The traditional Coati Optimization Algorithm (COA), a metaheuristic algorithm, holds significant value in addressing complex optimization problems. However, it suffers from issues including high-dimensional premature convergence and imbalance between exploration and exploitation. To address these limitations, this study proposes an Improved Chaotic Hybrid Coati Optimization Algorithm (ICHCOA). Initially, the Logistic chaotic mapping is employed to generate the initial population, thereby enhancing the uniformity of solution space distribution. Subsequently, a dynamic differential evolution strategy is designed for the exploration phase, which balances global search intensity through linearly decreasing crossover probability and nonlinear weight adjustment. Furthermore, an adaptive Cauchy perturbation mechanism is introduced, incorporating elite pool-guided exponentially decaying perturbation intensity to strengthen the ability of algorithm to escape local optima. Finally, during the development phase, Lévy flight and opposition-based learning strategies are integrated to improve local search precision. The proposed ICHCOA algorithm is validated against the COA, Whale Optimization Algorithm (WOA), Dung Beetle Optimizer (DBO), Grey Wolf Optimizer (GWO), and Harris Hawks Optimization (HHO) using both the CEC2017 benchmark suite and a practical welded beam design engineering case. Experimental results demonstrate that ICHCOA exhibits significantly superior convergence speed compared to other algorithms in 10-dimensional CEC2017 functions. The welded beam engineering case further confirms that ICHCOA achieves 99.8% improvement in stability compared to COA and WOA, while also outperforming all five comparison algorithms in convergence accuracy.