효율적인 최적화 문제 해법을 GIS와 연계하면 입지 선정 문제에서 공간적 재현의 중요성에 관한 통찰력을 제공할 수 있다. 특히 발견적 해법 중 라그란지안 완화법에 기반한 해법은 메타휴리스틱에 비해 이론적으로 정교하며 결과해의 품질이 보장된다. 본 연구는 최소의 시설물로 전체 수요를 커버할 수 있도록 시설물 입지를 최적화하는 LSCP 문제에 초점을 두었다. 구체적으로 LSCP 문제 구조 및 특성 분석을 통해 문제의 효율적 해결을 위한 라그란지안 기법을 개발하고 이를 GIS 환경에 구현, 실세계 자료에 대해 입지선정 분석을 수행하였다. 실험을 통해 개발된 알고리즘은 고품질의 결과를 효율적으로 제공한다는 점을 확인하였다.

In this study, we describe an analytical process for designing a low Earth orbit constellation for discontinuous regional coverage, to be used for a surveillance and reconnaissance space mission. The objective of this study was to configure a satellite constellation that targeted multiple areas near the Korean Peninsula. The constellation design forms part of a discontinuous regional coverage problem with a minimum revisit time. We first introduced an optimal inclination search algorithm to calculate the orbital inclination that maximizes the geometrical coverage of single or multiple ground targets. The common ground track (CGT) constellation pattern with a repeating period of one nodal day was then used to construct the rest of the orbital elements of the constellation. Combining these results, we present an analytical design process that users can directly apply to their own situation. For Seoul, for example, 39.0° was determined as the optimal orbital inclination, and the maximum and average revisit times were 58.1 min and 27.9 min for a 20-satellite constellation, and 42.5 min and 19.7 min for a 30-satellite CGT constellation, respectively. This study also compares the revisit times of the proposed method with those of a traditional Walker-Delta constellation under three inclination conditions: optimal inclination, restricted inclination by launch trajectories from the Korean Peninsula, and inclination for the sun-synchronous orbit. A comparison showed that the CGT constellation had the shortest revisit times with a non-optimal inclination condition. The results of this analysis can serve as a reference for determining the appropriate constellation pattern for a given inclination condition.