Drug discovery is a very time-consuming and costly endeavour due to its huge design space and to the lengthy and failure-fraught process of bringing a product to market. Automating the generation of candidate molecules exhibiting some of the desired properties can help. Among the standard formats to encode molecules, SMILES is a widespread string representation. We propose a constraint programming model showcasing the grammar constraint to express the design space of organic molecules using the SMILES notation. We show how some common physicochemical properties --- such as molecular weight and lipophilicity --- and structural features can be expressed as constraints in the model. We also contribute a weighted counting algorithm for the grammar constraint, allowing us to use a belief propagation heuristic to guide the generation. Our experiments indicate that such a heuristic is key to driving the search towards desired molecules.

Recent advances in ai have spurred interest in NeSy architectures that integrate neural and symbolic methods. In particular, combining a Constraint Programming (cp) model with a language model for constrained sequence generation tasks allows the neural component to capture domain knowledge while cp enforces structural constraints. In this paper we propose combining cp with a Masked Language Model (mlm) to perform Large Neighbourhood Search (lns). Unlike conventional left-to-right Large Language Models, mlm s can complete sequences with gaps in arbitrary positions, making them well-suited for this task. Meanwhile, lns provides a cp-based iterative framework to explore constrained subspaces whenever searching the whole space would be intractable. We evaluate NeSylns on tasks in constrained text generation and molecule discovery. Our experiments show that it can quickly generate many high-quality sentences and molecules, even for highly-constrained tasks.

Recent work has shown that classical planning tasks can be compactly factored into deterministic finite automata and solved optimally with constraint programming (CP). In this setting, finding a plan reduces to finding a word accepted by all automata through Regular constraints. So far, however, these automata have had to be carefully handcrafted from PDDL tasks. In this paper, we show that they can instead be generated automatically and used as the basis of CP models. We also show that the resulting framework is easily extensible with additional constraints from the planning literature that strengthen propagation. Our approach solves more tasks than the state of the art in end-to-end CP for classical planning in almost all domains.

Sequence models in machine learning often struggle to exhibit long-term structure. We consider this problem at inference time in the context of enforcing constraints that are not necessarily featured in the dataset on which the generative model was trained. The difficulty lies in imposing previously-unseen structure while staying close to the training dataset. It is particularly hard for long-term structure, which requires balancing foresight over many yet-to-be generated tokens and the immediacy of next-token predictions from the sequence model. We address this problem by introducing our neurosymbolic framework GeAI-BLAnC. The learned probabilities of the sequence model are mixed in with the marginal probabilities computed from a constraint programming / belief propagation framework applied to a constraint programming model expressing the desired structure. The next predicted token is then selected from the resulting probability distribution. Experiments in the context of molecule and music generation show that we can achieve the structure imposed post-training without straying too much from the structure of the dataset learned during training.

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.

The B2B Meeting Scheduling Optimization Problem (B2BSP) consists of scheduling a set of meetings between given pairs of participants to an event, minimizing idle time periods in participants' schedules, while taking into account participants’ availability and accommodation capacity. Therefore, it constitutes a challenging combinatorial problem in many real-world B2B events. This work presents a comparative study of several approaches to solve this problem. They are based on Constraint Programming (CP), Mixed Integer Programming (MIP) and Maximum Satisfiability (MaxSAT). The CP approach relies on using global constraints and has been implemented in MiniZinc to be able to compare CP, Lazy Clause Generation and MIP as solving technologies in this setting. A pure MIP encoding is also presented. Finally, an alternative viewpoint is considered under MaxSAT, showing the best performance when considering some implied constraints. Experimental results on real world B2B instances, as well as on crafted ones, show that the MaxSAT approach is the one with the best performance for this problem, exhibiting better solving times, sometimes even orders of magnitude smaller than CP and MIP.

This paper is a survey and an analysis of different ways of using deep learning (deep artificial neural networks) to generate musical content. We propose a methodology based on five dimensions for our analysis: Objective - What musical content is to be generated? Examples are: melody, polyphony, accompaniment or counterpoint. - For what destination and for what use? To be performed by a human(s) (in the case of a musical score), or by a machine (in the case of an audio file). Representation - What are the concepts to be manipulated? Examples are: waveform, spectrogram, note, chord, meter and beat. - What format is to be used? Examples are: MIDI, piano roll or text. - How will the representation be encoded? Examples are: scalar, one-hot or many-hot. Architecture - What type(s) of deep neural network is (are) to be used? Examples are: feedforward network, recurrent network, autoencoder or generative adversarial networks. Challenge - What are the limitations and open challenges? Examples are: variability, interactivity and creativity. Strategy - How do we model and control the process of generation? Examples are: single-step feedforward, iterative feedforward, sampling or input manipulation. For each dimension, we conduct a comparative analysis of various models and techniques and we propose some tentative multidimensional typology. This typology is bottom-up, based on the analysis of many existing deep-learning based systems for music generation selected from the relevant literature. These systems are described and are used to exemplify the various choices of objective, representation, architecture, challenge and strategy. The last section includes some discussion and some prospects.

The Business-to-Business Meeting Scheduling problem consists of scheduling a set of meetings between given pairs of participants to an event, while taking into account participants’ availability and accommodation capacity. A crucial aspect of this problem is that breaks in participants’ schedules should be avoided as much as possible. It constitutes a challenging combinatorial problem that needs to be solved for many real world brokerage events. In this paper we present a comparative study of Constraint Programming (CP), MixedInteger Programming (MIP) and Maximum Satisfiability (MaxSAT) approaches to this problem. The CP approach relies on using global constraints and has been implemented in MiniZinc to be able to compare CP, Lazy Clause Generation and MIP as solving technologies in this setting. We also present a pure MIP encoding. Finally, an alternative viewpoint is considered under MaxSAT, showing best performance when considering some implied constraints. Experiments conducted on real world instances, as well as on crafted ones, show that the MaxSAT approach is the one with the best performance for this problem, exhibiting better solving times, sometimes even orders of magnitude smaller than CP and MIP.

This paper addresses a class of two-stage robust optimization models with an exponential number of scenarios given implicitly. We apply Dantzig–Wolfe decomposition to exploit the structure of these models and show that the original problem reduces to a single-stage robust problem. We propose a Benders algorithm for the reformulated single-stage problem. We also develop a heuristic algorithm that dualizes the linear programming relaxation of the inner maximization problem in the reformulated model and iteratively generates cuts to shape the convex hull of the uncertainty set. We combine this heuristic with the Benders algorithm to create a more effective hybrid Benders algorithm. Because the master problem and subproblem in the Benders algorithm are mixed-integer programs, it is computationally demanding to solve them optimally at each iteration of the algorithm. Therefore, we develop novel stopping conditions for these mixed-integer programs and provide the relevant convergence proofs. Extensive computational experiments on a nurse planning problem and a two-echelon supply chain problem are performed to evaluate the efficiency of the proposed algorithms.

The quadratic multiknapsack problem consists of packing a set of items of various weights into knapsacks of limited capacities with profits being associated with pairs of items packed into the same knapsack. This problem has been solved by various heuristics since its inception, and more recently it has also been solved with an exact method. We introduce a generalization of this problem that includes pairwise conflicts as well as balance constraints, among other particularities. We present and compare constraint programming and integer programming approaches for solving this generalized problem. Summary of Contribution: The quadratic multiknapsack problem consists of packing a set of items of various weights into knapsacks of limited capacities -- with profits being associated with pairs of items packed into the same knapsack. This problem has been solved by various heuristics since its inception, and more recently it has also been solved with an exact method. We introduce a generalization of this problem which includes pairwise conflicts as well as balance constraints, among other particularities. We present and compare constraint programming and integer programming approaches for solving this generalized problem. The problem we address is clearly in the core of the operations research applications in which subsets have to be built and, in particular, we add the concept of fairness to the modeling and solution process by computationally evaluating techniques to take fairness into account. This is clearly at the core of computational evaluation of algorithms.

Reduction to a sequence of SAT problems has been a main approach for solving parallel planning problems for a long time. However, attempts at using constraint programming (CP) solvers for this purpose have witnessed relatively limited success. We show that existing CP formulations can deliver competitive results when a lazy clause generation solver (which is a hybrid of SAT and CP) is employed. This suggests promise for future cross-fertilization in SAT, CP, and AI planning.

The distinctive driving force of constraint programming (CP) to solve combinatorial problems has been a privileged access to problem structure through the high-level models it uses. We investigate a richer propagation medium for CP made possible by recent work on counting solutions inside constraints. Beliefs about individual variable-value assignments are exchanged between contraints and iteratively adjusted. Its advantage over standard belief propagation is that the higher-level models do not tend to create as many cycles, which are known to be problematic for convergence. We find that it significantly improves search guidance.

Decision trees are among the most popular classification models in machine learning. Traditionally, they are learned using greedy algorithms. However, such algorithms have their disadvantages: it is difficult to limit the size of the decision trees while maintaining a good classification accuracy, and it is hard to impose additional constraints on the models that are learned. For these reasons, there has been a recent interest in exact and flexible algorithms for learning decision trees. In this paper, we introduce a new approach to learn decision trees using constraint programming. Compared to earlier approaches, we show that our approach obtains better performance, while still being sufficiently flexible to allow for the inclusion of constraints. Our approach builds on three key building blocks: (1) the use of AND/OR search, (2) the use of caching, (3) the use of the CoverSize global constraint proposed recently for the problem of itemset mining. This allows our constraint programming approach to deal in a much more efficient way with the decompositions in the learning problem.

The combinatorial problems that constraint programming typically solves belong to the class of NP-hard problems. The AI planning community focuses on even harder problems: for example, classical planning is PSPACE-hard. A natural and well-known constraint programming approach to classical planning solves a succession of fixed plan-length problems, but with limited success. We revisit this approach in light of recent progress on general-purpose branching heuristics. We conduct an empirical comparison of our proposal against state-of-the-art planners.

Counting solutions for a combinatorial problem has been identified as an important concern within the Artificial Intelligence field. It is indeed very helpful when exploring the structure of the solution space. In this context, this paper revisits the computation process to count solutions for the global cardinality constraint in the context of counting-based search. It first highlights an error and then presents a way to correct the upper bound on the number of solutions for this constraint.

The distinctive driving force of constraint programming to solve combinatorial problems has been a privileged access to problem structure through the high-level models it uses. From that exposed structure in the form of so-called global constraints, powerful inference algorithms have shared information between constraints by propagating it through shared variables’ domains, traditionally by removing unsupported values. This paper investigates a richer propagation medium made possible by recent work on counting solutions inside constraints. Beliefs about individual variable-value assignments are exchanged between contraints and iteratively adjusted. It generalizes standard support propagation and aims to converge to the true marginal distributions of the solutions over individual variables. Its advantage over standard belief propagation is that the higher-level models featuring large-arity (global) constraints do not tend to create as many cycles, which are known to be problematic for convergence. The necessary architectural changes to a constraint programming solver are described and an empirical study of the proposal is conducted on its implementation. We find that it provides close approximations to the true marginals and that it significantly improves search guidance.

To solve combinatorial problems, Constraint Programming builds high-level models that expose much of the structure of the problem. The distinctive driving force of Constraint Programming has been this direct access to problem structure. This has been key to the design of powerful filtering algorihms but we could do much more. Considering the set of solutions to each constraint as a multivariate discrete distribution opens the door to more structure-revealing computations that may significantly change this solving paradigm. As a result we could improve our ability to solve combinatorial problems and our understanding of the structure of practical problems.

Branching heuristics based on counting solutions in constraints have been quite good at guiding search to solve constraint satisfaction problems. But do they perform as well for constraint optimization problems? We propose an adaptation of counting-based search for optimization, show how to modify solution density computation for some of the most frequently-occurring constraints, and empirically evaluate its performance on several benchmark problems.

This paper presents an efficient algorithm for an integrated operating room planning and scheduling problem. It combines the assignment of surgeries to operating rooms and scheduling over a short-term planning horizon. This integration results in more stable planning through consideration of the operational details at the scheduling level, and this increases the chance of successful implementation. We take into account the maximum daily working hours of surgeons, prevent the overlapping of surgeries performed by the same surgeon, allow time for the obligatory cleaning when switching from infectious to noninfectious cases, and respect the surgery deadlines. We formulate the problem using a mathematical programming model and develop a branch-and-price-and-cut algorithm based on a constraint programming model for the subproblem. We also develop dominance rules and a fast infeasibility-detection algorithm based on a multidimensional knapsack problem to improve the efficiency of the constraint programming model. The computational results show that our method has an average optimality gap of 2.81% and significantly outperforms a compact mathematical formulation in the literature.

One key challenge in statistical relational learning (SRL) is scalable inference. Unfortunately, most real-world problems in SRL have expressive models that translate into large grounded networks, representing a bottleneck for any inference method and weakening its scalability. In this paper we introduce Preference Relaxation (PR), a two-stage strategy that uses the determinism present in the underlying model to improve the scalability of relational inference. The basic idea of PR is that if the underlying model involves mandatory (i.e. hard) constraints as well as preferences (i.e. soft constraints) then it is potentially wasteful to allocate memory for all constraints in advance when performing inference. To avoid this, PR starts by relaxing preferences and performing inference with hard constraints only. It then removes variables that violate hard constraints, thereby avoiding irrelevant computations involving preferences. In addition it uses the removed variables to enlarge the evidence database. This reduces the effective size of the grounded network. Our approach is general and can be applied to various inference methods in relational domains. Experiments on real-world applications show how PR substantially scales relational inference with a minor impact on accuracy.

Many combinatorial problems require that their solutions achieve a certain balance of given features. For this important aspect of modeling, the spread and deviation constraints have been proposed in Constraint Programming to express balance among a set of variables by constraining their mean and overall deviation from the mean. To our knowledge, the only practical filtering algorithms known for these constraints achieve bounds consistency. In this paper we improve that filtering by presenting an efficient domain consistency algorithm that applies to both constraints. We also extend it to count solutions so that it can be used in counting-based search, a generic and effective family of branching heuristics that free the user from having to write problem-specific search heuristics. We provide a time complexity analysis of our contributions and empirically evaluate them on benchmark problems.

This article presents a review and a classification of interactive optimization methods. These interactive methods are used for solving optimization problems. The interaction with an end user or decision maker aims at improving the efficiency of the optimization procedure, enriching the optimization model, or informing the user regarding the solutions proposed by the optimization system. First, we present the challenges of using optimization methods as a tool for supporting decision making, and we justify the integration of the user in the optimization process. This integration is generally achieved via a dynamic interaction between the user and the system. Next, the different classes of interactive optimization approaches are presented. This detailed review includes trial and error, interactive reoptimization, interactive multiobjective optimization, interactive evolutionary algorithms, human-guided search, and other approaches that are less well covered in the research literature. On the basis of this review, we propose a classification that aims to better describe and compare interaction mechanisms. This classification offers two complementary views on interactive optimization methods. The first perspective focuses on the user’s contribution to the optimization process, and the second concerns the components of interactive optimization systems. Finally, on the basis of this review and classification, we identify some open issues and potential perspectives for interactive optimization methods.

Search-based approaches have been extensively applied to solve the problem of software test-data generation. Yet, test-data generation for object-oriented programming (OOP) is challenging due to the features of OOP, e.g., abstraction, encapsulation, and visibility that prevent direct access to some parts of the source code. To address this problem we present a new automated search-based software test-data generation approach that achieves high code coverage for unit-class testing. We first describe how we structure the test-data generation problem for unit-class testing to generate relevant sequences of method calls. Through a static analysis, we consider only methods or constructors changing the state of the class-under-test or that may reach a test target. Then we introduce a generator of instances of classes that is based on a family of means-of-instantiation including subclasses and external factory methods. It also uses a seeding strategy and a diversification strategy to increase the likelihood to reach a test target. Using a search heuristic to reach all test targets at the same time, we implement our approach in a tool, JTExpert, that we evaluate on more than a hundred Java classes from different open-source libraries. JTExpert gives better results in terms of search time and code coverage than the state of the art, EvoSuite, which uses traditional techniques.

Verification has become one of the main bottlenecks in the design process of embedded systems, particularly for Multiprocessor Systems-on-Chip (MPSoCs). Efficiently proving the correctness of a design is of extreme importance to reduce cost and time-to-market. Simulation is a common verification method, but complex systems usually require long simulation times. This work advocates Constraint Programming (CP) as a powerful tool for the verification of performance metrics of MPSoCs. Our methodology was evaluated using streaming applications mapped onto a target MPSoC. The resulting constraint-based scheduling problem allowed us to identify performance constraint violations in a fraction of the time required by simulation-based verification.

Designing a search heuristic for constraint programming that is reliable across problem domains has been an important research topic in recent years. This paper concentrates on one family of candidates: counting-based search. Such heuristics seek to make branching decisions that preserve most of the solutions by determining what proportion of solutions to each individual constraint agree with that decision. Whereas most generic search heuristics in constraint programming rely on local information at the level of the individual variable, our search heuristics are based on more global information at the constraint level. We design several algorithms that are used to count the number of solutions to specific families of constraints and propose some search heuristics exploiting such information. The experimental part of the paper considers eight problem domains ranging from well-established benchmark puzzles to rostering and sport scheduling. An initial empirical analysis identifies heuristic maxSD as a robust candidate among our proposals.eWe then evaluate the latter against the state of the art, including the latest generic search heuristics, restarts, and discrepancy-based tree traversals. Experimental results show that counting-based search generally outperforms other generic heuristics.

A tree search strategy is said to be adaptive when it dynamically identifies which areas of the tree are likely to contain good solutions, using information that is gathered during the search process. This study shows how an adaptive approach can be used to enhance the efficiency of the coordination process of an industrial supply chain. The result is a new adaptive method (called the adaptive discrepancy search), intended for search in nonbinary trees, and that is exploitable in a distributed optimization context. For the industrial case studied (a supply chain in the forest products industry), this allowed reducing nearly half the time needed to obtain the best solution in comparison with a standard nonadaptive method. The method has also been evaluated for use with synthesized problems in order to validate the results that are obtained and to illustrate different properties of the algorithm.

In this paper, we propose and compare two complementary heuristic approaches for solving the P-forest problem. The first one is a Greedy Randomized Adaptive Search Procedure (GRASP), and the second one is an interactive heuristic approach. Contrary to the GRASP, which is a fully automated approach, in the interactive heuristic the user contributes in a cooperative manner to the optimization process. The objective is to exploit the problem-domain expertise of the user in order to generate more realistic solutions that integrate aspects not captured by the objective function. These heuristics were implemented on a decision support system for solving a P-forest problem in the domain of forestry. We present experimental results on real problem instances of access road networks design. A comparison between manual planning and the two heuristics shows clear advantages for using the proposed interactive approach.

Distributed constraint optimization is increasingly used for problem solving by multiple agents. However, there are situations where the system is made up of heterogeneous agents, for which the context, the structure, and the business rules define the interactions that are possible between them. As an example, supply chains are made up of interdependent business units having some form of customer-supplier hierarchical relationships. The coordination space for these hierarchical situations can be described as a tree. Therefore, we propose a distributed algorithm (MacDS) that performs discrepancy-based search which is known to perform well for centralized problems. The proposed algorithm is complete and aims at producing good solutions in a short amount of time. It allows concurrent computation and is tolerant to message delays. It has been evaluated using real industrial supply chain problems, for which it showed good performance.