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In this paper, we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of differential evolution (DE) is derived. It is then demonstrated that, under some assumptions on the differential mutation strategy and on the local structure of the objective function, the proposed dynamical system has fixed points toward which it converges with probability one for an infinite number of generations. This property is used to derive an algorithm that performs better than standard DE 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.
Date of Publication: April 2011