## 1 Introduction
### Background
Thanks to these paths, all of the nodes in the WSNs use their energy in a balanced manner and, as a result, the sensor network is able to function for a longer period of time [22; 23]. In all of these clustering, routing, and mobility issues, the energy efficiency [24] measures for the WSNs and optimization methods that are more successful in the current WSNs implementations and that may create less fault operations have become the focus of attention of researchers [25]. Optimization methods include functional processes that are inspired by computational intelligence and metaheuristic methods. In most engineering problems for science, different techniques and protocols are developed in different fields, such as fuzzy logic, genetic algorithm, and artificial neural networks. The fact that these methods can be adapted, especially in WSNs, clearly shows that novel trends have been introduced in terms of optimization. In the field of computer science, different engineering problems and intelligent optimization methods that are based on the concept defined as biological or nature inspired take an important place [8]. In the way of some of the insects or other animals having behaviors, such as moving, searching for food, and interaction with each other based on behavior, such as swarm intelligence; optimization techniques, such as machine automation fault detection, balancing, finding optimal solution, decision making, effective alteration, and comparison with different methods are designed [26]. In WSNs, swarm intelligence and optimization [27] are sub-branches of artificial intelligence techniques that mathematically formulate the behaviors of colonial living animals, such as ants [28], bees, fish, and birds [29; 30]. With the structuring of these methods and with metaheuristic approach, innovative solutions are brought to the real world. Computer science researchers, therefore, simulate the characters of such animals in the form of swarms to learn the behavior of such animals and find solutions to complex problems [25]. For this purpose, simulations are performed in the same way as ant colony and particle swarm optimization, according to behaviors of insects, such as ants, bees, fireflies [31], or spiders or animals, such as fish, starfish, cat, kangaroo, chicken, elephant, whale, etc [32]. In addition, many researchers propose natural-oriented metaheuristic methods, such as the artificial immune system that was derived from the biological system and functions of humans, digital hormonal system, and bacterial nutrition and foraging optimization [33]. These methods sometimes shed light on NP-hard problems, such as clustering and routing, and sometimes on node distribution in the sensor network [34]. WSN development methods [35], such as improving network performance, discarding faulty nodes from the network, reducing energy consumption, or using an optimal number of nodes, can cope with this type of intelligence and nature-inspired optimization approaches [8; 26]. Although researchers have developed many clustering, routing, and optimization algorithms, there are still many shortcomings in the mobile WSNs in terms of node allocation, data collection, CH selection, or finding the shortest trajectory length. In existing studies, homogeneous nodes and networks are generally used. However, in the practice of real life, the existence of heterogeneous structures is undeniable. In most studies, CHs that are selected in the first round collect data. However, the CH set to be selected for all rounds and the detection of the location of each CH will facilitate the function of the mobile sink node. In addition, it will be more reasonable to construct paths that occur when MS travels CHs in the shortest manner or by minimizing energy flow and traffic. The optimal complexity of messages that are announced by CHs may be an indication of the designed routing mechanism.