Constraint satisfaction and optimization problems are an important class of problems in artificial intelligence, where a set of decisions need to be made together, so that some requirements are satisfied and perhaps also optimizing some criteria. There are many examples in industry such as vehicle routing, scheduling, and planning. The PhD would be in automated modelling and solving of combinatorial optimization and constraint satisfaction problems. The ultimate goal is for the user to be able to state the problem without considering how it will be solved, and for the modelling and solving tools to produce a solution efficiently. To do this, the tools must make choices of formulation and solving strategy automatically, and this is itself an artificial intelligence problem.
At York we have a strong track record in automated modelling, especially in reformulating an existing model to improve its efficiency. Most of our work in this area is implemented in the open-source tool Savile Row , which has various reformulation options and produces output for a wide range of solvers, including SAT, SMT, constraint programming (CP), and mixed-integer programming. By reformulating a model, Savile Row can in some cases improve the performance of a solver by hundreds or even thousands of times [1,2,3].
This project is to investigate the promising technique of solver feedback loops, where a solver is used in model reformulation (e.g. to pre-solve part of a problem  or derive implied constraints ). We already have some very promising results to build on, from basic kinds of solver feedback loop. The PhD will be concurrent with a research grant on a closely related topic. The grant will provide funding to employ a research associate (RA) to join the research group, and I would fully expect the RA to work with you on some aspects of your research.
Competent programming skills will be needed for this project, and undergraduate-level AI would be an advantage (particularly in the areas of search and logic).
Please send informal enquiries to Peter Nightingale, [Email Address Removed]