  In black-box optimization, it is essential to understand why an algorithm
instance works on a set of problem instances while failing on others and
provide explanations of its behavior. We propose a methodology for formulating
an algorithm instance footprint that consists of a set of problem instances
that are easy to be solved and a set of problem instances that are difficult to
be solved, for an algorithm instance. This behavior of the algorithm instance
is further linked to the landscape properties of the problem instances to
provide explanations of which properties make some problem instances easy or
challenging. The proposed methodology uses meta-representations that embed the
landscape properties of the problem instances and the performance of the
algorithm into the same vector space. These meta-representations are obtained
by training a supervised machine learning regression model for algorithm
performance prediction and applying model explainability techniques to assess
the importance of the landscape features to the performance predictions. Next,
deterministic clustering of the meta-representations demonstrates that using
them captures algorithm performance across the space and detects regions of
poor and good algorithm performance, together with an explanation of which
landscape properties are leading to it.
