## 1 Introduction  
A wireless sensor network (WSN) is composed of hundreds or thousands of tiny sensors with sensing and communication capabilities [1]. These sensors can monitor and detect aspects of their surrounding environment, and such data can be transmitted and communicated to other sensors or base stations, enabling coordination for the completion of specific tasks. WSNs are used extensively in numerous fields, including environmental monitoring, military operations, medicine, smart homes, animal conservation, and poaching prevention. In object tracking, a key application of WSNs--and the focus of this study--a group of sensors is deployed in a predetermined area to monitor the position, speed, and trajectory of objects (among other related characteristics). This collected information is then delivered to related base stations within a specified period of time for further application. Unlike global positioning systems, WSNs can leverage various sensing technologies (e.g., ultrasonic, infrared, electromagnetic, and laser sensors) to locate objects quickly and accurately [2]. Furthermore, sensors can identify an object and monitor its status. Because WSNs are compact, using them to achieve sufficient computing power and communication range is difficult. Energy consumption is the most critical constraint. WSNs can fail to connect if many sensors are depleted of energy. To achieve the requisite coverage in such circumstances, mobile sensors may need to be moved to suitable positions. Mobile sensors have become smaller and cheaper with advances in technology. For example, in [3], the researchers introduced a mobile sensor called Robomote. Occupying less than 0.000047 m\({}^{3}\) of space and costing less than $150, it was developed to explore problems in large-scale sensor networks. Although small and inexpensive, mobile sensors consume energy, and a mobile sensor consumes the most energy when it moves. The amount of energy consumed by a mobile sensor is usually related to the distance the sensor travels. Therefore, reducing the moving distance is a critical challenge for reducing energy consumption. In this study, we addressed the moving object coverage problem in a WSN by using a limited number of mobile sensors. This problem occurs when the full tracking of an object traveling on a predetermined trajectory in a specified area is required, but because of the insufficient number and limited sensing range of mobile wireless sensors, the object trajectory cannot be entirely covered by the deployed sensors. Thus, the mobile sensors must move from one position on the trajectory to another to achieve complete coverage. To conserve energy, a mobile sensor movement repertoire that minimizes the total traveled distance must be determined. Furthermore, to prolong the network lifetime, the remaining power of each mobile sensor must also be as balanced as possible. The complexity of the problem has grown due to the multiple objectives that must be achieved. In attempting to solve such a complex problem, traditional heuristic algorithms often can only obtain an approximate solution close to the optimal solution, and should only be used to solve smaller problems. In solving larger and more complex problems, the solution precision of traditional heuristic algorithms is poor and meta-heuristic algorithms should be used instead because of their strong global search performance. In a preliminary work [4], we addressed the key design aspect of using a genetic algorithm (GA) to identify optimal or near-optimal solutions to the moving object coverage problem with a small problem size. In this paper, we extend our previous work by mathematically formulating the moving object coverage problem and proposing two meta-heuristic nondeterministic algorithms, namely a GA and a discrete particle swarm optimization algorithm (DPSO), to solve the moving object coverage problem. The proposed algorithms can obtain more accurate solutions than can be obtained using traditional heuristic algorithms.