  The necessity to deal with uncertain data is a major challenge in decision
making. Robust optimization emerged as one of the predominant paradigms to
produce solutions that hedge against uncertainty. In order to obtain an even
more realistic description of the underlying problem where the decision maker
can react to newly disclosed information, multistage models can be used.
However, due to their computational difficulty, multistage problems beyond two
stages have received less attention and are often only addressed using
approximation rather than optimization schemes. Even less attention is paid to
the consideration of decision-dependent uncertainty in a multistage setting. We
explore multistage robust optimization via quantified linear programs, which
are linear programs with ordered variables that are either existentially or
universally quantified. Building upon a (mostly) discrete setting where the
uncertain parameters -- the universally quantified variables -- are only
restricted by their bounds, we present an augmented version that allows stating
the discrete uncertainty set via a linear constraint system that also can be
affected by decision variables. We present a general search-based solution
approach and introduce our solver Yasol that is able to deal with multistage
robust linear discrete optimization problems, with final mixed-integer recourse
actions and a discrete uncertainty set, which even can be decision-dependent.
In doing so, we provide a convenient model-and-run approach, that can serve as
baseline for computational experiments in the field of multistage robust
optimization, providing optimal solutions for problems with an arbitrary number
of decision stages.
