Influence maximization (IM) is a key problem in social network analysis, which has attracted attention of many scholars due to the wide range of applications, the variety of IM algorithms have been proposed from different perspectives. In this paper, we review IM algorithms from the perspective of meta-heuristic optimization, proposed a two-layer structure taxonomy to organize almost all the meta-heuristic IM algorithms. The initial layer, predicated upon the delineation of problem construction models, stratifies IM algorithms into two categories: single-objective and multi-objective IM algorithms. Subsequently, the secondary layer discerns between evolution-based and population intelligence-based IM algorithms, delineating them according to the underlying conceptual frameworks, a detailed exposition and analysis ensue. Subsequent scrutiny involves an exhaustive evaluation of the merits and demerits inherent in each IM algorithm, juxtaposing considerations such as time complexity and experimental validation methodologies. Furthermore, we distill myriad strategies aimed at enhancing accuracy and mitigating time complexity across the four phases of the algorithmic process. Finally, based on the above analysis, the challenges and future directions of IM problems are outlined from the perspective of algorithms, applications and models.