Towards a Generic Representation of Combinatorial Problems for Learning-Based Approaches

In recent years, there has been a growing interest in using learning-based approaches for solving combinatorial problems, either in an end-to-end manner or in conjunction with traditional optimization algorithms. In both scenarios, the challenge lies in encoding the targeted combinatorial problems into a structure compatible with the learning algorithm. Many existing works have proposed problem-specific representations, often in the form of a graph, to leverage the advantages of \textit{graph neural networks}. However, these approaches lack generality, as the representation cannot be easily transferred from one combinatorial problem to another one. While some attempts have been made to bridge this gap, they still offer a partial generality only. In response to this challenge, this paper advocates for progress toward a fully generic representation of combinatorial problems for learning-based approaches. The approach we propose involves constructing a graph by breaking down any constraint of a combinatorial problem into an abstract syntax tree and expressing relationships (e.g., a variable involved in a constraint) through the edges. Furthermore, we introduce a graph neural network architecture capable of efficiently learning from this representation. The tool provided operates on combinatorial problems expressed in the XCSP3 format, handling all the constraints available in the 2023 mini-track competition. Experimental results on four combinatorial problems demonstrate that our architecture achieves performance comparable to dedicated architectures while maintaining generality. Our code and trained models are publicly available at \url{https://github.com/corail-research/learning-generic-csp}.

Holy Grail 2.0: From Natural Language to Constraint Models

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.