Complex-Order Gold Rush Optimizer Algorithm

This study proposes an enhanced variant of the gold rush optimizer (GRO) algorithm, termed the complex-order gold rush optimizer (CoGRO) algorithm, to address two inherent theoretical limitations of the original GRO. First, GRO employs a random initialization strategy that lacks ergodicity and uniform coverage, leading to insufficient population diversity and a higher risk of premature convergence. Second, its position update mechanism relies solely on current-time information without incorporating historical search experience, which restricts the algorithm’s ability to model long-term dependencies and escape local optima in complex multimodal landscapes. To overcome these deficiencies, we introduce a chaotic LCS1 initialization to enhance population diversity through improved ergodic coverage, and we embed a complex-order derivative mechanism into the migration and collaboration updates to provide infinite memory capability. A comprehensive sensitivity analysis is conducted to examine the influence of control parameters on CoGRO’s performance, leading to the identification of an optimal parameter configuration. The effectiveness of the proposed algorithm is evaluated using the CEC2022 benchmark suite through ablation studies and comparative analyses with state-of-the-art algorithms. Experimental results on the CEC2022 benchmark suite comprising 12 test functions demonstrate that CoGRO significantly outperforms the original GRO, achieving an average solution accuracy improvement of 0.84% and an average standard deviation reduction of 67.6 across all 12 functions, with particularly notable improvements on hybrid and composition functions. Wilcoxon signed-rank tests confirm the statistical significance of these improvements (p<0.05). These results confirm the feasibility and effectiveness of CoGRO as an improved optimization method for complex engineering problems.