In the satellite operation phase, a ground station should continuously monitor the status of the satellite and sends out a tasking order, and a satellite should transmit data acquired in the space to the Earth. Therefore, the communication between the satellites and the ground stations is essential. However, a satellite and a ground station located in a specific region on Earth can be connected for a limited time because the satellite is continuously orbiting the Earth, and the communication between satellites and ground stations is only possible on a one-to-one basis. That is, one satellite can not communicate with plural ground stations, and one ground station can communicate with plural satellites concurrently. For such reasons, the efficiency of the communication schedule directly affects the utilization of the satellites. Thus, in this research, considering aforementioned unique situations of spacial communication, the mixed integer programming (MIP) model for the optimal communication planning between multiple satellites and multiple ground stations (MS-MG) is proposed. Furthermore, some numerical experiments are performed to verify and validate the mathematical model. The practical example for them is constructed based on the information of existing satellites and ground stations. The communicable time slots between them were obtained by STK (System Tool Kit), which is a well known professional software for space flight simulation. In the MIP model for the MS-MG problems, the objective function is also considered the minimization of communication cost, and ILOG CPLEX software searches the optimal schedule. Furthermore, it is confirmed that this study can be applied to the location selection of the ground stations.

We consider a satellite mission scheduling problem, which is a promising problem in recent satellite industry. This problem has various considerations such as customer importance, due date, limited capacity of energy and memory, distance of the location of each mission, etc. Also we consider the objective of each satellite such as general purpose satellite, strategic mission and commercial satellite. And this problem can be modelled as a general knapsack problem, which is famous NP-hard problem, if the objective is defined as to maximize the total mission score performed. To solve this kind of problem, heuristic algorithm such as taboo and genetic algorithm are applied and their performance are acceptable in some extent. To propose more efficient algorithm than previous research, we applied a particle swarm optimization algorithm, which is the most promising method in optimization problem recently in this research. Owing to limitation of current study in obtaining real information and several assumptions, we generated 200 satellite missions with required information for each mission. Based on generated information, we compared the results by our approach algorithm with those of CPLEX. This comparison shows that our proposed approach give us almost accurate results as just less than 3% error rate, and computation time is just a little to be applied to real problem. Also this algorithm has enough scalability by innate characteristic of PSO. We also applied it to mission scheduling problem of various class of satellite. The results are quite reasonable enough to conclude that our proposed algorithm may work in satellite mission scheduling problem.

위상 최적화 문제는 다양한 밀도 분포를 가지는 설계영역에서 목적함수와 요소단위의 설계 민감도의 반복적인 계산을 요구한다. 최근 제안된 2단계 축소기법은 축소 시스템을 구축하는데 매우 효과적이며 고유치 문제와 동적 문제의 해석에 정확도와 효율성을 동시에 제공한다. 본 논문에서는 구조 위상 최적화 문제에서 해석 부분과 민감도 계산 부분에 2단계 동적 축소기법을 사용한다. 축소시스템에 대한 위상 최적화 결과는 축소되지 않은 전체 시스템에 대한 최적화 결과와 비교하여도 공학적으로 요구되는 정확도 범위 내에서 2단계 축소기법이 높은 정확도와 계산 효율을 보장하는 것을 보여준다.