466 research outputs found
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 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 biimpulsive transfer from the Earth to the asteroid Apophis and two low-thrust multigravity assist transfers—and demonstrate the possible benefit of the novel approach. Further, we will present a multiobjective evolutionary algorithm which is designed for this purpose
Approximate solutions in space mission design
In this paper, we address multi-objective space mission design problems. From a practical point of view, it is often the case that,during the preliminary phase of the design of a space mission, the solutions that are actually considered are not 'optimal' (in the Pareto sense)but belong to the basin of attraction of optimal ones (i.e. they are nearly
optimal). This choice is motivated either by additional requirements that the decision maker has to take into account or, more often, by robustness considerations. For this, we suggest a novel MOEA which is a modification of the well-known NSGA-II algorithm equipped with a recently
proposed archiving strategy which aims at storing the set of approximate solutions of a given MOP. Using this algorithm we will examine some space trajectory design problems and demonstrate the benefit of the novel approach
On the benefit of ∈-efficient solutions in multi objective space mission design
In this work we consider multi-objective space mission design problems. We will
show that it makes sense from the practical point of view to consider in addition to the
(Pareto) optimal solutions also nearly optimal ones since this increases significantly the
number of options for the decision maker, 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 several low-thrust multi-gravity assist transfers -
and demonstrate the possible benefit of the novel approach. Further, we will present an
evolutionary multi-objective algorithm which is designed for this purpose
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 – in the design space – 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 e–approximate 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 a Finite Size Representation of the Set of Approximate Solutions of an MOP
Recently, a framework for the approximation of the entire set of
-efficient solutions (denote by ) of a multi-objective
optimization problem with stochastic search algorithms has been proposed. It
was proven that such an algorithm produces -- under mild assumptions on the
process to generate new candidate solutions --a sequence of archives which
converges to in the limit and in the probabilistic sense. The
result, though satisfactory for most discrete MOPs, is at least from the
practical viewpoint not sufficient for continuous models: in this case, the set
of approximate solutions typically forms an -dimensional object, where
denotes the dimension of the parameter space, and thus, it may come to
perfomance problems since in practise one has to cope with a finite archive.
Here we focus on obtaining finite and tight approximations of , the
latter measured by the Hausdorff distance. 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
Convergence of Stochastic Search Algorithms to Finite Size Pareto Set Approximations
In this work we study the convergence of generic stochastic search algorithms toward the Pareto set of continuous multi-objective optimization problems. The focus is on obtaining a finite approximation that should capture the entire solution set in a suitable sense, which will be defined using the concept of -dominance. Under mild assumptions about the process to generate new candidate solutions, the limit approximation set will be determined entirely by the archiving strategy. We investigate two different archiving strategies which lead to a different limit behavior of the algorithms, yielding bounds on the obtained approximation quality as well as on the cardinality of the resulting Pareto set approximation. Finally, we demonstrate the potential for a possible hybridization of a given stochastic search algorithm with a particular local search strategy -- multi-objective continuation methods -- by showing that the concept of -dominance can be integrated into this approach in a suitable way
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