Target searching is one of the challenging research areas in defense. Different types of sensor networks are deployed for searching targets in critical zones. The selection of optimal strategies for the sensor nodes under certain constraints is the key issue in target searching problem. This paper addresses a number of target searching problems related to various defense scenarios and introduces new strategic approaches to facilitate the search operation for the mobile sensors in a two-dimensional bounded space. The paper classifies the target searching problems into two categories: preference-based and traversal distance based. In the preference based problems, the strategies for the mobile sensors are determined by Stable Marriage Problem, College Admission Problem, and voting system; they are analyzed with suitable examples. Alternatively, traversal distance based problems are solved by our proposed graph searching approaches and analyzed with randomly chosen examples. Results obtained from the examples signify that our proposed models can be applied in defense-related target searching problems.