Precise determination of the orbital elements of binary stars using Differential Evolution

Abstract

This paper presents an 'adaptive probability of crossover' technique, as a variation of the differential evolution algorithm (ACDE), for optimal parameter estimation in the general curve-fitting problem. The technique is applied to the determination of orbital elements of a spectroscopic binary system (eta Bootis). In the ACDE, Varying the crossover probability rate (Cr) provides faster convergence than keeping it constant. The Cr is determined for each trial parameter vector ('individual') as a function of fit goodness. The adaptation automatically updates control parameter to an appropriate value, without requiring prior knowledge of the relationship between particular parameter settings and a given problem optimization characteristics. The presented analysis of eta Bootis derives best-fitting Keplerian and phasing curves. Error estimation of the optimal parameters is also included. Comparison of the results with previously published values suggests that the ACDE technique has a useful applicability to astrophysical data analysis.

Enhanced Hybrid Differential Evolution for Earth-Moon Low-Energy Transfer Trajectory Optimization

“…In 2007, an improved DE algorithm was applied by Lei et al [21] into two-impulse transfer trajectory problem. In 2011, Attia [35] presented an adaptive probability of crossover technique as a variation of the differential evolution algorithm, for optimal parameter estimation in the general curve-fitting problem. And the technique was successfully applied to the determination of orbital elements of a spectroscopic binary system (eta Bootis).…”