  In this paper, an ensemble metaheuristic algorithm (denoted as LX-BBSCA) is
introduced. It combines the strengths of Laplacian Biogeography-Based
Optimization (LX-BBO) and the Sine Cosine Algorithm (SCA) to address structural
engineering design optimization problems. Our primary objective is to mitigate
the risk of getting stuck in local minima and accelerate the algorithm's
convergence rate. We evaluate the proposed LX-BBSCA algorithm on a set of 23
benchmark functions, including both unimodal and multimodal problems of varying
complexity and dimensions. Additionally, we apply LX-BBSCA to tackle five
real-world structural engineering design problems, comparing the results with
those obtained using other metaheuristics in terms of objective function values
and convergence behavior. To ensure the statistical validity of our findings,
we employ rigorous tests such as the t-test and the Wilcoxon rank test. The
experimental outcomes consistently demonstrate that the ensemble LX-BBSCA
algorithm outperforms not only the basic versions of BBO, SCA, and LX-BBO but
also other state-of-the-art metaheuristic algorithms.
