To address the shortcomings of the basic Gray Wolf Optimization (GWO) algorithm in solving complex problems, such as relying on the initial population, converging too early, and easily falling into local optimality, a chaotic reverse learning initialization strategy, a nonlinear control parameter convergence strategy, and a dynamic position update strategy are introduced to develop a multi-strategy fusion Improved Gray Wolf Optimization (IGWO) algorithm, and this method is used to solve function optimization problems. First, a chaotic backward learning initialization strategy, based on logistic mapping and backward learning, is adopted to improve the random initialization of the GWO algorithm and enhance the traversal and diversity of the initial population. Second, a nonlinear control parameter for local perturbation is constructed to avoid the problem of premature convergence of the GWO algorithm due to linear convergence and to balance the exploration and exploitation ability of the GWO algorithm. Finally, a location guidance strategy based on dynamic weights and individual memory is proposed to effectively improve the algorithm’s optimization accuracy and computational efficiency; meanwhile, the Gaussian-Cauchy mutation strategy of superior selection is introduced to optimize the location update of optimal individual $\alpha $ wolves and improve the ability of the population to jump out of local extremes. Simulation experiments are conducted for 11 classical test functions, and the results show that the proposed improved algorithm IGWO for gray wolves is superior to 10 other standard swarm intelligence optimization algorithms and 4 other improved optimization algorithms in terms of solution accuracy, convergence speed, and algorithm stability. It provides a new optimization algorithm for solving complex optimization problems.