Manual modeling in Constraint Programming is a substantial bottleneck, which Constraint Acquisition (CA) aims to automate. However, passive CA methods are prone to over-fitting, often learning models that include spurious global constraints when trained on limited data, while purely active methods can be query-intensive. We introduce a hybrid CA framework specifically designed to address the challenge of over-fitting in CA. Our approach integrates passive learning for initial candidate generation, a query-driven interactive refinement phase that utilizes probabilistic confidence scores (initialized by machine learning priors) to systematically identify over-fitted constraints, and a specialized subset exploration mechanism to recover valid substructures from rejected candidates. A final active learning phase ensures model completeness. Extensive experiments on diverse benchmarks demonstrate that our interactive refinement phase is crucial for achieving high target model coverage and overall model accuracy from limited examples, doing so with manageable query complexity. This framework represents a substantial advancement towards robust and practical constraint acquisition in data-limited scenarios.

Constraint Acquisition (CA) aims to widen the use of constraint programming by assisting users in the modeling process. However, most CA methods suffer from a significant drawback: they learn a single set of individual constraints for a specific problem instance, but cannot generalize these constraints to the parameterized constraint specifications of the problem. In this paper, we address this limitation by proposing GenCon, a novel approach to learn parameterized constraint models capable of modeling varying instances of the same problem. To achieve this generalization, we make use of statistical learning techniques at the level of individual constraints. Specifically, we propose to train a classifier to predict, for any possible constraint and parameterization, whether the constraint belongs to the problem. We then show how, for some classes of classifiers, we can extract decision rules to construct interpretable constraint specifications. This enables the generation of ground constraints for any parameter instantiation. Additionally, we present a generate-and-test approach that can be used with any classifier, to generate the ground constraints on the fly. Our empirical results demonstrate that our approach achieves high accuracy and is robust to noise in the input instances.

The significance of learning constraints from data is underscored by its potential applications in real-world problem-solving. While constraints are popular for modeling and solving, the approaches to learning constraints from data remain relatively scarce. Furthermore, the intricate task of modeling demands expertise and is prone to errors, thus constraint acquisition methods offer a solution by automating this process through learnt constraints from examples or behaviours of solutions and non-solutions. This work introduces a novel approach grounded in Deep Neural Network (DNN) based on Symbolic Regression that, by setting suitable loss functions, constraints can be extracted directly from datasets. Using the present approach, direct formulation of constraints was achieved. Furthermore, given the broad pre-developed architectures and functionalities of DNN, connections and extensions with other frameworks could be foreseen.

Constraint Programming (CP) has been successfully used to model and solve complex combinatorial problems. However, modeling is often not trivial and requires expertise, which is a bottleneck to wider adoption. In Constraint Acquisition (CA), the goal is to assist the user by automatically learning the model. In (inter)active CA, this is done by interactively posting queries to the user, e.g., asking whether a partial solution satisfies their (unspecified) constraints or not. While interac tive CA methods learn the constraints, the learning is related to symbolic concept learning, as the goal is to learn an exact representation. However, a large number of queries is still required to learn the model, which is a major limitation. In this paper, we aim to alleviate this limitation by tightening the connection of CA and Machine Learning (ML), by, for the first time in interactive CA, exploiting statistical ML methods. We propose to use probabilistic classification models to guide interactive CA to generate more promising queries. We discuss how to train classifiers to predict whether a candidate expression from the bias is a constraint of the problem or not, using both relation-based and scope-based features. We then show how the predictions can be used in all layers of interactive CA: the query generation, the scope finding, and the lowest-level constraint finding. We experimentally evaluate our proposed methods using different classifiers and show that our methods greatly outperform the state of the art, decreasing the number of queries needed to converge by up to 72%.

Constraint Acquisition (CA) systems can be used to assist in the modeling of constraint satisfaction problems. In (inter)active CA, the system is given a set of candidate constraints and posts queries to the user with the goal of finding the right constraints among the candidates. Current interactive CA algorithms suffer from at least two major bottlenecks. First, in order to converge, they require a large number of queries to be asked to the user. Second, they cannot handle large sets of candidate constraints, since these lead to large waiting times for the user. For this reason, the user must have fairly precise knowledge about what constraints the system should consider. In this paper, we alleviate these bottlenecks by presenting two novel methods that improve the efficiency of CA. First, we introduce a bottom-up approach named GrowAcq that reduces the maximum waiting time for the user and allows the system to handle much larger sets of candidate constraints. It also reduces the total number of queries for problems in which the target constraint network is not sparse. Second, we propose a probability-based method to guide query generation and show that it can significantly reduce the number of queries required to converge. We also propose a new technique that allows the use of openly accessible CP solvers in query generation, removing the dependency of existing methods on less well-maintained custom solvers that are not publicly available. Experimental results show that our proposed methods outperform state-of-the-art CA methods, reducing the number of queries by up to 60%. Our methods work well even in cases where the set of candidate constraints is 50 times larger than the ones commonly used in the literature.

In most optimization problems, users have a clear understanding of the function to optimize (e.g., minimize the makespan for scheduling problems). However, the constraints may be difficult to state and their modelling often requires expertise in Constraint Programming. Active constraint acquisition has been successfully used to support non-experienced users in learning constraint networks through the generation of a sequence of queries. In this paper, we propose Learn&Optimize, a method to solve optimization problems with known objective function and unknown constraint network. It uses an active constraint acquisition algorithm which learns the unknown constraints and computes boundaries for the optimal solution during the learning process. As a result, our method allows users to solve optimization problems without learning the overall constraint network.

Constraint acquisition systems such as QuAcq and MultiAcq can assist non-expert users to model their problems as constraint networks by classifying (partial) examples as positive or negative. For each negative example, the former focuses on one constraint of the target network, while the latter can learn a maximum number of constraints. Two bottlenecks of the acquisition process where both these algorithms encounter problems are the large number of queries required to reach convergence, and the high cpu times needed to generate queries, especially near convergence. In this paper we propose algorithmic and heuristic methods to deal with both these issues. We first describe an algorithm, called MQuAcq, that blends the main idea of MultiAcq into QuAcq resulting in a method that learns as many constraints as MultiAcq does after a negative example, but with a lower complexity. A detailed theoretical analysis of the proposed algorithm is also presented. %We also present a technique that boosts the performance of constraint acquisition by reducing the number of queries significantly. Then we turn our attention to query generation which is a significant but rather overlooked part of the acquisition process. We describe %in detail how query generation in a typical constraint acquisition system operates, and we propose heuristics for improving its efficiency. Experiments from various domains demonstrate that our resulting algorithm that integrates all the new techniques does not only generate considerably fewer queries than QuAcq and MultiAcq, but it is also by far faster than both of them, in average query generation time as well as in total run time, and also largely alleviates the premature convergence problem.

We learn constraint networks by asking the user partial queries. That is, we ask the user to classify assignments to subsets of the variables as positive or negative. We provide an algorithm that, given a negative example, focuses onto a constraint of the target network in a number of queries logarithmic in the size of the example. We give information theoretic lower bounds for learning some simple classes of constraint networks and show that our generic algorithm is optimal in some cases. Finally we evaluate our algorithm on some benchmarks.

Constraint programming can be divided very crudely into modeling and solving. Modeling defines the problem, in terms of variables that can take on different values, subject to restrictions (constraints) on which combinations of variables are allowed. Solving finds values for all the variables that simultaneously satisfy all the constraints. However, the impact of constraint programming has been constrained by a lack of "user-friendliness''. Constraint programming has a major "declarative" aspect, in that a problem model can be handed off for solution to a variety of standard solving methods. These methods are embedded in algorithms, libraries, or specialized constraint programming languages. To fully exploit this declarative opportunity however, we must provide more assistance and automation in the modeling process, as well as in the design of application-specific problem solvers. Automated modelling and solving in constraint programming presents a major challenge for the artificial intelligence community. Artificial intelligence, and in particular machine learning, is a natural field in which to explore opportunities for moving more of the burden of constraint programming from the user to the machine. This paper presents technical challenges in the areas of constraint model acquisition, formulation and reformulation, synthesis of filtering algorithms for global constraints, and automated solving. We also present the metrics by which success and progress can be measured.