criterion introduces parameters that need to be tuned for a
specific problem which, in result increases the complexity of the algo-
rithm. To overcome this issue, Farshchin et al. [36] introduced a col-
laborative multi-population framework that utilized a TLBO algorithm
and called it school-based optimization (SBO). SBO extends the simple
model of teaching and learning within a classroom modeled by TLBO to
a school of numerous collaborative classrooms where teachers can be
reassigned to other classrooms and thus share knowledge across the
school. Farshchin et al. [36] showed that SBO outperforms basic TLBO
in finding low-weight designs of truss structures with frequency con-
straints in a continuous search space.
In this paper, the effectiveness of SBO in solving discrete optimi-
zation problems is investigated. The objective of these optimization
problems is to minimize total weight of steel frames subjected to both
strength and displacement requirements as specified by the American
Institute of Steel Construction (AISC) Load Resistance Factor Design
(LRFD) [37]. Three often cited benchmark frame structures are de-
signed to provide a comparison between the performance of SBO and
https://doi.org/10.1016/j.engstruct.2018.05.085
Received 14 March 2017; Received in revised form 8 May 2018; Accepted 20 May 2018
⁎
Corresponding author.
E-mail address: cvcamp@memphis.edu (C.V. Camp).
Engineering Structures 171 (2018) 326–335
0141-0296/ © 2018 Elsevier Ltd. All rights reserved.
T
