A dynamical system perspective on evolutionary heuristics applied to space trajectory optimization problems

In this paper we propose a generalized formulation of the evolutionary heuristic governing the movement of the individuals of Differential Evolution in the search space. The basic heuristic of Differential Evolution is casted in form of discrete dynamical system and extended to improve local convergence. It is demonstrated that under some assumptions on the local structure of the objective function, the proposed dynamical system, has fixed points towards which it converges asymptotically. This property is used to derive an algorithm that performs better than standard Differential Evolution on some space trajectory optimization problems. The novel algorithm is then extended with a guided restart procedure that further increases the performance reducing the probability of stagnation in deceptive local minima.