Nowadays, many people illegally migrate to other countries by sea because of warfare or internal conflict in their countries, and thousands of people lose their lives for this reason. Besides, illegal trafficking of drugs or historical artifacts, illegal fishing, and various terrorist activities are conducted through the seas. Maritime surveillance operations are of great importance to prevent all these threats and maintain national security. In this study, the problem of surveillance and exploration which is performed by helicopters on the seas is discussed. A solution approach based on simulated annealing is proposed for the solution of the problem and the proposed algorithm has been tested on various scenarios. This methodology, at least to our knowledge, is used for the first time in the Moving Target Traveling Salesman Problem-Time Window. The proposed solution approach was tested on 50 different scenarios where the target number ranged from 20 to 100. As a result, in all of these scenarios, it has been determined that all of the targets have been destroyed with minimum operation time within the acceptable solution period. Thanks to this method, it is aimed at intervening quickly to illegal activities on the seas and contributing to the prevention of deaths due to refugee boats.