Constrained optimization under uncertainty for decision-making problems:
  Application to Real-Time Strategy games
  Decision-making problems can be modeled as combinatorial optimization
problems with Constraint Programming formalisms such as Constrained
Optimization Problems. However, few Constraint Programming formalisms can deal
with both optimization and uncertainty at the same time, and none of them are
convenient to model problems we tackle in this paper.
  Here, we propose a way to deal with combinatorial optimization problems under
uncertainty within the classical Constrained Optimization Problems formalism by
injecting the Rank Dependent Utility from decision theory. We also propose a
proof of concept of our method to show it is implementable and can solve
concrete decision-making problems using a regular constraint solver, and
propose a bot that won the partially observable track of the 2018 {\mu}RTS AI
competition.
  Our result shows it is possible to handle uncertainty with regular Constraint
Programming solvers, without having to define a new formalism neither to
develop dedicated solvers. This brings new perspective to tackle uncertainty in
Constraint Programming.
