Multi-algorithm optimization and dimensional assessment of steel castellated beams with sinusoidal web openings subjected to static loads

Abstract

Sinusoidal castellated beams are increasingly applied in modern steel structures due to their enhanced stiffness-to-weight ratio, yet their optimal design remains largely unexplored. This study introduces a novel multi-algorithmic optimization framework for the design of sinusoidal castellated steel beams, a topic that has received limited attention in the literature. Spanning five different beam lengths (300–700 cm), the approach integrates five metaheuristic algorithms Cyclical Parthenogenesis Algorithm CPA, Improved Ray Optimization IRO, Tug of War Optimization Algorithm TWO, Vibrating Particles System Algorithm VPS, and Imperialist Competitive Algorithm ICA to optimize and assess structural designs based on four key criteria: construction cost, processing time, dimensional consistency, and solution stability. Among the tested methods, CPA and TWO consistently delivered the most cost-efficient and dimensionally robust solutions, while VPS yielded the most economical results, particularly for 700 cm length. Dimensional optimization focused on four core section variables, allowing the identification of algorithm-specific behaviors under sinusoidal web constraints. Moreover, the dimensional assessment did not only optimize the four section variables but also revealed each algorithm’s perspective in selecting the most appropriate dimension under design constraints, aligned with potential failure modes an aspect not previously addressed in castellated beam studies. In addition, convergence trend and sensitivity analyses revealed span length to be the dominant factor influencing optimization outcomes. This research offers the first comprehensive evaluation of sinusoidal castellated beam design using a multi-criteria optimization strategy, providing actionable insights for structural engineers seeking efficient and stable design configurations.