Constellation optimization using an evolutionary algorithm with a variable-length chromosome

This work presents a new evolutionary algorithm that searches over the space of satellite constellations to optimize coverage-related metrics (e.g. minimizing average revisit time or maximizing daily visibility time) while simultaneously minimizing the number of satellites and their semi-major axes. It utilizes a variable-length chromosome to represent a satellite constellation, two specialized operators to handle the variable-length chromosomes, and an adaptive operator selector that adjusts the search strategy during the optimization. The proposed chromosome encodes an m satellite constellation with m n-tuples, where each satellite is defined by an n-tuple (e.g. a subset of the orbital elements). Currently, evolutionary algorithms that optimize constellations employ a fixed-length chromosome where either 1) the maximum number of satellites in the constellation is pre-specified and each satellite has an extra Boolean variable that dictates whether to manifest the satellite in the constellation or 2) the algorithm is run several times, each time exploring constellations with a specific number of satellites. The chromosome representation in the former method has low-locality and is redundant, both of which makes the search more difficult for an evolutionary algorithm. The latter method does not take advantage of good partial solutions or schemata discovered for a constellation of a given size that could inform the design of another constellation with a different number of satellites. In contrast, a variable-length chromosome grows and contracts as the algorithm explores constellations with different numbers of satellites and significantly reduces the redundancy in the chromosome representation. The efficacy and efficiency of an optimization run using the proposed variable-length chromosome representation is benchmarked against a fixed-length chromosome on a multiobjective constellation design problem whose goal is to simultaneously minimize the global average revisit time, the number of satellites in the constellation, and the average semi-major axis of the satellites. Results show that the search conducted with the variable-length chromosome reaches a high-quality solution set using thousands of fewer function evaluations than a search with a fixed-length chromosome.