Approximate Solutions in Space Mission Design

Schütze, Oliver; Vasile, Massimiliano; Coello, Carlos A. Coello

doi:10.1007/978-3-540-87700-4_80

Cited by 17 publications

(22 citation statements)

References 12 publications

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“…A characterization of Dellnitz et al 2005). The box collections show different coverings of the Pareto set MOEAs specialized on space mission design can be found in Coverstone-Caroll et al (2000), Lee et al (2005), Vasile et al (2006) as well as Schütze et al (2008c). An introduction of how subdivision techniques work is given in the next subsection.…”

Section: Multi-objective Optimizationmentioning

confidence: 98%

A multi-objective approach to the design of low thrust space trajectories using optimal control

Dellnitz

Ober‐Blöbaum

Post

et al. 2009

Celest Mech Dyn Astr

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In this article, we introduce a novel three-step approach for solving optimal control problems in space mission design. We demonstrate its potential by the example task of sending a group of spacecraft to a specific Earth L 2 halo orbit. In each of the three steps we make use of recently developed optimization methods and the result of one step serves as input data for the subsequent one. Firstly, we perform a global and multi-objective optimization on a restricted class of control functions. The solutions of this problem are (Pareto-)optimal with respect to V and flight time. Based on the solution set, a compromise trajectory can be chosen suited to the mission goals. In the second step, this selected trajectory serves as initial guess for a direct local optimization. We construct a trajectory using a more flexible control law and, hence, the obtained solutions are improved with respect to control effort. Finally, we consider the improved result as a reference trajectory for a formation flight task and compute trajectories for several spacecraft such that these arrive at the halo orbit in a prescribed relative configuration. The strong points of our three-step approach are that the 123 34 M. Dellnitz et al.challenging design of good initial guesses is handled numerically by the global optimization tool and afterwards, the last two steps only have to be performed for one reference trajectory.

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Section: Multi-objective Optimizationmentioning

confidence: 98%

A multi-objective approach to the design of low thrust space trajectories using optimal control

Dellnitz

Ober‐Blöbaum

Post

et al. 2009

Celest Mech Dyn Astr

Self Cite

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“…So far, the only existing algorithm for the computation of P Q,ǫ is P Q,ǫ -NSGA-II proposed by Schütze et al, 20 which is based on the well-known NSGA-II. 4 P Q,ǫ -NSGA-II uses the same ranking strategy as its base MOEA, and thus, the highest pressure of the population is taken toward the Pareto set.…”

Section: Of 21mentioning

confidence: 99%

“…One can for instance consider instead of (19) the two values of (20) and (21) separately: (20) measures the convergence of A toward P Q,ǫ while (21) gives an idea about the spread of the entries of A along the set of interest. One potential drawback of the indicators (20) and (21)-and hence also of (19)-is that single outliers can give a false impression on the approximation quality, a problem which is hard to overcome when using stochastic search algorithms. Instead, the distances can be averaged leading to the following alternatives to (20) and (21), respectively.…”

Section: Iiib Performance Metricsmentioning

confidence: 99%

“…One potential drawback of the indicators (20) and (21)-and hence also of (19)-is that single outliers can give a false impression on the approximation quality, a problem which is hard to overcome when using stochastic search algorithms. Instead, the distances can be averaged leading to the following alternatives to (20) and (21), respectively.…”

Section: Iiib Performance Metricsmentioning

confidence: 99%

“…The additional consideration of approximate solutions in multi-objective space mission design problems is new and will be addressed in this paper (a preliminary study of this paper can be found in Schütze et al 20 ). Crucial for this approach is the efficient computation of the enlarged set of 'optimal' points (the second scope of this paper) since in many cases the 'classical' multi-objective approach is a challenge itself.…”

Section: Introductionmentioning

confidence: 99%

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Computing the Set of Epsilon-Efficient Solutions in Multiobjective Space Mission Design

Schütze

Vasile

Coello

2011

Journal of Aerospace Computing, Information, and Communication

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This version is available at https://strathprints.strath.ac.uk/30237/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. In this work, we consider multi-objective space mission design problems. We will start from the need, from a practical point of view, to consider in addition to the (Pareto) optimal solutions also nearly optimal ones. In fact, extending the set of solutions, for a given mission, to those nearly optimal significantly increases the number of options for the decision maker and gives a measure of the size of the launch windows corresponding to each optimal solution, i.e. a measure of its robustness. Whereas the possible loss of such approximate solutions compared to optimal-and possibly even 'better'-ones is dispensable. For this, we will examine several typical problems in space trajectory design-a bi-impulsive transfer from the Earth to the asteroid Apophis and two low-thrust multi-gravity assist transfers-and demonstrate the possible benefit of the novel approach. Further, we will present a multi-objective evolutionary algorithm which is designed for this purpose. Computing the Set of epsilon-efficient Solutions in

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A Survey of Diversity Oriented Optimization: Problems, Indicators, and Algorithms

Basto‐Fernandes

Yevseyeva

Deutz

et al. 2017

EVOLVE – A Bridge Between Probability, Set Oriented Numerics and Evolutionary Computation VII

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Approximate Solutions in Space Mission Design

Cited by 17 publications

References 12 publications

A multi-objective approach to the design of low thrust space trajectories using optimal control

A multi-objective approach to the design of low thrust space trajectories using optimal control

Computing the Set of Epsilon-Efficient Solutions in Multiobjective Space Mission Design

A Survey of Diversity Oriented Optimization: Problems, Indicators, and Algorithms

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