Epsilon efficiency

White, D. J.

doi:10.1007/bf00940762

Cited by 134 publications

(55 citation statements)

References 4 publications

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“…Note that we define ε-efficient and weakly ε-efficient solutions for the MOP, but -optimal and strictly -optimal solutions for the SOP, in accordance with the standard terminology established in the literature, here namely Loridan (1982Loridan ( , 1984 and White (1986).…”

Section: Then Xmentioning

confidence: 99%

Exact generation of epsilon-efficient solutions in multiple objective programming

Engau

Wiecek

2006

OR Spectrum

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. AbstractIt is a common characteristic of many multiple objective programming problems that the efficient solution set can only be identified in approximation: since this set often contains an infinite number of points, only a discrete representation can be computed, and due to numerical difficulties, each of these points itself might in general be only approximate to some efficient point. From among the various approximation concepts, this paper considers the notion of epsilon-efficiency which has also been shown to be of relevance other than merely for the purpose to approximate solutions.

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Section: Then Xmentioning

confidence: 99%

Exact generation of epsilon-efficient solutions in multiple objective programming

Engau

Wiecek

2006

OR Spectrum

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“…2 Approximate solutions in multi-objective optimization have been studied by many researchers so far, 12,13,26 however, the only studies which deal (albeit theoretically) with the computation of the entire set of approximate solutions have been undertaken by Schütze et al 18,19 A first attempt to investigate the benefit of considering approximate solutions in space mission design has been done by Vasile and Locatelli,23 albeit for the single-objective case.…”

Section: Introductionmentioning

confidence: 99%

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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“…to allow (or tolerate) nearly optimal solutions ( [6], [15]), to approximate the set of optimal solutions ( [8]), or in order to discretize this set ( [5], [11]). -efficient solutions or approximate solutions have also been used to tackle a variety of real world problems including portfolio selection problems ( [16]), a location problem ( [1]), or a minimal cost flow problem ( [8]).…”

Section: Introductionmentioning

confidence: 99%

“…The computation of such approximate solutions has been addressed in several studies. In most of them, scalarization methods have been empoyed (e.g., [15], [1], [3]). By their nature, such algorithms can deliver only single solutions by one single execution.…”

Section: Introductionmentioning

confidence: 99%

Computing finite size representations of the set of approximate solutions of an MOP with stochastic search algorithms

Schuetze

Coello

Tantar

et al. 2008

Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation

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In this work we study the convergence of generic stochastic search algorithms toward the entire set of approximate solutions of continuous multi-objective optimization problems. Since the dimension of the set of interest is typically equal to the dimension of the parameter space, we focus on obtaining a finite and tight approximation, measured by the Hausdorff distance. Under mild assumptions about the process to generate new candidate solutions, the limit approximation set will be determined entirely by the archiving strategy. We propose and investigate a novel archiving strategy theoretically and empirically. For this, we analyze the convergence behavior of the algorithm, yielding bounds on the obtained approximation quality as well as on the cardinality of the resulting approximation, and present some numerical results.

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Epsilon efficiency

Cited by 134 publications

References 4 publications

Exact generation of epsilon-efficient solutions in multiple objective programming

Exact generation of epsilon-efficient solutions in multiple objective programming

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

Computing finite size representations of the set of approximate solutions of an MOP with stochastic search algorithms

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