FINDING SYMMETRIC HALO ORBITS FRAMED AS A GLOBAL OPTIMIZATION PROBLEM USING MONOTONIC BASIN HOPPING

In this work we use the stochastic optimization algorithm Monotonic Basin Hopping to find symmetric halo orbits of a prescribed amplitude in the Sun-Earth and Earth-Moon systems through posing the search as an optimization problem. By minimizing deviations from qualifications that lead to a symmetric halo orbit, such an orbit is found. Stochastic methods are well suited for this problem due to its highly multi-modal nature. Monotonic Basin Hopping is proposed here since it can take advantage of the clustering of sub-optima around an orbit of desired precision by using a zero-mean random distribution for its hop operations; this work uses a Gaussian distribution. The result is a fast means of finding halo orbits of a desired amplitude that are symmetric within a prescribed tolerance.