# A Quantum-Based Beetle Swarm Optimization Algorithm for Numerical Optimization
## 1 Introduction  
Population-based intelligence algorithms have been widely used in many fields because of their simple principle, easy implementation, strong scalability, and high optimization efficiency, such as in UAV path planning [1; 2; 3], combinatorial optimization [4; 5], and community detection [6; 7]. With the increase in the speed of intelligent computing and the development of artificial intelligence, many excellent intelligent algorithms have been proposed such as the seagull optimization algorithm (SOA) [8], artificial bee colony (ABC) algorithm [9], and gray wolf optimization (GWO) algorithm [10]. In addition, there are several intelligent algorithms that were proposed earlier and developed relatively well, such as the particle swarm optimization (PSO) algorithm [11], genetic algorithm (GA) [12], ant colony optimization (ACO) algorithm [13], starling murmuration optimizer (SWO) [14] algorithm, and simulated annealing (SA) algorithm [15]. In 2017, the BAS algorithm was proposed by [PERSON] [16]. The largest difference between the BAS algorithm and other intelligent algorithms is that the BAS algorithm only needs one beetle to search. Due to the advantages of having a simple principle, fewer parameters, and less calculation, it has been successfully applied to the following optimization fields. [PERSON] et al., proposed an enhanced BAS with zeroing neural networks for solving constrained optimization problems online [17]. [PERSON] et al., solved the shortcomings of the low positioning accuracy of sensors in Internet of Things applications using the BAS algorithm [18]. [PERSON] et al., optimized the trajectory of a five-link biped robot based on the longhorn BAS algorithm [19]. [PERSON] et al., implemented a dynamic attitude configuration ofa wearable wireless body sensor network through a BAS strategy [20]. [PERSON] et al., proposed a strategy based on the BAS algorithm to search for the optimal control parameters of a complex nonlinear system [21]. Although the BAS algorithm exhibits its unique advantages in terms of the calculation amount and principle, the BAS algorithm drastically reduces the optimization performance and even fails to search with high probability when dealing with multidimensional (more than three-dimensional) problems. The reason is that the BAS algorithm is a single search algorithm and, during the search process, the individual can only move towards one extreme point. In multidimensional problems, there is often more than one extreme point, so it is likely to fall into a local extreme point. On the other hand, the step size during the exploration of the beetle decreases exponentially, which means that the beetles may not be able to jump out of local optima. For these reasons, the BAS algorithm is not equipped to handle complex problems with three or more dimensions. In order to solve the BAS algorithm's defect of not being able to handle high-dimensional problems, a quantum-based beetle swarm optimization algorithm inspired by quantum evolution is proposed in this paper [22]. On the one hand, quantum bits were used to represent the current best solution as a linear superposition of the probability states of \"0\" and \"1\" to improve the early exploration capability of the QBSO algorithm. On the other hand, replacing the individual search with a swarm search and a dynamic step adjustment strategy was introduced to improve the exploitation capability of the beetles. Our work has two main contributions:  
* We solved the shortcoming of the BAS algorithm in that it cannot handle high-dimensional optimization problems, and the designed QBSO algorithm has an excellent performance in solving 30-dimensional CEC benchmark functions. * We used quantum representation to deal well with the balance between the population size in terms of the exploratory power and the algorithmic speed, using fewer individuals to represent more information about the population. The structure of this article is as follows.