1,166 research outputs found
On the detection of nearly optimal solutions in the context of single-objective space mission design problems
When making decisions, having multiple options available for a possible realization of the same project can be advantageous. One way to increase the number of interesting choices is to consider, in addition to the optimal solution x*, also nearly optimal or approximate solutions; these alternative solutions differ from x* and can be in different regions â in the design space â but fulfil certain proximity to its function value f(x*). The scope of this article is the efficient computation and discretization of the set E of eâapproximate solutions for scalar optimization problems. To accomplish this task, two strategies to archive and update the data of the search procedure will be suggested and investigated. To make emphasis on data storage efficiency, a way to manage significant and insignificant parameters is also presented. Further on, differential evolution will be used together with the new archivers for the computation of E. Finally, the behaviour of the archiver, as well as the efficiency of the resulting search procedure, will be demonstrated on some academic functions as well as on three models related to space mission design
Computing the set of Epsilon-efficient solutions in multiobjective space mission design
In this work, we consider multiobjective 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 signiďŹcantly 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 optimalâand possibly even âbetterââones is dispensable. For this, we will examine several typical problems in space trajectory designâa biimpulsive transfer from the Earth to the asteroid Apophis and two low-thrust multigravity assist transfersâand demonstrate the possible beneďŹt of the novel approach. Further, we will present a multiobjective evolutionary algorithm which is designed for this purpose
Laser beam steering for GRACE Follow-On intersatellite interferometry
The GRACE Follow-On satellites will use, for the first time, a Laser Ranging Interferometer to measure intersatellite distance changes from which fluctuations in Earthâs geoid can be inferred. We have investigated the beam steering method that is required to maintain the laser link between the satellites. Although developed for the specific needs of the GRACE Follow-On mission, the beam steering method could also be applied to other intersatellite laser ranging applications where major difficulties are common: large spacecraft separation and large spacecraft attitude jitter. The beam steering method simultaneously coaligns local oscillator beam and transmitted beam with the laser beam received from the distant spacecraft using Differential Wavefront Sensing. We demonstrate the operation of the beam steering method on breadboard level using GRACE satellite attitude jitter data to command a hexapod, a six-degree-of-freedom rotation and translation stage. We verify coalignment of local oscillator beam/ transmitted beam and received beam of better than 10 Îźrad with a stability of 10 Îźrad/ Hzââââ in the GRACE Follow-On measurement band of 0.002...0.1 Hz. Additionally, important characteristics of the beam steering setup such as Differential Wavefront Sensing signals, heterodyne efficiency, and suppression of rotation-to-pathlength coupling are investigated and compared with analysis results
Multi-objective Optimization by Uncrowded Hypervolume Gradient Ascent
Evolutionary algorithms (EAs) are the preferred method for solving black-box
multi-objective optimization problems, but when gradients of the objective
functions are available, it is not straightforward to exploit these
efficiently. By contrast, gradient-based optimization is well-established for
single-objective optimization. A single-objective reformulation of the
multi-objective problem could therefore offer a solution. Of particular
interest to this end is the recently introduced uncrowded hypervolume (UHV)
indicator, which takes into account dominated solutions. In this work, we show
that the gradient of the UHV can often be computed, which allows for a direct
application of gradient ascent algorithms. We compare this new approach with
two EAs for UHV optimization as well as with one gradient-based algorithm for
optimizing the well-established hypervolume. On several bi-objective
benchmarks, we find that gradient-based algorithms outperform the tested EAs by
obtaining a better hypervolume with fewer evaluations whenever exact gradients
of the multiple objective functions are available and in case of small
evaluation budgets. For larger budgets, however, EAs perform similarly or
better. We further find that, when finite differences are used to approximate
the gradients of the multiple objectives, our new gradient-based algorithm is
still competitive with EAs in most considered benchmarks. Implementations are
available at https://github.com/scmaree/uncrowded-hypervolume.Comment: T.M.D. and S.C.M. contributed equally. The final authenticated
version is available in the conference proceedings of Parallel Problem
Solving from Nature - PPSN XVI. Changes in new version: removed statement
about Pareto compliance in abstract; added related work; corrected minor
mistake
PSA based multi objective evolutionary algorithms
It has generally been acknowledged that both proximity to the Pareto front and a certain diversity along the front, should be targeted when using evolutionary multiobjective optimization. Recently, a new partitioning mechanism, the Part and Select Algorithm (PSA), has been introduced. It was shown that this partitioning allows for the selection of a well-diversified set out of an arbitrary given set, while maintaining low computational cost. When embedded into an evolutionary search (NSGA-II), the PSA has significantly enhanced the exploitation of diversity. In this paper, the ability of the PSA to enhance evolutionary multiobjective algorithms (EMOAs) is further investigated. Two research directions are explored here. The first one deals with the integration of the PSA within an EMOA with a novel strategy. Contrary to most EMOAs, that give a higher priority to proximity over diversity, this new strategy promotes the balance between the two. The suggested algorithm allows some dominated solutions to survive, if they contribute to diversity. It is shown that such an approach substantially reduces the risk of the algorithm to fail in finding the Pareto front. The second research direction explores the use of the PSA as an archiving selection mechanism, to improve the averaged Hausdorff distance obtained by existing EMOAs. It is shown that the integration of the PSA into NSGA-II-I and Πp -EMOA as an archiving mechanism leads to algorithms that are superior to base EMOAS on problems with disconnected Pareto fronts. Š 2014 Springer International Publishing Switzerland
The set-based hypervolume Newton method for bi-objective optimization
Algorithms and the Foundations of Software technolog
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