Evaluation Protocol Sensitivity in Frequency-Constrained Truss Optimization: A Comparative Study of Adaptive and Evolutionary Metaheuristics

Metaheuristic algorithm benchmarking in frequency-constrained truss optimization (TPFC) has been shown to be sensitive to evaluation protocols, yet this sensitivity has not been systematically investigated. This study addresses this gap by introducing a dual protocol benchmarking framework to quantify protocol-induced ranking bias across five metaheuristic algorithms, including the Polar Fox Algorithm, NSM-LSHADE-CnEpSin, NSM-LSHADE-SPACMA, NSM-MadDE, and NSM-BO. The algorithms are evaluated on five frequency-constrained truss benchmarks with 10, 37, 52, 72, and 200 bars, under two FE-based protocols with MaxFEs of 10,000 × D and 20,000 × D. Under the standardized protocol, LSHADE variants achieve the highest rankings, while the Polar Fox Algorithm ranks lowest despite demonstrating strong early-stage search efficiency, primarily due to its non-uniform FE allocation. Under the extended protocol, the performance gap of the Polar Fox Algorithm is reduced by 44 to 79 percent, with rankings improving to second and third, while ranking reversals are observed on larger-scale problems. These findings show that algorithmic rankings in TPFC optimization are strongly dependent on evaluation protocols rather than reflecting intrinsic algorithmic quality. Furthermore, fixed FE ceilings are shown to disadvantage adaptive and exploration-intensive algorithms. The proposed dual-protocol framework provides a generalizable basis for protocol-aware benchmarking, revealing the conditions under which FE-based comparisons may systematically favor uniform-allocation methods in constrained structural optimization.