We envisage two approaches for formulating the
optimization models: The first consists of developing integer
programming models based on a single criterion and than on
multiple criteria. This is a natural approach since a route plan is
based on the idea of whether a given geographical area (cell) belongs
or not to the path. The second approach will be based on constraint
programming. This approach
allows a clean
separation between the statement of the problem (the variables and the
constraints) and the resolution algorithms. In particular, it will
allow us to search for operationally
plans and take into account logical constraints in addition to
constraints. The challenges we face are three-fold due to the
aspects, uncertainty, and complexity:
criteria: The first step is to
identify and select the performance criteria associated
with a mission such as well as the constraints that will be taken into
and the level of detail (e.g.
individual mission vs. aggregate plan). Decision-makers often respond
well to a
“natural” representation of their preferences
through a set of thresholds. These may for instance
include (i) minimally acceptable performance levels (ii)
thresholds beyond which additional betterment is of lesser interest.
language of thresholds is intuitive, quite general, and accommodates
qualitative rating scales. All these aspects must be validated with
in dynamic contexts: Observation
conditions future courses of action. In a search context, the converse
influencing future observation opportunities) can also be expected.
programs where actions influence future states are known to be
more difficult. One avenue around this could consist in discretizing
observation decision loop. However, balancing model accuracy against
complexity will not be a trivial task.
complexity: Strategies to overcome complexity are
model-specific. We may resort to
a priori decomposition (a fixed
hierarchy of sub-models), and algorithmic
decomposition (e.g. column generation). We may also resort to
solve sub-models. Extensive experimentation will be required and
measures will be defined to evaluate solutions'