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.

In facility location problems we seek to locate a set of facilities in an area, where clients may be present, so that some criterion is optimized. For instance, in the p-center problem we seek to minimize the maximum distance between any client and its closest facility, whereas in the p-dispersion problem we seek to maximize the minimum distance between any two facilities. Hence, in the former we have a minmax objective, whereas in the latter we have a maxmin objective. Recently, a variant of p-dispersion where distance constraints exist between facilities was studied from a CP and ILP perspective. An incomplete CP solver that uses a greedy heuristic to prune branches was shown to significantly outperform Gurobi and OR-Tools in terms of execution time, although it failed to discover optimal or near-optimal solutions in many instances. We enhance this work in two directions, regarding the effectiveness and the applicability of the approach. We first show how local search can be used to obtain better estimations of the bound at each node, resulting in more focused pruning, which allows for optimal or near-optimal solutions to be discovered in many more instances. Then, we demonstrate how the framework can be applied on the p-center problem with distance constraints, comparing it to ILP and CP models implemented in Gurobi and OR-Tools, respectively.

In facility location problems we seek to locate a set of facilities in an area, where clients may be present, so that some criterion is optimized. In the p-median problem we seek to minimize the sum of distances between demand points and their nearest facility, whereas in the p-dispersion problem we seek to maximize the closest distance between any two facilities. Recently, a variant of p-dispersion where distance constraints exist between facilities was studied from a Constraint Programming (CP) and Integer Linear Programming (ILP) perspective. An incomplete CP solver that uses a greedy heuristic to prune branches during search was shown to significantly outperform the ILP solver Gurobi and the CP solver OR-Tools in terms of execution time. Following that work, we consider a variant of the p-median problem where distance constraints exist between facilities and between facilities and demand points. This problem can be used to model the requirements that arise when locating semi-obnoxious facilities. We first introduce ILP and CP models and implement them in Gurobi and OR-Tools. Then, we demonstrate how a heuristic CP solver can be developed and applied on the p-median problem with distance constraints, comparing it to Gurobi and OR-Tools.

Constraint Programming (CP) is a successful methodology for solving combinatorial problems from various domains. Efficiently modeling the problem at hand as a Constraint Satisfaction Problem is a crucial, but difficult task in CP. Toward this, a recent approach that is attracting increasing interest is Constraint Acquisition, i.e., the (semi)automatic learning of constraints through examples of solutions and non-solutions. This paper introduces a hybrid methodology that combines passive and active learning strategies to acquire both global and fixed arity constraints. This hybrid approach leverages the strengths of both techniques to address their individual limitations. Passive learning rapidly learns constraints from example solutions, while active learning refines and contextualizes constraints through user interaction. The core of the methodology consists of a passive learning module where subsets of variables are compared against global constraints and are validated using a CP solver. Constraints consistently present across multiple solution sets are identified as global constraints that belong to the model. Then, fixed arity constraints are refined through an active learning module with user input. Experiments across various problem types, from simple to complex, demonstrate the efficiency of the proposed hybrid methodology.

Constraint programming provides a powerful framework for modeling and solving combinatorial problems. However, manually defining the required constraints can be a challenging task that requires a high level of expertise. Constraint acquisition (CA) techniques aim to semi-automate this process by learning constraints from examples of solutions and non-solutions. One important factor that can impact the effectiveness of CA is the diversity of the example solutions provided. This paper investigates how solution diversity influences passive learning approaches for CA across three distinct problems and various diversity metrics. Our results demonstrate that solution diversity significantly influences the quality of learned constraints, highlighting the importance of diverse solution sets. In addition, we show how we can predict whether a given set of solutions will enable accurate constraint learning using a machine learning (ML) model. Our experimental evaluation shows that the ML model can accurately predict the recall of the CA system based on the solution set’s diversity metrics and the number of solutions.

Learning constraint networks is known to require a number of membership queries exponential in the number of variables. In this paper, 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, called QuAcq2, that, given a negative example, elucidates a constraint of the target network in a number of queries logarithmic in the size of the example. The whole constraint network can then be learned with a polynomial number of partial queries. 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. We provide a version of QuAcq2 with a cutoff mechanism that controls the time to generate a query. Our experiments illustrate the good behavior of QuAcq2 in practice, especially in the case where QuAcq2 is executed to learn the missing constraints in a partially filled constraint model. Our experiments also show that QuAcq2 requires significantly fewer queries to learn a network than its predecessor QuAcq1.

In the (maxmin) p-dispersion problem we seek to locate a set of facilities in an area so that the minimum distance between any pair of facilities is maximized. We study a variant of this problem where there exist constraints specifying the minimum allowed distances between the facilities. This type of problem, which we call PDDP, has not received much attention within the literature on location and dispersion problems, despite its relevance to real scenarios. We propose both ILP and CP methods to solve the PDDP. Regarding ILP, we give two formulations derived from a classic and a state-of-the-art model for p-dispersion, respectively. Regarding CP, we first give a generic model that can be implemented within any standard CP solver, and we then propose a specialized heuristic Branch&Bound method. Experiments demonstrate that the ILP formulations are more efficient than the CP model, as the latter is unable to prove optimality in reasonable time, except for small problems, and is usually slower in finding solutions of the same quality than the ILP models. However, although the ILP approach displays good performance on small to medium size problems, it cannot efficiently handle larger ones. The heuristic CP-based method can be very efficient on larger problems and is able to quickly discover solutions to problems that are very hard for an ILP solver.

Non-intrusive load monitoring (NILM) has been on the rise for more than three decades. Its main objective is non-intrusive load disaggregation into individual operating appliances. Recent studies have shown that a higher sampling rate in the aggregated measurements allows better performance regarding load disaggregation. In addition, recent developments in deep learning and, in particular, convolutional neural networks (CNNs) have facilitated load disaggregation using CNN models. Several methods have been described in the literature that combine both a higher sampling rate and a CNN-based NILM framework. However, these methods use only a small number of cycles of the aggregated signal, which complicates the practical application of real-time NILM. In this work, a high sampling rate time-driven CNN-based NILM framework is also proposed. However, a novel current harmonic distortion image extracted from 60 cycles of the aggregated signal is proposed, resulting in 1 s appliance classification with low computational complexity. Appliance classification performance is evaluated using the PLAID3 dataset for both single and combined appliance operation. In addition, a comparison is made with a method from the literature. The results highlight the robustness of the novel feature and confirm the real-time applicability of the proposed NILM framework.

The p-median problem concerns the location of facilities so that the sum of distances between the demand points and their nearest facility is minimized. We study a variant of this classic location problem where minimum distance constraints exist both between the facilities and between the facilities and the demand points. This specific type of problem can be used to model situations where the facilities to be located are semi-obnoxious. But despite its relevance to real life scenarios, it has received little attention within the vast literature on location problems. We present twelve ILP models for this problem, coupling three formulations of the p-median problem with four formulations of the distance constraints. We utilize Gurobi Optimizer v9.0.3 in order to compare these ILP models on a large dataset of problems. Experimental results demonstrate that the classic p-median model proposed by ReVelle \& Swain and the model proposed by Rosing et al. are the best performers.

Precision agriculture is a new and evolving discipline that uses advanced technologies to increase the efficiency of agricultural inputs in a profitable and environmentally friendly way. Emerging techniques, such as Internet of Things, Artificial Intelligence, Big Data analytics, and Unmanned Aerial/Ground Vehicles can be utilized in order to make informed management decisions aiming to increase crop production. In this paper, we present the architecture of VELOS, a smart ecosystem for pest management and irrigation of bean farms in the Greece Region Prespa. VELOS leverages the aforementioned techniques for extracting knowledge in order to create integrated solutions to effectively support decision-making for efficiently managing pesticides and irrigation applications and scheduling

Several methods for dynamically adapting the local consistency property applied by a CP solver during search have been put forward in recent and older literature. We propose the classification of such methods in three categories depending on the level of granularity where decisions about which local consistency property to apply are taken: node , variable , and value oriented. We then present a detailed review of existing methods from each category, and evaluate them theoretically according to several criteria. Taking one recent representative method from each class, we then perform an experimental study. Results show that simple variable and value oriented methods are quite efficient when the older dom/ddeg heuristic is used for variable ordering, while a carefully tuned node oriented method does not seem to offer notable improvement compared to standard arc consistency propagation. In contrast, under the more realistic setting of dom/wdeg, the variable and value oriented methods cannot compete with standard propagation, while the node oriented method is very efficient. Finally, we obtain a new adaptive propagation method by integrating the variable and value oriented approaches and adding an amount of randomization The resulting method is simple, competitive, and almost parameter-free.

Constraint acquisition can assist non-expert users to model their problems as constraint networks. In active constraint acquisition, this is achieved through an interaction between the learner, who posts examples, and the user who classifies them as solutions or not. Although there has been recent progress in active constraint acquisition, the focus has only been on learning satisfaction problems with hard constraints. In this paper, we deal with the problem of learning soft constraints in optimization problems via active constraint acquisition, specifically in the context of the Max-CSP. Towards this, we first introduce a new type of queries in the context of constraint acquisition, namely partial preference queries, and then we present a novel algorithm for learning soft constraints in Max-CSPs, using such queries. We also give some experimental results. 2012 ACM Subject Classification Theory of computation → Constraint and logic programming

Learning constraint networks is known to require a number of membership queries exponential in the number of variables. In this paper, 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, called QUACQ, 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. The whole constraint network can then be learned with a polynomial number of partial queries. 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.

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. Then we turn our attention to query generation which is a significant but rather overlooked part of the acquisition process. We describe 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.

Interactive constraint acquisition is a special case of query-directed learning, also known as "exact" learning. It is used to assist non-expert users in modeling a constraint problem automatically by posting examples to the user that have to be classified as solutions or non-solutions. One significant issue that has not been addressed in the literature of constraint acquisition is the possible presence of uncertainty in the answers of the users. We address this by introducing Limited Membership Queries, where the user has the option of replying "I don't know", corresponding to "omissions" in exact learning. We present two algorithms for handling omissions. The first one deals with omissions that are independent events, while the second assumes that omissions are related to gaps in the user's knowledge. We present theoretical results about both methods and we evaluate them on benchmark problems. Importantly, our second algorithm can not only learn (a part of) the target network, but also the constraints that cause the user's uncertainty.

MQuAcq is an algorithm for active constraint acquisition that has been shown to outperform previous algorithms such as QuAcq and MultiAcq. In this paper, we exhibit two important drawbacks of MQuAcq. First, for each negative example, the number of recursive calls to the main procedure of MQuAcq can be non-linear, making it impractical for large problems. Second, MQuAcq, as well as QuAcq and MultiAcq, does not take into account the structure of the learned problem. We propose MQuAcq-2, a new algorithm based on MQuAcq that integrates solutions to both these problems. MQuAcq-2 exploits the structure of the learned problem by focusing the queries it generates to quasi-cliques of constraints. When dealing with a negative query, it only requires a linear number of iterations. MQuAcq-2 outperforms MQuAcq, especially on large problems.

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. We propose methods that deal with both these issues. The first one is an algorithm 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. The second is a technique that helps reduce the number of queries significantly. The third is based on the use of partial queries to cut down the time required for convergence. Experiments demonstrate that our resulting algorithm, which 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, both in average query generation time and in total run time.

Constraint programming (CP) is a powerful paradigm for various types of hard combinatorial problems. Constraint propagation techniques, such as arc consistency (AC), are used within solvers to prune inconsistent values from the domains of the variables and narrow down the search space. Local consistencies stronger than AC have the potential to prune the search space even more, but they are not widely used because they incur a high run time penalty in cases where they are unsuccessful. All constraint propagation techniques are sequential by nature, and thus they cannot be scaled up to modern multicore machines. For this reason, research on parallelizing constraint propagation is very limited. Contributing towards this direction, we exploit the parallelization possibilities of modern CPUs in tandem with strong local propagation methods in a novel way. Instead of trying to parallelize constraint propagation algorithms, we propose two search algorithms that apply different propagation methods in parallel. Both algorithms consist of a master search process, which is a typical CP solver, and a number of slave processes, with each one implementing a strong propagation method. The first algorithm runs the different propagators synchronously at each node of the search tree explored in the master process, while the second one can run them asynchronously at different nodes of the search tree. Preliminary experimental results on well-established benchmarks display the promise of our research by illustrating that our algorithms have execution times equal to those of serial solvers, in the worst case, while being faster in most cases.