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 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 towards 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 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.

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This paper analyzes 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 -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.vector for the selection of solution vector components f = objective function F = amplification control factor in Differential Evolution j s = number of successful runs J = transition matrix or mapping function in the search process M p = mutation probability N = total number of function evaluations N L = number of transfer legs N P = number of planets N p = normal distribution function N = neighborhood of a solution in the search space n = total number of repeated runs n pop = size of the population P n feval = function evaluation counter P = population p = optimization problem p s = success rate r 1 , r 2 = random numbers in particle swarm optimization r p = normalized radius of the pericenter S = selection function T = transfer time, day t 0 = departure time, MJD2000 u = control vector in the search process v = variation of the solution vector or velocity in the search space w = weighting factor x = solution vector x c = candidate point x l = local minimum = position of a deep-space maneuver as percentage of the transfer time = attitude angle of the gravity assist hyperbola, km/s = variation of the objective function v = variation in velocity, km/s = escape declination, rad r = reduction in the objective value = modulus of the difference between two solutions = escape right ascension, rad p = true proportion of success = velocity limiting factor = size of the neighborhood N Subscripts h = subseries index counter i, j = variable numbers l = local search algorithm or local minimum k = search process iteration number Superscript T = transpose

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 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. IntroductionDifferential evolution (DE), proposed by Price et al. (2006), is a well-known population-based evolutionary algorithm for solving global optimisation problems over continuous spaces. Literature indicates that DE exhibits very good performance over a wide variety of optimisation problems (Das and Suganthan 2011). However, although being a very efficient optimiser, its local search ability has long been questioned and work has been done to improve its local con-Communicated by V. Loia.

Presented is a robust optimization strategy for the aerodynamic design of horizontal axis wind turbine rotors including the variability of the annual energy production due to the uncertainty of the blade geometry caused by manufacturing and assembly errors. The energy production of a rotor designed with the proposed robust optimization approach features lower sensitivity to stochastic geometry errors with respect to that of a rotor designed with the conventional deterministic optimization approach that ignores these errors. The geometry uncertainty is represented by normal distributions of the blade pitch angle, and the twist angle and chord of the airfoils. The aerodynamic module is a blade-element momentum theory code. Both Monte Carlo sampling and the univariate reduced quadrature technique, a novel deterministic uncertainty analysis method, are used for uncertainty propagation. The performance of the two approaches is assessed in terms of accuracy and computational speed. A two-stage multi-objective evolutionbased optimization strategy is used. Results highlight that, for the considered turbine type, the sensitivity of the annual energy production to rotor geometry errors can be reduced by reducing the rotational speed and increasing the blade loading. The primary objective of the paper is to highlight how to incorporate an efficient and accurate uncertainty propagation strategy in wind turbine design. The formulation of the considered design problem does not include all the engineering constraints adopted in real turbine design, but the proposed probabilistic design strategy is fairly independent of the problem definition and can be easily extended to turbine design systems of any complexity

This paper addresses the problem of autonomous scheduling of space objects' observations from a network of tracking stations to enhance the knowledge of their orbit while respecting allocated resources. This task requires the coupling of a state estimation routine and an optimisation algorithm. As for the former, a sequential filtering approach to estimate the satellite state distribution conditional on received indirect measurements has been employed. To generate candidates, i.e. observation campaigns, a Structured-Chromosome Genetic Algorithm optimiser has been developed, which is able to address the issue of handling mixed-discrete global optimisation problems with variable-size design space. The search algorithm bases its strategy on revised genetic operators that have been reformulated for handling hierarchical search spaces. The presented approach aims at supporting the space sector by tracking both operational satellites and non-collaborative space debris in response to the challenge of a constantly increasing population size in the near Earth environment. The potential of the presented methodology is shown by solving the optimisation of a tracking window schedule for a very low Earth satellite operating in a highly perturbed dynamical environment.

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