## 1 Introduction
In Reference [43], the MVO was used to optimize the parameters of support vector machines. [PERSON] [44] solved the clustering problem by using the search ability of the MVO. Thus far, the studies conducted indicate that swarm intelligence algorithms can effectively solve many practical optimization problems. The no free lunch (NFL) theorem [45] has proven logically that swarm intelligence algorithms cannot be regarded the most suitable solution for all optimization problems. In other words, the specific swarm intelligence algorithm may perform effectively in one group of problems but not for another group of problems. In the case of GWO, the original version of GWO can solve problems by using continuous variables. On this basis, the algorithm can be modified to solve binary or discrete problems. [PERSON] [46] proposed the combination of the evolutionary operator with GWO to solve binary problems. A similar evolutionary operator was used in the literature [47]. [PERSON] [48] combined the crossover and mutation operators with GWO to solve economic scheduling problems. Additionally, the binary version of GWO inspired by quantum mechanics was also proposed in the literature [49]. Moreover, [PERSON] [50] designed an initialization method based on the greedy idea and mutation and position update strategies by combining the dynamic weighted average with the static average to solve path planning problems, including the lack of GWO development ability and inflexible position update strategy. In terms of combining the advantages of different algorithms, the method that mixes multiple algorithms to improve performance has also been widely used. [PERSON] [51] proposed the hybrid GWO and PSO optimization algorithm to improve convergence speed and the ability to determine global optimal values. [PERSON] [52] adopted a hybrid algorithm based on the ACO and GWO to optimize assembly sequence planning. [PERSON] [53] proposed a hybrid GWO and BA method to solve global function optimization problems. [PERSON] [54] proposed a hybrid GWO and flower pollination algorithm to improve algorithm performance. The other combination optimization methods include GWO and DE [55], GWO and SCA [56], GWO and BBO [57], WOA and PSO [58], and WOA and BO [59]. The NFL theorem allows the research in the field of swarm intelligence to be extremely active, which is one of the important reasons why a large number of scholars have committed to improve the current algorithm and propose new swarm intelligence algorithms. No existing algorithm in the reviewed literature simulates the behavior of anas platyrhynchos, hence, our attempt to model the behavior of this animal and design a new swarm intelligence algorithm based on the model. Inspired by the swarm behavior of anas platyrhynchos, this study proposes a novel swarm intelligence algorithm referred as the anas platyrhynchos optimizer (APO). In general, researchers pursue a lot of performance in order to improve performance. Although the performance is improved, the introduction of additional parameters not only complicates the algorithm, but also masks the core mechanism of the swarm intelligence algorithm to a certain extent. In this study, starting from the core of the cluster intelligence algorithm, we designed the APO algorithm period to have not only better performance but also as few parameters as possible. The performance of the algorithm was tested on 23 classical benchmark functions and compared with PSO, DE, WOA, and GWO, to verify the effectiveness of APO algorithm. To further verify the performance of the algorithm in practical engineering applications, APO was used to solve the cooperative path planning problem of multi-UAVs, and the results were compared with GWO, IGWO, HGWO, PSO, and DE algorithms. The main contributions of this paper are to propose a new SI technique with inspiration from the behavior of anas platyrhynchos. A new swarm intelligence algorithm is proposed, and its performance was verified in this paper.