In response to the shortcomings of the current Harris hawks algorithm in terms of convergence, local development ability, and global search ability, this paper proposes an improved Harris hawks algorithm (PREHHO) to address the aforementioned issues. In the population initialization stage, the algorithm uses a piecewise mapping function to make the population distribution more uniform; in the exploration stage, use elite selection strategy to increase the convergence speed of the algorithm; during the exploration phase, PREHHO uses a restart strategy to jump out of local optima. In order to verify the effectiveness of the new algorithm in solving problems, this paper tested it using the CEC2017 function set and compared it with five swarm intelligence optimization algorithms in the 10D, 30D, and 50D dimensions. The experimental results showed that the PREHHO algorithm proposed in this paper has strong optimization ability compared to other intelligent optimization algorithms.