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.

In this paper, we analyze the performance of some global search algorithms on a number of space trajectory design problems. A rigorous testing procedure is introduced to measure the ability of an algorithm to identify the set of ²-optimal solutions. From the analysis of the test results, a novel algorithm is derived. The development of the novel algorithm starts from the redefinition of some evolutionary heuristics in the form of a discrete dynamical system. The convergence properties of this discrete dynamical system are used to derive a hybrid evolutionary algorithm that displays very good performance on the particular class of problems presented in this paper

This paper addresses the preliminary robust design of a small/medium–scale reentry unmanned space vehicle. A hybrid optimization technique is proposed that couples an evolutionary multi-objective algorithm with a direct-transcription method for optimal control problems. Uncertainties on the aerodynamic forces and vehicle mass are integrated in the design process, and the hybrid algorithm searches for geometries that 1) minimize the mean value of the maximum heat flux, 2) maximize the mean value of the maximum achievable distance, and 3) minimize the variance of the maximum heat flux. The evolutionary part handles the system-design parameters of the vehicle and the uncertain functions, while the direct-transcription method generates optimal control profiles for the reentry trajectory of each individual of the population. During the optimization process, artificial neural networks are used to approximate the aerodynamic forces required by the direct-transcription method. The artificial neural networks are t...

This paper proposes a multi-population adaptive version of inflationary differential evolution algorithm. Inflationary differential evolution algorithm (IDEA) combines basic differential evolution (DE) with some of the restart and local search mechanisms of Monotonic Basin Hopping (MBH). In the adaptive version presented in this paper, the DE parameters \({ CR}\) and F are automatically adapted together with the size of the local restart bubble and the number of local restarts of MBH. The proposed algorithm implements a simple but effective mechanism to avoid multiple detections of the same local minima. The novel mechanism allows the algorithm to decide whether to start or not a local search. The algorithm has been extensively tested over more than fifty test functions from the competitions of the Congress on Evolutionary Computation (CEC), CEC 2005, CEC 2011 and CEC 2014, and compared against all the algorithms participating in those competitions. For each test function, the paper reports best, worst, median, mean and standard deviation values of the best minimum found by the algorithm. Comparisons with other algorithms participating in the CEC competitions are presented in terms of relative ranking, Wilcoxon tests and success rates. For completeness, the paper presents also the single population adaptive IDEA, that can adapt only \(\textit{CR}\) and F, and shows that this simpler version can outperform the multi-population one if the radius of the restart bubble and the number of restarts are properly chosen.