## 1 Introduction  
A wireless sensor network (WSN) comprises many tiny sensors that can both acquire data and communicate. These sensors can monitor their environment and transmit the acquired data to other sensors or base stations to coordinate specific tasks [1]. WSNs are widely used in many fields, such as smart homes, military operations, environmental monitoring, animal conservation, medicine, and poaching prevention. Most studies have assumed that sensors are omnidirectional; however, this assumption may not hold for other types of sensors with directional sensing ranges, such as video, ultrasonic, or infrared [2]. Such sensors are called \"directional sensors\". The sensing range of an omnidirectional sensor node is a circular disk, whereas that of a directional sensor is a smaller, sector-like sensing area determined by its sensing angle. Research results for omnidirectional sensor networks cannot be directly applied to directional sensor networks (DSNs), which comprise numerous directional sensors. Many challenges specific to DSNs still require investigation. Several methods of amplifying the sensing capabilities of sensor nodes have been proposed. One involves placing several of the same type of directional sensors on one sensor node, with each sensor facing a different direction. In [3], four pairs of ultrasonic sensors on a single node were used for omnidirectional detection of ultrasonic signals. Another technique is placing the sensor node on a mobile device to enable it to move and change direction. Third, sensor nodes can be equipped with devices that enable them to switch directions or to rotate. This third technique was adopted in the DSN investigated in this study. A key challenge in DSN coverage is gathering data from a predetermined area. Coverage problems can be categorized as area coverage or target coverage problems. In area coverage, the purpose is to monitor a predetermined region; that of target coverage is to determine a set of sensors that can provide coverage for a set of targets [2]. Another challenge in DSNs is energy-consumption management; reducing energy usage can extend the network lifetime because sensor nodes are typically battery powered and, thus, can only continuously operate for a limited period of time [4]. In this study, we focused the target coverage problem for a DSN with a set of directional sensors that can rotate to any direction. Specifically, the full coverage of a set of targets in a predetermined region is required, but the limited sensing range of directional sensors prevents the targets from being entirely covered by the deployed sensors. Thus, rotating the directional sensors may be necessary to cover as many targets as possible. To increase the network lifetime, a scheduling technique in which some sensor nodes were active and others were inactivated was used to reduce energy use while maximizing the target coverage. This problem has increased complexity because of its multiple objectives. For such complex problems, the exact solution can be obtained by exhausting a lot of computational effort which increases exponentially with the problem size. The solutions obtained by traditional heuristic algorithms are only near to the optimal; thus, these algorithms should only be used to solve smaller or simple problems. As the problem size increases, the metaheuristic algorithms can be used to improve the solutions because of their high performance in a global search. Many metaheuristic algorithms, such as genetic algorithm (GA) [5; 6; 7], particle swarm optimization (PSO) [8], differential evolution (DE) [9], simulated annealing (SA) [10; 11], and ant-colony optimization (ACO) [12; 13], have been introduced for solving complex optimization problems that cannot be solved using traditional deterministic algorithms in the last two decades and some of them may lead to real improvement in optimization algorithms [14; 15]. However, they will easily fall into the local optimal and the cost of computation iteration will increase explosively when the problem scale increases.