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This paper presents an algorithm for multiobjective optimization that blends together a number of heuristics. A population of agents combines heuristics that aim at exploring the search space both globally and in a neighborhood of each agent. These heuristics are complemented with a combination of a local and global archive. The novel agentbased algorithm is tested at first on a set of standard problems and then on three specific problems in space trajectory design. Its performance is compared against a number of state-of-the-art multiobjective optimisation algorithms that use the Pareto dominance as selection criterion: NSGA-II, PAES, MOPSO, MTS. The results demonstrate that the agent-based search can identify parts of the Pareto set that the other algorithms were not able to capture. Furthermore, convergence is statistically better although the variance of the results is in some cases higher.

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This paper presents a set of analytical formulae for the perturbed Keplerian motion of a spacecraft under the effect of a constant control acceleration. The proposed set of formulae can treat control accelerations that are fixed in either a rotating or inertial reference frame. Moreover, the contribution of the J 2 zonal harmonic is included in the analytical formulae. It will be shown that the proposed analytical theory allows for the fast computation of long, multi-revolution spirals while maintaining good accuracy. The combined effect of different perturbations and of the shadow regions due to solar eclipse is also included. Furthermore, a simplified control parameterisation is introduced to optimise thrusting patterns with two thrust arcs and two cost arcs per revolution. This simple parameterisation is shown to ensure enough flexibility to describe complex low thrust spirals. The accuracy and speed of the proposed analytical formulae are compared against a full numerical integration with different integration schemes. An averaging technique is then proposed as an application of the analytical formulae. Finally, the paper presents an example of design of an optimal low-thrust spiral to transfer a spacecraft from an elliptical to a circular orbit around the Earth.

This paper presents a novel approach for the preliminary design of Low-Thrust (LT), many-revolution transfers. The main feature of the novel approach is a considerable reduction in the control parameters and a consequent gain in computational speed. Each spiral is built by using a predefined pattern for thrust direction and switching structure. The pattern is then optimised to minimise propellant consumption and transfer time. The variation of the orbital elements due to the propulsive thrust is computed analytically from a first-order solution of the perturbed Keplerian motion. The proposed approach allows for a realistic estimation of ∆V cost and time of flight required to transfer a spacecraft between two arbitrary orbits. Eccentricity and plane changes are both taken into account. The novel approach is applied here to the design of missions for the removal of space debris by means of an Ion Beam Shepherd (IBS) Spacecraft. In particular, two slightly different variants of the proposed low-thrust control model are used for the two main phases of the debris removal mission, i.e. the rendezvous with the target object and its removal. Thanks to their relatively low computational cost they can be included in a multiobjective optimisation problem in which the sequence and timing of the removal of five hypothetical pieces of debris are optimised in order to minimise both propellant consumption and mission duration. Recent guidelines issued by international spacer regulatory institutions such as the United NationsCommittee for the Peaceful Uses of Outer Space (COPUOS) [2] and the Inter-Agency Space Debris Coordination Committee (IADC) [3] prescribe some actions to be followed by national or private agencies putting satellites into orbit in order to mitigate debris growth. For example, it is demanded that every new mission in Low Earth Orbit (LEO) must be planned such that the satellite itself must re-enter in the Earth's atmosphere within 25 years after the end of the mission. Alternatively, for higher orbits like Geostationary