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 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.
Although the following papers do not deal with uncertainty, they all focus on solving optimization problems in RTS games, in particular StarCraft. Thus @cite_3 propose to model with the optimal building placement to make a wall at a base entrance in order to make easier its defense. @cite_0 @cite_9 propose a and solver, GHOST, that we used for our experiments. Their Constraint Programming solver as been designed to output good quality solution within some tenth of milliseconds, make it usable in RTS games.
@cite_0 @cite_9 @cite_3
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GHOST is a framework to help game developers to model and implement their own optimization problems, or to simply instantiate a problem already encoded in GHOST. Previous works show that GHOST leads to high-quality solutions in some tens of milliseconds for three RTS-related problems: build order, wall-in placement and target selection. In this paper, we present two new problems in GHOST: pathfinding and resource allocation. The goal of this paper is to show the robustness of the framework, having very good results for a problem it is not designed for (pathfinding), and to show its flexibility, where it is easy to propose different models of the same problem (resource allocation problem). This paper presents GHOST , a combinatorial optimization framework that a real-time strategy (RTS) AI developer can use to model and solve any problem encoded as a constraint satisfaction optimization problem (CSP COP). We show a way to model three different problems as a CSP COP, using instances from the RTS game StarCraft as test beds. Each problem belongs to a specific level of abstraction (the target selection as reactive control problem, the wall-in as a tactics problem, and the build order planning as a strategy problem). In our experiments, GHOST shows good results computed within some tens of milliseconds. We also show that GHOST outperforms state-of-the-art constraint solvers, matching them on the resources allocation problem, a common combinatorial optimization problem. This paper presents a constraint optimization approach to walling in real-time strategy (RTS) games. Walling is a specific type of spatial reasoning, typically employed by human expert players and not currently fully exploited in RTS game AI, consisting on finding configurations of buildings to completely or partially block paths. Our approach is based on local search, and is specifically designed for the real-time nature of RTS games. We present experiments in the context of the RTS game StarCraft showing promising results.