Application of Genetic Algorithm for Optimal Design of Portal
Frame Structures
Onwuka D.O., Njoku F.C., Okorie D., and Ukachukwu O. C.
Department of Civil Engineering, Federal University of Technology Owerri, Imo State Nigeria
Received: 10 November 2025; Accepted: 18 November 2025; Published: 22 November 2025
ABSTRACT
This study developed and applied a MATLAB-based Genetic Algorithm (GA) program for the optimal design
of steel portal frames with the aim of minimising cross-sectional area, weight, and cost. A single-span pitched-
roof frame of 30 m span, 7 m eave height, and 3.5 m overheight was analysed, with variations in frame spacing
from 6 m to 7.5 m, using S275 steel and BS 5950 design provisions. The GA optimisation consistently converged
to efficient solutions, achieving 4–13 % cost savings and up to 10 % weight reduction compared with the
empirical method. Results further showed that the column plastic modulus was approximately 50 % greater than
that of the rafter, rafter depth was about span/55, and purlin depth was roughly one-quarter of the rafter depth.
Although minor variations occurred due to stochastic algorithm behaviour, all runs produced results within the
same performance bounds. The findings confirm the reliability of the developed GA framework as a practical
and computationally efficient tool for designing cost-effective and structurally sound steel portal frames.
Keywords: Genetic algorithm, optimisation, portal frame, steel structures, cost efficiency, MATLAB
INTRODUCTION
Portal frames are among the most widely used structural systems for single-storey industrial, agricultural, and
commercial buildings because they provide large clear spans with relatively low material cost, rapid
construction, and simple detailing. Their efficiency in spanning 20ꢀm–40ꢀm without intermediate supports makes
them essential for warehouses, factories, and retail halls worldwide (Salamaꢀetꢀal.,ꢀ2023). The growing demand
for sustainable, economical, and high-performance building systems has intensified interest in
optimisation-based design strategies that reduce both embodied carbon and overall project cost while satisfying
strength, stability, and serviceability requirements (Salamaꢀetꢀal.,ꢀ2023; Huangꢀetꢀal.,ꢀ2023).
Designing portal frames involves numerous discrete and continuous variables — member sizes, spacing, rafter
pitch, haunch geometry, and connection stiffness — that interact non-linearly through code-based constraints.
Conventional derivative-based or enumerative optimisation methods are often inefficient in such mixed design
spaces: they are prone to local minima and computationally expensive for large search domains (Whitworth
&ꢀTsavdaridis,ꢀ2020). In contrast, population-based metaheuristic algorithms, particularly genetic algorithms
(GAs), have proved highly effective because they do not rely on gradient information and can explore wide,
non-convex feasible regions while accommodating discrete design variables (Grecoꢀetꢀal.,ꢀ2023;
Stulpinasꢀ&ꢀDaniūnas,ꢀ2024).
Recent developments in structural optimisation have demonstrated the capability of GAs and their hybrid
variants to achieve significant reductions in steel weight and cost. Studies integrating multi-objective
formulations (such as NSGA-II or Pareto-based ranking) enable designers to balance conflicting objectives,
including cost, stiffness, and environmental impact (Salamaꢀetꢀal.,ꢀ2023; Whitworth &ꢀTsavdaridis,ꢀ2020). For
instance, Salama etꢀal. (2023) applied an embodied-carbon minimisation strategy to single-story steel portal
frames, reporting reductions of about 14ꢀ%-26ꢀ% relative to prismatic-member configurations. Martins, Correia,
Ljubinković, &ꢀSimõesꢀdaꢀSilva (2023) carried out cost optimisation of steel I-girder cross-sections using GA,
showing substantial material savings. Meanwhile, Stulpinas &ꢀDaniūnas (2024) optimised thin-walled
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