Simple Algorithms Outsmart Heavyweights in Earthquake-Resistant Roof Design

Engineers have long faced a stubborn dilemma when designing the vast steel space truss roofs that span stadiums, hangars, and industrial halls: the structures must be light enough to be economical, yet strong enough to survive some of the most violent ground motions nature can deliver. A new study published in the Bulletin of Earthquake Engineering by Muhammet Yurdakul of Karadeniz Technical University in Türkiye tackles that dilemma head-on, combining cutting-edge computational optimization with detailed nonlinear seismic simulation. The results suggest that some of the newest and simplest optimization algorithms in the metaheuristic toolbox can match the performance of established methods while cutting the computational bill nearly in half.

The research focuses on the Steel Space Truss Roof Structure, or SSTRS, a three-dimensional lattice of steel members whose individual tube sizes collectively determine both the weight of the roof and its capacity to resist gravity and seismic loads. Because each member can, in principle, be drawn from a catalog of available profiles, the design space is enormous, and searching it exhaustively is impossible. This is where metaheuristic algorithms come in: inspired loosely by natural processes such as learning and evolution, they explore the design space intelligently, iteratively refining candidate solutions until an optimal or near-optimal configuration emerges.

Yurdakul’s framework pits four algorithms against one another. Three belong to the relatively recent Rao family, developed by engineer R. Venkata Rao: the standard Rao-1 and Rao-2, and a self-adaptive variant called SapRao. These algorithms are notable for being metaphor-free, meaning they rely on straightforward mathematical comparisons between the best and worst candidate designs in a population rather than elaborate analogies drawn from animal behavior or physical phenomena. They are benchmarked against the well-established Teaching-Learning-Based Optimization algorithm, or TLBO, which simulates a classroom in which learners improve through interaction with teachers and with one another.

The computational engine behind the study is an integrated SAP2000-MATLAB environment. MATLAB scripts drive the finite element software SAP2000 through its Open Application Programming Interface, automating the otherwise laborious cycle of model updating, structural analysis, and constraint checking. Each candidate design is subjected to multiple load scenarios, including dead load, wind, snow, cladding, and seismic actions, with the sizing rules drawn from codes such as the AISC allowable stress design provisions, the Turkish building earthquake code, and Turkish loading standards. The automation means that thousands of design iterations, each requiring a full structural analysis, can be executed without human intervention.

To assess seismic performance, the study goes well beyond simplified equivalent static methods. Both fixed-base and seismically isolated versions of the truss roof were analyzed using nonlinear time-history analyses under scaled bi-directional ground motions, including the often-neglected vertical components of earthquake shaking. The ground motion suites distinguish between near-fault records, which carry the characteristic velocity pulses and directional effects of shaking close to a rupturing fault, and far-fault records, which lack those intense directivity pulses but can still be demanding in their own way. This distinction matters, because the two classes of motion excite structures differently and can expose different vulnerabilities.

The headline computational finding is striking. The standard Rao-1 algorithm achieved exactly the same minimum structural weights as TLBO across the evaluated fixed-base seismic design suites, yet it did so with a 50.68 percent reduction in total execution time. In a field where a single optimization run can consume hours or days of computing, halving the runtime without sacrificing solution quality is a meaningful advance. It suggests that the elegant simplicity of the Rao formulation, far from being a limitation, may actually be an asset when the underlying structural analyses are themselves computationally expensive.

The seismic findings carry equally important implications for practice. Near-fault ground motions induced locally elevated structural demands in the truss, concentrating forces and displacements in ways that designers of long-span roofs cannot afford to ignore. Perhaps more surprising, far-fault records with large displacement pulses could still produce relatively high response ratios even in the seismically isolated configuration. The result is a caution against the assumption that isolation alone guarantees protection: the character of the ground motion, not merely its proximity to the fault, governs how much demand reaches the superstructure.

That said, the isolation system proved remarkably effective at filtering out severe accelerations. Across all optimization algorithms and all ground motion records, the optimized weight of the isolated structure converged to exactly 47.4 percent of the maximum weight obtained for the fixed-base case. In other words, decoupling the roof from the ground through seismic isolation allowed the members to be sized at less than half the weight required for a conventionally fixed design, a difference that translates directly into material savings, lower fabrication costs, and a reduced carbon footprint for large-span construction.

The study situates itself within a rapidly growing body of work on metaheuristic structural optimization, which spans genetic algorithms, particle swarm methods, and hybrid schemes applied to trusses, domes, and bridges. It also connects to an active literature on optimizing seismic isolation systems, including friction pendulum bearings and other sliding devices, whose nonlinear behavior must be captured realistically in analysis. By bringing these two threads together, optimizing the steel superstructure while simultaneously evaluating a nonlinear isolation system under realistic, bi-directional, multi-component earthquake loading, the research offers one of the more complete pictures to date of how long-span roofs can be designed for seismic regions.

For engineers, the practical message is twofold. First, the choice of optimization algorithm matters less for the quality of the final design than for the cost of finding it, and simple, metaphor-free algorithms like Rao-1 deserve a place in the production toolkit. Second, seismic isolation can deliver dramatic weight savings for space truss roofs, but the design must be verified against both near-fault and far-fault suites, because large displacement pulses in distant records can still push response ratios upward. As computational tools become ever more tightly integrated with design codes, studies of this kind point toward a future in which earthquake-resistant long-span structures are not only safer but substantially lighter and cheaper to build.

Subject of Research: Metaheuristic optimization and seismic response of steel space truss roof structures with base isolation

Article Title: Metaheuristic-based optimization of steel space truss roof structures with seismic isolation

Article References: Yurdakul, M. (2026). Metaheuristic-based optimization of steel space truss roof structures with seismic isolation. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02702-7

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02702-7

Keywords: structural optimization, metaheuristic algorithms, Rao algorithms, TLBO, steel space truss, seismic isolation, near-fault ground motions, far-fault ground motions, nonlinear time-history analysis, SAP2000, MATLAB, earthquake engineering