## 1 Introduction  
The swarm intelligence algorithm is an important optimization method. This type of algorithm is highly suitable for problems that are difficult to be solved effectively or even cannot be solved by traditional technology, as establishing an effective formal model, such as NP-hard problems, is difficult to accomplish. The traveling salesman problem (TSP) is one of the most classical NP-hard problems. In TSP, a traveling salesman is expected to identify the shortest path to visit \(n\) cities in a country. Suppose that the traveling salesman arrives at a country with only 21 cities and visits the cities in any order (from one city and moves directly to another city), the size of the search space in this problem can be calculated as \((n-1)!\). This formulation suggests that the TSP with \(n=21\) entails \(2.432902\times 10^{18}\) possible travel searches. If a person takes one second to calculate a single travel, then 770 million years are needed to search the whole search space. If a computer with a 2.0 GHz CPU (i.e., 2 billion instructions per second) is used, then 38 years are required to identify all possible paths. If a city is added to this problem, then the time is increased accordingly to nearly 810 years. However, Reference [1] has shown that the swarm intelligence algorithm is outstanding in solvingthese problems. Consequently, the swarm intelligence algorithm has become widely popular among researchers in recent years. The swarm intelligence algorithm is inspired by the behavior of social creatures such as ants, termites, birds, and fish. The most popular swarm intelligence algorithm at the beginning of algorithm development is particle swarm optimization (PSO). The PSO algorithm [2] was proposed by [PERSON] and [PERSON], and it was inspired by the social behavior of birds. With the popularization and development of the swarm intelligence concept, a variety of swarm intelligence algorithms have been proposed in succession, namely, ant colony optimization (ACO) [3], bat algorithm (BA) [4], dragonfly optimization [5], grasshopper optimization algorithm (GOA) [6], moth flame optimization algorithm (MFOA) [7], gray wolf optimization (GWO) [8], and whale optimization algorithm (WOA) [9], all of which have been widely used in recent years. Nature is the infinite source of inspiration in computational science, and more swarm intelligence algorithms are expected in the future. Swarm intelligence algorithms have been widely applied to various practical engineering issues in recent years. Whale optimization algorithm, which was proposed in 2016, has been cited more than 1600 times as of April 2020 based on Google Scholar indicators and has been widely used in different fields such as energy [10; 11], computer networks [12; 13], cloud computing [14], image processing and machine vision [15; 16], electronics and electrical engineering [17; 18], antenna design [19], feature selection [20; 21; 22], aerospace [23], path planning [24], and structural optimization [25; 26]. Moreover, GOA has been successfully applied to the trajectory optimization of multiple solar-powered UAVs [27], short-term load forecasting [28], electrical characterization of proton exchange membrane fuel cell stacks [29], data clustering [30], scheduling of thermal system [31], analyzing vibration signals from rotating machinery [32], short-term wind electric power forecasting [33], optional distribution system reconfiguration and distributed generation placement [34], classification for biomedical purpose [35], design of linear antenna arrays [36], automatic seizure detection of EEG signals [37], designing automatic voltage regulator systems [38], training neural network [39], and other issues. The multiverse optimizer (MVO) algorithm has also been widely used in different fields. In References [40; 41], MVOs were used to train multilayer perceptron neural networks. [PERSON] [42] combined the MVO and the artificial neutral network to develop an intrusion detection system.