An improved differential evolution algorithm and its applications to orbit design

Yao, Wei and Luo, Jianjun and Macdonald, Malcolm and Wang, Mingming and Ma, Weihua (2017) An improved differential evolution algorithm and its applications to orbit design. Journal of Guidance, Control and Dynamics. ISSN 1533-3884 (In Press)

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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.