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A hybrid evolutionary algorithm which synergistically exploits differential evolution, genetic algorithms and particle swarm optimization, has been developed and applied to spacecraft trajectory optimization. The cooperative procedure runs the three basic algorithms in parallel, while letting the best individuals migrate to the other populations at prescribed intervals. Rendezvous problems and round-trip Earth-Mars missions have been considered. The results show that the hybrid algorithm has better performance compared to the basic algorithms that are employed. In particular, for the rendezvous problem, a 100% efficiency can be obtained both by differential evolution and the genetic algorithm only when particular strategies and parameter settings are adopted. On the other hand, the hybrid algorithm always attains the global optimum, even though nonoptimal strategies and parameter settings are adopted. Also the number of function evaluations, which must be performed to attain the optimum, is reduced when the hybrid algorithm is used. In the case of Earth-Mars missions, the hybrid algorithm is successfully employed to determine mission opportunities in a large search space.

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A nested direct/indirect method is used to find the optimal design for a microgravity platform which is based on a hybrid sounding rocket. The direct optimization of the parameters that affect the motor design is coupled with the indirect trajectory optimization to maximize a given mission performance index. A gas-pressure feed system is used, with three different propellant combinations. The feed system exploits a pressurizing gas, namely, helium, when hydrogen peroxide or liquid oxygen is used as an oxidizer. The simplest blowdown design is compared with a more complex pressurizing system, which has an additional gas tank that allows for a phase with constant propellant tank pressure. Only self-pressurization is considered with nitrous oxide; two different models are used to describe the behavior of the tank pressurization. The simplest model assumes liquid/vapor equilibrium. A two-phase model is also proposed: Saturated vapor and superheated liquid are considered and the liquid/vapor mass transfer evaluation is based on the liquid spinodal line. Results show that the different tank-pressurization models yield minimal differences of the optimal motor characteristics. Performance differs slightly due to the different mass of the residual oxidizer. The propellant comparison for the present case shows better performance for hydrogen peroxide/ polyethylene with respect to liquid oxygen/hydroxyl-terminated polybutadiene, while nitrous oxide/hydroxylterminated polybutadiene remains attractive for system simplicity and low costs. Nomenclature A b = burning surface area, m 2 A p = port area, m 2 A t = nozzle throat area, m 2 a = regression constant, m 12n kg n s n 1 C F = thrust coefficient c l = liquid oxidizer specific heat capacity J=kg K c = characteristic velocity, m=s D = drag vector, N D = rocket outer diameter, m F = thrust vector, N F = thrust magnitude, N G O = oxidizer mass flux, kg=s m 2 g = gravity acceleration, m=s 2 h = specific enthalpy, J=kg h ev = specific latent heat of vaporization, J=kg J = throat area to initial port area ratio L = overall length, m L b = fuel grain length, m M = rocket mass, kg m = mass, kg m Ot = mass of oxidizer in the tank, kg n = mass-flux exponent n x = longitudinal acceleration, g p = pressure, Pa p din = dynamic pressure, kPa R = port radius, m R t = throat radius, m r = position vector, m T = temperature, K t = time, s t g = time spent above 100 km, s u = specific internal energy, J=kg V = volume, m 3 v = velocity vector, m=s Z = hydraulic resistance, 1=kg m z = normalized altitude = mixture ratio = specific heat ratio " = nozzle area ratio = vapor compressibility factor = regression rate, m=s = density, kg=m 3 Subscripts a = auxiliary gas BD = beginning of blowdown phase c = combustion chamber at nozzle entrance cv = condensing vapor e = nozzle exit el = evaporating liquid F = fuel g = pressurizing gas i = initial value l = liquid oxidizer lim = superheated liquid limit O = oxidizer p = overall propellant (oxidizer fuel) res = tank residual sat = saturation SL = sea leve...