Recently, a framework for the approximation of the entire set of
ϵ-efficient solutions (denote by Eϵ) 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 Eϵ 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 n-dimensional object, where n
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 Eϵ, 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