Improved Differential Evolution Algorithm and Its Applications to Orbit Design

Abstract

Differential Evolution (DE) is a basic and robust evolutionary strategy that has been applied to determining the global optimum for complex optimization problems[1–5]. It was introduced in 1995 by Storn and Price [1] and has been successfully applied to optimization problems including nonlinear, non-differentiable, non-convex, and multi-model functions. DE algorithms show good convergence, high-reliability, simplicity, and a reduced number of controllable parameters [2]. Olds and Kluever [3] applied DE to an interplanetary trajectory optimization problem and demonstrated the effectiveness of DE to produce rapid solutions. Madavan [4] discussed various modifications to the DE algorithm, improved its computational efficiency, and applied it to aerodynamic shape optimization problems. DE algorithms are easy to use, as they require only a few robust control variables, which can be drawn from a well-defined numerical interval. However, the existing various DE algorithms also have limitations, being susceptible to instability and getting trapped into local optima[2]. Notable effort has been spent addressing this by coupling DE algorithms with other optimization algorithms (for example, Self Organizing Maps (SOM) [6], Dynamic Hill Climbing (DHC) [7], Neural Networks (NN) [7], Particle Swarm Optimization (PSO) [8]). In these cases, the additional algorithm is used as an additional loop within the optimization process, creating a hybrid system with an inner and outer loop. Such hybrid algorithms are inherently more complex and so the computation cost is increased. Attempting to address this, a self-adaptive DE was designed and applied to the orbit design problem for prioritized multiple targets by Chen[5]. However, the self-adaptive feature is somewhat limited as it relates only to the number of generations within the optimization. A Self-adaptive DE which can automatically adapt its learning strategies and the associated parameters during the evolving procedure was proposed by Qin and Suganthan[9] and 25 test functions were used to verify the algorithm.