Abstract
Solving Constraint Optimization Problems (COPs) can be dramatically simplified by boundary estimation, that is providing tight boundaries of cost functions. By feeding a supervised Machine Learning (ML) model with data composed of the known boundaries and extracted features of COPs, it is possible to train the model to estimate the boundaries of a new COP instance. In this paper, we first give an overview of the existing body of knowledge on ML for Constraint Programming (CP), which learns from problem instances. Second, we introduce a boundary estimation framework that is applied as a tool to support a CP solver. Within this framework, different ML models are discussed and evaluated regarding their suitability for boundary estimation, and countermeasures to avoid unfeasible estimations that avoid the solver finding an optimal solution are shown. Third, we present an experimental study with distinct CP solvers on seven COPs. Our results show that near-optimal boundaries can be learned for these COPs with only little overhead. These estimated boundaries reduce the objective domain size by 60-88% and can help the solver find near-optimal solutions early during the search.
Highlights
Constraint Optimization Problems (COPs) are commonly solved by systematic tree search, such as branch-and-bound, where a specialized solver prunes those parts of the search space with a worse cost than the current best solution
In this part of the paper, we present one application of predictive machine learning for constraint optimization, namely Bion, a novel boundary estimation technique
Predictive Machine Learning (ML) has been shown to be very successful in supporting many important applications of Constraint Programming (CP), including algorithm configuration and selection, learning constraint models, and providing additional insights to support CP solvers
Summary
Constraint Optimization Problems (COPs) are commonly solved by systematic tree search, such as branch-and-bound, where a specialized solver prunes those parts of the search space with a worse cost than the current best solution. The second part of the paper discusses a boundary estimation method called Bion, which combines logic-driven constraint optimization and data-driven ML, for solving. COPs. An ML-based estimation model predicts boundaries for the objective variable of a problem instance, which can be exploited by a CP solver to prune the search space. Estimating tight bounds in a problem- and solver-agnostic way is still an open problem [3] Such a generic method would allow many COP instances to be solved more efficiently. Bion is a two-phase procedure: first, an objective boundary for the problem instance is estimated with a previously trained ML regression model; second, the optimization model is extended by a boundary constraint on the objective variable, and a constraint solver is used to solve the problem instance.
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