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@article{LopVerDreDoe2025,
  author = { Manuel L{\'o}pez-Ib{\'a}{\~n}ez  and  Diederick Vermetten  and  Johann Dreo  and  Carola Doerr },
  title = {Using the Empirical Attainment Function for Analyzing
                  Single-objective Black-box Optimization Algorithms},
  journal = {IEEE Transactions on Evolutionary Computation},
  year = 2025,
  annote = {Pre-print: \url{https://doi.org/10.48550/arXiv.2404.02031}},
  doi = {10.1109/TEVC.2024.3462758},
  abstract = {A widely accepted way to assess the performance of iterative
                  black-box optimizers is to analyze their empirical cumulative
                  distribution function (ECDF) of pre-defined quality targets
                  achieved not later than a given runtime. In this work, we
                  consider an alternative approach, based on the empirical
                  attainment function (EAF) and we show that the target-based
                  ECDF is an approximation of the EAF. We argue that the EAF
                  has several advantages over the target-based ECDF. In
                  particular, it does not require defining a priori quality
                  targets per function, captures performance differences more
                  precisely, and enables the use of additional summary
                  statistics that enrich the analysis. We also show that the
                  average area over the convergence curves is a
                  simpler-to-calculate, but equivalent, measure of anytime
                  performance. To facilitate the accessibility of the EAF, we
                  integrate a module to compute it into the IOHanalyzer
                  platform. Finally, we illustrate the use of the EAF via
                  synthetic examples and via the data available for the BBOB
                  suite.},
  keywords = {EAF-based ECDF}
}

@incollection{LopPaqStu09emaa,
  editor = { Thomas Bartz-Beielstein  and  Marco Chiarandini  and  Lu{\'i}s Paquete  and  Mike Preuss },
  year = 2010,
  address = {Berlin~/ Heidelberg},
  publisher = {Springer},
  booktitle = {Experimental Methods for the Analysis of
                  Optimization Algorithms},
  author = { Manuel L{\'o}pez-Ib{\'a}{\~n}ez  and  Lu{\'i}s Paquete  and  Thomas St{\"u}tzle },
  title = {Exploratory Analysis of Stochastic Local Search
                  Algorithms in Biobjective Optimization},
  pages = {209--222},
  doi = {10.1007/978-3-642-02538-9_9},
  abstract = {This chapter introduces two Perl programs that
                  implement graphical tools for exploring the
                  performance of stochastic local search algorithms
                  for biobjective optimization problems. These tools
                  are based on the concept of the empirical attainment
                  function (EAF), which describes the probabilistic
                  distribution of the outcomes obtained by a
                  stochastic algorithm in the objective space. In
                  particular, we consider the visualization of
                  attainment surfaces and differences between the
                  first-order EAFs of the outcomes of two
                  algorithms. This visualization allows us to identify
                  certain algorithmic behaviors in a graphical way.
                  We explain the use of these visualization tools and
                  illustrate them with examples arising from
                  practice.}
}
