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Aiming at the defects of the Aquila optimizer (AO) in dealing with some complex optimization problems, such as slow convergence speed, low convergence accuracy, and easy to fall into local optimum, in this paper, a hybrid Aquila optimizer (HAO) algorithm based on Gauss map and crisscross operator is proposed. First, Gauss map is introduced to initialize the Aquila population to improve the quality of the initial population. Then use the crisscross operator to promote the exchange of information within the population and maintain the diversity of the population in each iteration, which not only enhances the ability of the algorithm to jump out of the local optimum but also accelerates the global convergence of the algorithm. The results of experiments using 21 classical benchmark functions indicate that HAO has better global search ability, faster convergence speed, and better stability than AO. The overall optimization performance of HAO in different dimensions is better than particle swarm optimization (PSO) algorithm, gray wolf optimization (GWO) algorithm, whale optimization algorithm (WOA), and crisscross optimization (CSO) algorithm. Finally, the results of K -means clustering optimization on six University of California (UCI) standard data sets demonstrate that HAO has significant advantages over three algorithms that are good at clustering optimization. [ABSTRACT FROM AUTHOR]