Global optimisation of multiple gravity assist trajectories

Multiple gravity assist (MGA) trajectories represent a particular class of space trajectories in which a spacecraft exploits the encounter with one or more celestial bodies to change its velocity vector; they have been essential to reach high Delta-v targets with low propellant consumption. The search for optimal transfer trajectories can be formulated as a mixed combinatorial-continuous global optimisation problem; however, it is known that the problem is difficult to solve, especially if deep space manoeuvres (DSM) are considered. This thesis addresses the automatic design of MGA trajectories through global search techniques, in answer to the requirements of having a large number of mission options in a short time, during the preliminary design phase. Two different approaches are presented. The first is a two-level approach: a number of feasible planetary sequences are initially generated; then, for each one, families of the MGA trajectories are built incrementally. The whole transfer is decomposed into sub-problems of smaller dimension and complexity, and the trajectory is progressively composed by solving one problem after the other. At each incremental step, a stochastic search identifies sets of feasible solutions: this region is preserved, while the rest of the search space is pruned out. The process iterates by adding one planet-to-planet leg at a time and pruning the unfeasible portion of the solution space. Therefore, when another leg is added to the trajectory, only the feasible set for the previous leg is considered and the search space is reduced. It is shown, through comparative tests, how the proposed incremental search performs an effective pruning of the search space, providing families of optimal solutions with a lower computational cost than a non-incremental approach. Known deterministic and stochastic methods are used for the comparison. The algorithm is applied to real MGA case studies, including the ESA missions BepiColombo and Laplace. The second approach performs an integrated search for the planetary sequence and the associated trajectories. The complete design of an MGA trajectory is formulated as an autonomous planning and scheduling problem. The resulting scheduled plan provides the planetary sequence for a MGA trajectory and a good estimation of the optimality of the associated trajectories. For each departure date, a full tree of possible transfers from departure to destination is generated. An algorithm inspired by Ant Colony Optimization (ACO) is devised to explore the space of possible plans. The ants explore the tree from departure to destination, adding one node at a time, using a probability function to select one of the feasible directions. Unlike standard ACO, a taboo-based heuristics prevents ants from re-exploring the same solutions. This approach is applied to the design of optimal transfers to Saturn (inspired by Cassini) and to Mercury, and it demonstrated to be very competitive against known traditional stochastic population-based techniques

Stochastic Optimisation for Complex Mixed-Integer Programming Problems in Asteroid Tour Missions

Deep space exploration is key to understand the origin of our Solar System and address the Earth impact risk. Space Trajectory Design (STD) has evolved and incremented in complexity due to the interest within the space community to explore multiple celestial bodies in a single mission. This thesis focuses on an Asteroid Tour Trajectory in the context of the CASTAway mission. CASTAway is a mission proposal for European Space Agency’s 5th call of medium-size missions to explore the Asteroid Main Belt. The objective is not to find the global optima but find feasible sequences of asteroid fly-bys, as per feasible tours of 12 asteroids of a total Δv of less than 9 km/s is meant. The complexity of the problem is given by the large number of possible permutations of 12-asteroid tour solutions – even with a reduced catalogue of 158 asteroids – and because of being a Mixed-Integer Non-Linear Programming (MINLP) problem. Because of this, metaheuristics are used to tackle the problem. A novel problem modelling that achieves uniqueness on the cost paths of the Search Space and a novel ACO solver is presented, with the general objective for the whole CASTPath project of finding a robust low computational heuristic. Due to the scientific interest on having diversity in the sequences, a similarity measurement tool is also developed. Several test cases with different ACO tuning parameters are run on a High Performance Computer. Results show that this algorithm outperforms the previous heuristics on CASTPath obtaining the lowest Δv (7.27 km/s) achieved by an heuristic and finding multiple feasible sequences (97 in 1 h). Moreover, the new problem modelling has allowed within the research group, to find the global optima (6.98 km/s) for this asteroid catalogue by Dynamic Programming

A hyper-heuristic approach to automated generation of mutation operators for evolutionary programming

Evolutionary programming can solve black-box function optimisation problems by evolving a population of numerical vectors. The variation component in the evolutionary process is supplied by a mutation operator, which is typically a Gaussian, Cauchy, or Lévy probability distribution. In this paper, we use genetic programming to automatically generate mutation operators for an evolutionary programming system, testing the proposed approach over a set of function classes, which represent a source of functions. The empirical results over a set of benchmark function classes illustrate that genetic programming can evolve mutation operators which generalise well from the training set to the test set on each function class. The proposed method is able to outperform existing human designed mutation operators with statistical significance in most cases, with competitive results observed for the rest

Imagining Earth: Concepts of Wholeness in Cultural Constructions of Our Home Planet

While concepts of Earth have a rich tradition, more recent examples show a distinct quality: Though ideas of wholeness might still be related to mythical, religious, or utopian visions of the past, "Earth" itself has become available as a whole. This raises several questions: How are the notions of one Earth or our Planet imagined and distributed? What is the role of cultural imagination and practices of signification in the imagination of "the Earth"? Which theoretical models can be used or need to be developed to describe processes of imagining Planet Earth? This collection invites a wide range of perspectives from different fields of the Humanities to explore the means of imagining Earth

Stochastics global optimization methods and their applications in Chemical Engineering

Ph.DDOCTOR OF PHILOSOPH

Imagining Earth

While concepts of Earth have a rich tradition, more recent examples show a distinct quality: Though ideas of wholeness might still be related to mythical, religious, or utopian visions of the past, ''Earth'' itself has become available as a whole. This raises several questions: How are the notions of one Earth or our Planet imagined and distributed? What is the role of cultural imagination and practices of signification in the imagination of ''the Earth''? Which theoretical models can be used or need to be developed to describe processes of imagining Planet Earth? This collection invites a wide range of perspectives from different fields of the Humanities to explore the means of imagining Earth

Simulated Annealing

The book contains 15 chapters presenting recent contributions of top researchers working with Simulated Annealing (SA). Although it represents a small sample of the research activity on SA, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. In fact, one of the salient features is that the book is highly multidisciplinary in terms of application areas since it assembles experts from the fields of Biology, Telecommunications, Geology, Electronics and Medicine

Transhumanism and Society: The Social Debate Over Human Enhancement

This book provides an introductory overview to the social debate over enhancement technologies with an overview of the transhumanists\u27 call to bypass human nature and conservationists\u27 argument in defense of it. The author present this controversy as it unfolds in the contest between transhumanists proponents and conservationists, who push back with an argument to conserve human nature and to ban enhancement technologies. Readers are informed about the discussion over humanism, the tension between science and religion, and the interpretation of socio-technological revolutions; and are invited to make up their own mind about one of the most challenging topics concerning the social and ethical implications of technological advancements