# Constrained optimization under uncertainty for decision-making problems: Application to Real-Time Strategy games

## TL;DR

This paper introduces a method to incorporate uncertainty into combinatorial optimization problems using classical Constraint Programming by integrating Rank Dependent Utility, demonstrated through a competitive game-playing bot.

## Contribution

It presents a novel approach to handle uncertainty within traditional Constraint Programming frameworks without developing new formalisms or solvers.

## Key findings

- Successfully integrated uncertainty handling into standard Constraint Programming.
- Developed a competitive game-playing bot for the 2018 {}RTS AI competition.
- Showed that existing solvers can address complex decision-making under uncertainty.

## Abstract

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.