## 1 Introduction
In the context of an aircraft-engine integration application as the one hereby considered, this does allow for a direct interface between the optimization code and the engine performance software to obtain estimates for thrust and fuel consumption, instead of resorting to simplified functional representations for the latter; in fact, when considering the detailed modeling of an aircraft powerplant, small discontinuities in these quantities and/or their derivatives are typical as a result of bleed valve, guide vane, nozzle, bleed and power extraction schedules. Furthermore, because of their very good global search capabilities and contrary to gradient-based optimization methods, population-based schemes do not require an initial guess by the user and can thus been applied to problems with solutions that are hard to estimate [15]. Combining the above with a simple and straightforward implementation leads to a significant reduction in the effort required for case setup and makes trajectory optimization accessible to users without the otherwise-necessary mathematical background or system knowledge. As a result, given the ever-increasing computational power that is available, the use of such schemes has become widespread over the last decades, replacing, in many cases, methods that are more traditional. [PERSON] and [PERSON] [15] developed a modified real-coded genetic algorithm for constrained trajectory optimization to be used for providing appropriate initial solutions to gradient-based direct trajectory optimization methods. The proposed algorithm was applied to a space vehicle's reentry trajectory problem and produced solutions that approached the vicinity of the optimal solution. [PERSON] and [PERSON] [16] applied the Particle Swarm Optimization (PSO) technique (an optimization method inspired by the social behavior of animals) to a series of space trajectory optimization cases and showed that the method is efficient, reliable and accurate in determining optimal trajectories for problems with a limited number of unknown parameters. [PERSON], [PERSON] and [PERSON] [17] reached the same conclusions while examining the application of PSO to spacecraft reentry trajectory optimization. [PERSON], [PERSON] and [PERSON] [18] employed PSO to generate optimal multiple-burn rendezvous trajectories and used the solutions to initialize a gradient-based optimization process; good agreement between the results of the two methods was observed, demonstrating the effectiveness of the PSO scheme. Common features of all the approaches presented above are the use of a direct-shooting-equivalent problem formulation, employing parameterized curves to produce control time histories with a finite number of input variables and the implementation of constraints by means of penalty functions, selections that are dictated by the particular characteristics of the selected optimization schemes. A rather interesting feature of population-based optimization algorithms that has recently been exploited in the field of trajectory optimization is their ability to handle multiple objectives in a single optimization run [19; 20]; in a so-called multi-objective optimization case, instead of a single solution, the optimizer seeks for a set of solutions that correspond to the optimal compromises between contradicting targets; the latter form a front in the objective space, named the Pareto front. This capability partly compensates for the higher computational cost of population-based methods, since multiple runs of a comparable gradient-based optimization method are required to produce the same amount of solutions. Considering the development of an aircraft/engine integration methodology that will address the climb performance of candidate aircraft/engine configurations, the use of a climb path optimization methodology was required, to allow for a \"fair\" comparison of configurations with different performance characteristics.