We study the p-dispersion problem with distance constraints (pDD), a variant of the well-known p-dispersion problem. In a pDD, the goal is to locate a set of facilities so as to maximize the minimum distance between any two of them, subject to additional constraints specifying minimum allowed distances. Two CP models for the pDD have recently been proposed. The first is a typical model that includes the global constraints Minimum and Element and explicitly represents the objective function, connecting it to the decision variables. However, as problem size grows, this model becomes increasingly inefficient. The second model adopts a simplistic approach that only uses binary constraints, essentially treating the pDD as a satisfaction problem. In this paper, after demonstrating the deficiencies of these models, we propose a new compact model that captures the problem through ternary constraints, instead of global or binary ones. We prove that, rather surprisingly, the pruning of the decision variables' domains achieved in our new model is equivalent to that achieved in the model with global constraints, resulting in the same search tree under the same variable and value ordering. Experiments demonstrate that our new model is by far superior to the existing ones, both in terms of solution quality and run times.

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.

Constraint Programming (CP) is widely used to solve combinatorial problems, but its core process, namely constraint modelling, requires significant expertise and is considered to be a bottleneck for wider adoption. Aiming to alleviate this bottleneck, recent studies have explored using Large Language Models (LLMs) to transform combinatorial problem descriptions into executable constraint models. However, the existing evaluation datasets for constraint modelling are often limited to small, homogeneous, or domain-specific instances, which do not capture the diversity of real-world scenarios. This work addresses this gap by introducing CP-Bench, a novel benchmark that includes a diverse set of well-known combinatorial problems sourced from the CP community, structured explicitly for evaluating LLM-driven CP modelling. With this dataset, and given the variety of constraint modelling frameworks, we compare and evaluate the modelling capabilities of LLMs for three distinct constraint modelling systems, which vary in abstraction level and underlying syntax. Notably, the results show higher performance when modelling with a high-level Python-based framework. Additionally, we systematically evaluate the use of prompt-based and inference-time compute methods across different LLMs, which further increase accuracy, reaching up to 70% on this highly challenging benchmark.

Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from contextual features. This gives rise to predict-then-optimize problems, where a machine learning model predicts problem parameters that are then used to make decisions via optimization. A growing body of work on decision-focused learning (DFL) addresses this setting by training models specifically to produce predictions that maximize downstream decision quality, rather than accuracy. While effective, DFL is computationally expensive, because it requires solving the optimization problem with the predicted parameters at each loss evaluation. In this work, we address this computational bottleneck for linear optimization problems, a common class of problems in both DFL literature and real-world applications. We propose a solver-free training method that exploits the geometric structure of linear optimization to enable efficient training with minimal degradation in solution quality. Our method is based on the insight that a solution is optimal if and only if it achieves an objective value that is at least as good as that of its adjacent vertices on the feasible polytope. Building on this, our method compares the estimated quality of the ground-truth optimal solution with that of its precomputed adjacent vertices, and uses this as loss function. Experiments demonstrate that our method significantly reduces computational cost while maintaining high decision quality.

The integration of constraint programming (CP) together with machine learning (ML) has emerged as a promising direction for tackling complex decision-making and combinatorial optimization problems. While CP offers expressive modeling capabilities and formal guarantees, ML provides adaptive methods for learning from data and generalizing across instances. This survey presents a comprehensive overview of recent advances in combining CP and ML. We first show how ML has been used to improve the CP toolbox, both in modeling and in the efficiency of solving. Then, we examine how CP can support ML, particularly in providing structure, guarantees, and symbolic reasoning capabilities. Finally, we identify key open challenges inherent to such hybrid approaches and outline promising directions for future research. This survey provides a first conceptual and structured review of recent advancements in this emerging field, aiming to serve as a resource for practitioners and researchers in both the CP and ML communities. To keep the progress up to date, a curated list of references is hosted on an accompanying repository (https://github.com/corail-research/CPML-paper-list) and is open to community contributions.

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. does this partial solution satisfy your (unspecified) constraints or not. While interactive 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 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 queries to the most promising parts. 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 programming (CP) modeling languages, like MiniZinc, Essence and CPMpy, play a crucial role in making CP technology accessible to non-experts. Both solver-independent modeling frameworks and solvers themselves are complex pieces of software that can contain bugs, which undermines their usefulness. Mutational fuzz testing is a way to test complex systems by stochastically mutating input and verifying preserved properties of the mutated output. We investigate different mutations and verification methods that can be used on the constraint specifications directly. This includes methods proposed in the context of SMT problem specifications, as well as new methods related to global constraints, optimization, and solution counting/preservation. Our results show that such a fuzz testing approach improves the overall code coverage of a modeling system compared to only unit testing, and is able to find bugs in the whole toolchain, from the modeling language transformations themselves to the underlying solvers.

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.

Objective characterization of pain intensity is necessary under certain clinical conditions. The portable electroencephalogram (EEG) is a cost-effective assessment tool and lately, new methods using efficient analysis of related dynamic changes in brain activity in the EEG recordings proved that these can reflect the dynamic changes of pain intensity. In this paper, a novel method for automated assessment of pain intensity using EEG data is presented. EEG recordings from twenty-two (22) healthy volunteers are recorded with the Emotiv EPOC+ using the Cold Pressor Test (CPT) protocol. The relative power of each brain band's energy for each channel is extracted and the stochastic forest algorithm is employed for discrimination across five classes, depicting the pain intensity. Obtained results in terms of classification accuracy reached high levels (72.7%), which renders the proposed method suitable for automated pain detection and quantification of its intensity.

Smart Farming is a development that emphasizes on the use of modern technologies in the cyber-physical field management cycle. Technologies such as the Internet of Things (IoT) and Cloud Computing have accelerated the digital transformation of the conventional agricultural practices promising increased production rate and product quality. The adoption of smart farming though is hampered because of the lack of models providing guidance to practitioners regarding the necessary components that constitute IoT based monitoring systems. To guide the process of designing and implementing Smart farming monitoring systems, in this paper we propose a generic reference architecture model, taking also into consideration a very important non-functional requirement, the energy consumption restriction. Moreover, we present and discuss the technologies that incorporate the four layers of the architecture model that are the Sensor Layer, the Network Layer, the Service Layer and the Application Layer. A discussion is also conducted upon the challenges that smart farming monitoring systems face.

Emerging technologies such as Internet of Things (IoT) can provide significant potential in Precision Agriculture enabling the acquisition of real-time environmental data. IoT devices like Unmanned Aerial Vehicles (UAVs) equipped with cameras, sensors, and GPS receivers can deliver a variety of IoT services and applications related to fields management, by capturing images from great heights. However, there are many issues to be resolved before the effective use of UAVs in the agriculture domain, including the data collection and processing methods. There is still no standardized workflow and processes for most UAV-based applications for Precision Agriculture. In this paper, we summarize the data acquisition methods and technologies to acquire images in UAV-based Precision Agriculture and appoint the benefits and drawbacks of each one. We also review popular data analysis methods of remotely sensed imagery and discuss the outcomes of each method and its potential application in the farming operations.

In this paper, a novel stochastic approach for the induction of the decision trees in a tree-structured ensemble classifier is presented. The proposed algorithm is based on a stochastic process to induct each decision tree, assigning a probability for the selection of the split attribute in every tree node, designed in order to create strong and independent trees. A selection of 33 well-known classification datasets have been employed for the evaluation of the proposed algorithm, obtaining high classification results, in terms of Classification Accuracy, Average Sensitivity and Average Precision. Furthermore, a comparative study with Random Forest, Random Subspace and C4.5 is performed. The obtained results indicate the importance of the proposed algorithm, since it achieved the highest overall results in all metrics.

Diagnosis and staging of liver diseases are essential for the therapeutic efficacy of medication and treatment strategies. Measuring the Collagen Proportional Area (CPA) in liver biopsies recently becomes an effective tool for the assessment of fibrosis in liver tissues. State of the art image processing techniques are employed to analyze biopsy images, providing objective assessment of diseases severity. In current work a novel modification of K-means clustering is proposed for image segmentation of liver biopsies. More specifically, supervised restriction of centroids movement is utilized. In the first stage, a training set of images are employed to extract a hypercube for each class. Then, one centroid is initialized inside each hypercube and during the iterations of the clustering is allowed to move only inside the hypercube. For the evaluation of the proposed method 8 liver biopsy images are employed and classification results along with CPA values are computed for each image.