Constraint Programming Research Articles

Offline reinforcement learning for learning to dispatch for job shop scheduling

Abstract The Job Shop Scheduling Problem (JSSP) is a complex combinatorial optimization problem. While online Reinforcement Learning (RL) has shown promise by quickly finding acceptable solutions for JSSP, it faces key limitations: it requires extensive training interactions from scratch leading to sample inefficiency, cannot leverage existing high-quality solutions from traditional methods like Constraint Programming (CP), and require simulated environments to train in, which are impracticable to build for complex scheduling environments. We introduce Offline Learned Dispatching (Offline-LD), an offline reinforcement learning approach for JSSP, which addresses these limitations by learning from historical scheduling data. Our approach is motivated by scenarios where historical scheduling data and expert solutions are available or scenarios where online training of RL approaches with simulated environments is impracticable. Offline-LD introduces maskable variants of two Q-learning methods, namely, Maskable Quantile Regression DQN (mQRDQN) and discrete maskable Soft Actor-Critic (d-mSAC), that are able to learn from historical data, through Conservative Q-Learning (CQL), whereby we present a novel entropy bonus modification for d-mSAC, for maskable action spaces. Moreover, we introduce a novel reward normalization method for JSSP in an offline RL setting. Our experiments demonstrate that Offline-LD outperforms online RL on both generated and benchmark instances when trained on only 100 solutions generated by CP. Notably, introducing noise to the expert dataset yields comparable or superior results to using the expert dataset, with the same amount of instances, a promising finding for real-world applications, where data is inherently noisy and imperfect.

Constraint Programming for Automatic User Interface Construction

Constraint Programming for Automatic User Interface Construction

Conflict coordination method for complex product performance specifications based on game theory

Abstract The proper specifying performance specifications of a complex product under design is the first key step and prerequisite for a successful product design, which determines the length of the design cycle and the success or failure of the design. Usually, a set of design parameters can contribute to a set of complex product performance specifications in a complex and conflict way, resulting in a set of conflicting performance specifications, coupled with a set of conflicting design parameters. Therefore, to proper determine a set of performance specifications' values, how to coordinate conflicting design parameters' values to have well-balanced performance specifications' values is a challenging problem in complex product design. This paper proposes a conflict coordination method for determining performance specifications' values based on game theory. The method has a novel way to identify the conflicts among design parameters against performance specifications based on constraint satisfaction problem solving and sensitivity analysis. Among identified conflicting design parameters, a game-theory-based coordination model for best reasonably setting up the conflicting design parameters is developed for obtaining well-balanced performance specifications. This coordination model incorporates non-cooperative and master-slave gaming mechanism, and it is solved by a hybrid game balanced solving algorithm based on elite information exchange strategy and NSGA-II. The feasibility and effectiveness of the proposed method are verified with a case study.

Smart Classroom Scheduling and Resource Optimization for Educational Institutions: Integrating AI and Multi-Objective Decision Support

The demand for high-quality education delivery in increasingly dynamic and competitive educational markets has intensified the need for intelligent and adaptive scheduling systems. Manual classroom scheduling methods, which rely on human decision-making, often fail to optimize critical resources such as classrooms, teachers, and student time, leading to inefficiencies and economic losses. This paper proposes a comprehensive Smart Classroom Scheduling and Optimization System (LMSOPT) that leverages Artificial Intelligence (AI), advanced time-series forecasting, constraint-based multi-objective optimization, and real-time data integration. The proposed system employs Long Short-Term Memory (LSTM) neural networks for highly accurate demand forecasting, alongside heuristic and metaheuristic optimization algorithms such as Constraint Programming (CP), Genetic Algorithms (GA), and Tabu Search. The system aims to dynamically balance multiple conflicting objectives: maximizing classroom occupancy rates, minimizing student waiting times, and aligning teacher availability with student preferences. The expected contributions are multifold: significant operational cost savings, measurable improvements in resource utilization, increased student satisfaction, and the creation of an extensible research framework for AI applications in education management. The study aligns with national strategies for digital transformation and supports the vision of data-driven decision-making in educational administration. Empirical results and comparative analyses are presented to validate the system’s effectiveness and demonstrate its replicability for institutions of various scales.

Quadratic unconstrained binary optimization and constraint programming approaches for lattice-based cyclic peptide docking

The peptide-protein docking problem is an important problem in structural biology that facilitates rational and efficient drug design. In this work, we explore modeling and solving this problem with the quantum-amenable quadratic unconstrained binary optimization (QUBO) formalism. Our work extends recent efforts by incorporating the objectives and constraints associated with peptide cyclization and peptide-protein docking in the two-particle model on a tetrahedral lattice. We propose a “resource efficient” QUBO encoding for this problem, and baseline its performance with a novel constraint programming (CP) approach. We implement an end-to-end framework that enables the evaluation of our methods on instances from the Protein Data Bank (PDB). Our results show that the QUBO approach, using a classical simulated annealing solver, is able to find feasible conformations for problems with up to 6 peptide residues and 34 target protein residues (PDB 3WNE, 5LSO), but has trouble scaling beyond this problem size. In contrast, the CP approach can solve the largest instance in our test set, containing 11 peptide residues and 49 target protein residues (PDB 2F58). We conclude that while QUBO can be used to successfully tackle this problem, its scaling limitations and the strong performance of the CP method suggest that it may not be the best choice.

A Flexible Scheduling Framework for Repetitive Construction Projects Based on Constraint Programming

A Flexible Scheduling Framework for Repetitive Construction Projects Based on Constraint Programming

Balancing human–robot collaborative assembly lines: A constraint programming approach

Balancing human–robot collaborative assembly lines: A constraint programming approach

Quantum Concolic Testing

This paper presents the first concolic testing framework explicitly designed for quantum programs. The framework introduces quantum constraint generation methods for quantum control statements that quantify quantum states and offers a symbolization method for quantum variables. Based on this framework, we generate path constraints for each concrete execution path of a quantum program. These constraints guide the exploration of new paths, with a quantum constraint solver determining outcomes to create novel input samples, thereby enhancing branch coverage. Our framework has been implemented in Python and integrated with Qiskit for practical evaluation. Experimental results show that our concolic testing framework improves branch coverage, generates high-quality quantum input samples, and detects bugs, demonstrating its effectiveness and efficiency in quantum programming and bug detection. Regarding branch coverage, our framework achieves more than 74.27% on quantum programs with under 5 qubits.

FANDANGO: Evolving Language-Based Testing

Language-based fuzzers leverage formal input specifications (languages) to generate arbitrarily large and diverse sets of valid inputs for a program under test. Modern language-based test generators combine grammars and constraints to satisfy syntactic and semantic input constraints. ISLA, the leading input generator in that space, uses symbolic constraint solving to solve input constraints. Using solvers places ISLA among the most precise fuzzers but also makes it slow. In this paper, we explore search-based testing as an alternative to symbolic constraint solving. We employ a genetic algorithm that iteratively generates candidate inputs from an input specification, evaluates them against defined constraints, evolving a population of inputs through syntactically valid mutations and retaining those with superior fitness until the semantic input constraints are met. This evolutionary procedure, analogous to natural genetic evolution, leads to progressively improved inputs that cover both semantics and syntax. This change boosts the efficiency of language-based testing: In our experiments, compared to ISLA, our search-based FANDANGO prototype is faster by one to three orders of magnitude without sacrificing precision. The search-based approach no longer restricts constraints to constraint solvers' (miniature) languages. In FANDANGO, constraints can use the whole Python language and library. This expressiveness gives testers unprecedented flexibility in shaping test inputs. It allows them to state arbitrary goals for test generation: ''Please produce 1,000 valid test inputs where the voltage field follows a Gaussian distribution but never exceeds 20 mV.''

On the Replica Symmetric Solution in General Diluted Spin Glasses

ABSTRACTWe present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random ‐uniform hypergraphs with sparsity parameter . Our result shows that there exist two key regimes in which the model exhibits replica symmetry and the free energy can be explicitly represented as the evaluation of an energy functional at the unique fixed point of a recursive distributional equation. One is called the high‐temperature regime, where the temperature and the sparsity parameter are essentially inversely proportional to each other; the other is the subcritical regime defined as . In particular, the fact that the second regime is independent of the temperature parameter further allows us to deduce an analogous representation of the ground state energy in the subcritical regime. Along the way, we revisit several well‐known formulas and also derive new ones for the free and ground state energies in the constraint satisfaction problem, Potts model, XY model, and continuous hardcore model.

A Heuristic Constraint Programming Method for the p-Median Problem With Distance Constraints

In a facility location problem, we seek to locate a set of facilities in an area, where demand points (clients) may be present, so that some criterion is optimized. A well-known facility location problem is the p-median problem, where we seek to minimize the sum of distances between demand points and their nearest facility. 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 integer linear programming and constraint programming (CP) models and implement them in Gurobi and OR-Tools, respectively. Then, we describe a greedy heuristic that can be used to prune branches during a search within an incomplete CP solver. We also introduce a number of domain-specific value ordering heuristics that can be applied within such a solver. The developed method is evaluated under different problem generation models, and compared to Gurobi and OR-Tools. The results demonstrate that our method is more robust than the two complete solvers, significantly outperforming either of them in certain classes of problems, both in terms of run times and the quality of the solutions found.

Actor‐Critic Optimization Based Adaptive Task Scheduling Using Deep Double Dueling Q Network for Heterogeneous Cloud Environments

ABSTRACTIn the rapidly evolving domain of cloud computing, the efficient scheduling of dependent tasks is critical for optimizing resource utilization and achieving key objectives such as minimizing latency and maximizing throughput. This paper presents the Actor‐Critic Optimization based Adaptive Task Scheduling using Deep Double Dueling Q Network (ACTS‐D3QN) in heterogeneous cloud environments enhances cloud task scheduling by incorporating advanced machine learning and optimization techniques. The D3QN framework is structured as an actor‐critic model, where the actor component handles task scheduling and resource allocation, and the critic component refines these schedules. The actor component of D3QN integrates a Proportional Integral Derivative (PID) Controller for adaptive scheduling, ensuring real‐time optimization of resource allocation while adhering to strict deadlines and dynamically managing workloads. Additionally, the system introduces a Dynamic Data Placement Algorithm with Predictive Caching (DDPPC), aimed at improving data locality and minimizing data transfer times. To balance operational costs with performance, a Modified NSGA‐III algorithm is employed in the critic component of D3QN for multi‐objective optimization. Furthermore, constraint programming is leveraged for efficient task‐to‐resource matching. Experimental results demonstrate that the ACTS‐D3QN method achieves significant improvements, including a 22.14% reduction in makespan and a 20.0% increase in throughput, thereby validating its effectiveness in dynamic cloud environments.

QSF: Multi-objective Optimization Based Efficient Solving for Floating-Point Constraints

Floating-point constraint solving is challenging due to the complex representation and non-linear computations. Search-based constraint solving provides an effective method for solving floating-point constraints. In this paper, we propose QSF to improve the efficiency of search-based solving for floating-point constraints. The key idea of QSF is to model the floating-point constraint solving problem as a multi-objective optimization problem. Specifically, QSF considers both the number of unsatisfied constraints and the sum of the violation degrees of unsatisfied constraints as the objectives for search-based optimization. Besides, we propose a new evolutionary algorithm in which the mutation operators are specially designed for floating-point numbers, aiming to solve the multi-objective problem more efficiently. We have implemented QSF and conducted extensive experiments on both the SMT-COMP benchmark and the benchmark from real-world floating-point programs. The results demonstrate that compared to SOTA floating-point solvers, QSF achieved an average speedup of 15.72X under a 60-second timeout and an impressive 87.48X under a 600-second timeout on the first benchmark. Similarly, on the second benchmark, QSF delivered an average speedup of 22.44X and 29.23X, respectively, under the two timeout configurations. Furthermore, QSF has also enhanced the performance of symbolic execution for floating-point programs.

Fast Hypertree Decompositions via Linear Programming: Fractional and Generalized

Efficient query evaluation in databases and solving constraint satisfaction problems (CSPs) are crucial for improving performance in many real-world applications, from large-scale data management to decision-making systems. These problems naturally admit hypergraph representations, and are efficiently solvable using hypertree decomposition techniques, when the decomposition width is small. However, these techniques require finding small-width decompositions efficiently. This remains a significant challenge despite research from both the database and theory communities. In this work we present Ralph (Randomized Approximation using Linear Programming for Hypertree-Decompositions), a fast algorithm to compute low width fractional and generalized hypertree decompositions for input hypergraphs, as well as lower bounds for these widths. We build on the recent breakthrough by Korchemna et al. [FOCS 2024], which introduced the first polynomial time approximation algorithm for fractional (generalized) hypertree width. Our approach combines this theoretical advancement with practical heuristic improvements utilizing (mixed-integer) linear programs. Along the way, we present new algorithms with strong theoretical guarantees. Through empirical evaluation on the nearly 3700 instances of HyperBench, a well established benchmark suite for hypertree decompositions, we find near optimal decompositions for all previously solved instances and low width decompositions for all 500 previously unsolved instances, effectively pushing state-of-the-art.

Solving Floating-Point Constraints with Continuous Optimization

The Satisfiability Modulo Theory (SMT) problem over floating-point operations presents a significant challenge. State-of-the-art SMT solvers often run into difficulties when dealing with large, complex floating-point constraints. Recently, a new approach to floating-point constraint solving emerges, utilizing mathematical optimization (MO) methods as an engine of their solving approach. Despite the novelty, these methods can fall short in both effectiveness and efficiency due to issues of the translated functions (e.g., discontinuity) and inherent limitations of their underlying MO method (e.g., imprecise search process, scalability issues). Driven by these weaknesses of prior solvers, this paper introduces a new MO-based approach that is shown highly potent in solving floating-point constraints. Specifically, on the benchmarks of JFS (a recent solver based on fuzzing), Grater, a realization of our approach, solves as many constraints as Bitwuzla and one more than CVC5 but runs over 10 times faster and over 40 times faster than Bitwuzla and CVC5 in median solving time across all benchmarks. It is worth mentioning that Bitwuzla and CVC5 are the strongest solvers for floating-point constraints according to results of the annual international SMT solver competition (SMT-COMP). Together, they have won all gold medals for QF_FPArith and FPArith divisions, which focus on floating-point constraints solving, over the past three years. To further evaluate Grater, we select over 100 most difficult benchmarks from the FP SMT-LIB, a logic regularly used in SMT-COMP. The difficulty is measured by the complexity of the composition (e.g., number of variables, clauses) and the interdependencies within constraints. Grater again solves the same number of constraints as Bitwuzla and CVC5 while running over 10 times faster than both solvers in average solving time, and over 50 times (resp. 30 times) faster than Bitwuzla (resp. CVC5) in median solving time. We release the source code of Grater, along with all evaluation data, including detailed comparisons of Grater against each baseline solver (i.e., Z3, CVC5, Bitwuzla, JFS, XSat, and CoverMe), at https://github.com/grater-exp/grater-experiment to facilitate reproducibility.

Thrust: A Prophecy-Based Refinement Type System for Rust

We introduce Thrust, a new verification tool for ensuring functional correctness in Rust, distinguished by its strengths in automated verification, including the synthesis of inductive invariants for loops and recursive functions. Thrust is built on a novel dependent refinement type system for Rust and refinement type inference techniques based on Constrained Horn Clause (CHC) solvers. Leveraging advantages of the type system, Thrust also supports semi-automated verification utilizing user type annotations to complement CHC solvers in cases where automatic constraint solving is unsuccessful, as well as modular verification at the function and subexpression levels. Thrust also achieves precise verification, especially for programs involving pointer aliasing and borrowing, without sacrificing the benefits of automated verification, by incorporating the notion of prophecy into the refinement type system: it not only enables strong updates by leveraging the “aliasing XOR mutability” guarantee provided by Rust’s type system, but also achieves propagation of update information to the original owner upon mutable borrow release through the use of a prophecy variable. Incorporating prophecy into a refinement type system is itself challenging and requires certain tricks, as discussed in this paper, making a theoretical contribution and paving the way for further research into prophecy-based refinement type systems. While our type system addresses the challenge, we keep it simple for extensibility, specifically by delegating the guarantee of “aliasing XOR mutability,” and, more technically, the “well-borrowedness” of the program in the sense of the stacked borrows aliasing model, to Rust’s type system, allowing us to focus on reasoning about functional correctness and propagating update information through prophecy variables. Compared to RustHorn, another automated verification tool based on prophecy, our approach leverages the strengths of refinement types to support modular verification, higher-order functions, and refinement of data stored in algebraic data structures. We implemented Thrust, a refinement type inference tool as a plugin for the Rust compiler, and evaluated it using RustHorn benchmarks, as well as additional new benchmarks, including those that are beyond the capabilities of RustHorn and other semi-automated verification tools, obtaining promising results.

Relational Abstractions Based on Labeled Union-Find

We introduce a new family of abstractions based on a data structure that we call labeled union-find , an extension of the classic efficient union-find data structure where edges carry labels. These labels have a composition operation that obey the group axioms. Like union-find, the labeled version can efficiently compute the transitive closure of a relation, but it is not limited to equivalence relations; it can represent any injective transformation between equivalence classes, which includes two-variables per equality (TVPE) constraints of the form y = a × x + b . Using abstract interpretation theory, we study the properties deriving from the use of abstract relations as labels, and the combination of labeled union-find with other representations of constraints, allowing both improvements in precision and simplification of existing constraints. Due to its efficiency, the labeled union-find abstractions could find many uses; we use it in two use cases, program analysis based on abstract interpretation and constraint solving for SMT, with encouraging preliminary results.

A Uniform Framework for Handling Position Constraints in String Solving

We introduce a novel decision procedure for solving the class of position string constraints, which includes string disequalities, ¬prefixof, ¬suffixof, str.at, and ¬str.at. These constraints are generated frequently in almost any application of string constraint solving. Our procedure avoids expensive encoding of the constraints to word equations and, instead, reduces the problem to checking conflicts on positions satisfying an integerconstraint obtained from the Parikh image of a polynomial-sized finite automaton with a special structure. By the reduction to counting, solving position constraints becomes NP-complete and for some cases even falls into PTime. This is much cheaper than the previously used techniques, which either used reductions generating word equations and length constraints (for which modern string solvers use exponential-space algorithms) or incomplete techniques. Our method is relevant especially for automata-based string solvers, which have recently achieved the best results in terms of practical efficiency, generality, and completeness guarantees. This work allows them to excel also on position constraints, which used to be their weakness. Besides the efficiency gains, we show that our framework may be extended to solve a large fragment of ¬contains (in NExpTime), for which decidability has been long open, and gives a hope to solve the general problem. Our implementation of the technique within the Z3-Noodler solver significantly improves its performance on position constraints.

Integrating Nurse Preferences Into AI-Based Scheduling Systems: Qualitative Study

BackgroundNurse scheduling is a complex challenge in health care, impacting both patient care quality and nurse well-being. Traditional scheduling methods often fail to consider individual preferences, leading to dissatisfaction, burnout, and high turnover. Inadequate scheduling practices, including restricted autonomy and lack of transparency, can further reduce nurse morale and negatively affect patient outcomes. Research suggests that participative scheduling approaches incorporating nurse preferences can improve job satisfaction. Artificial intelligence (AI) and mathematical optimization methods, such as mixed-integer programming (MIP), constraint programming (CP), genetic programming (GP), and reinforcement learning (RL), offer potential solutions to optimize scheduling and address these challenges.ObjectiveThis study aims to develop a framework for integrating nurses’ preferences into AI-supported scheduling methods by gathering qualitative insights from nurses and supervisors and mapping these to mathematical and AI-based scheduling techniques.MethodsFocus group interviews were conducted with 21 participants (nurses, supervisors, and temporary staff) from Swiss health care institutions to understand experiences and preferences related to staff scheduling. Qualitative data were analyzed using open and axial coding to extract key themes. These themes were then mapped to AI methodologies, including MIP, CP, GP, and RL, based on their suitability to address identified scheduling challenges.ResultsThe study revealed key priorities in nurse scheduling. Fairness and participation were highlighted by 85% (18/21) of interview participants, emphasizing the need for transparent and inclusive scheduling. Flexibility and autonomy were preferred by 76% (16/21), favoring shift swaps and self-scheduling. AI expectations were mixed: 62% (13/21) saw potential for improved efficiency and fairness, while 38% (8/21) expressed concerns over reliability and loss of human oversight. Mapping to AI methods showed MIP as effective for fair shift allocation, CP for complex rule-based conditions, GP for handling unforeseen absences, and RL for dynamic schedule adaptation in hospital environments. A preliminary AI implementation of MIP in a training hospital unit (35 staff members) showed how to design a system from a mathematical perspective.ConclusionsAI-supported scheduling systems can significantly enhance fairness, transparency, and efficiency in nurse scheduling. However, concerns regarding AI reliability, adaptability to individual needs, and human oversight must be addressed. A hybrid approach integrating AI recommendations with human decision-making may be optimal. Future research should explore the broader implementation of AI-driven scheduling models and assess their impact on nurse satisfaction and patient outcomes over time.

Beyond Kanban: POLCA-Constrained Scheduling for Job Shops

This study investigates the integration of finite capacity scheduling with POLCA-based workload control in high-mix, low-volume production environments. We propose a proactive scheduling approach that embeds POLCA constraints into a constraint programming (CP) model, aiming to reconcile the trade-offs between utilization efficiency and system responsiveness. The proposed methodology is evaluated in two phases. First, a simplified job shop simulation compares a traditional reactive POLCA implementation with the CP-based proactive approach under varying system configurations, demonstrating significant reductions in lead times, tardiness, and deadlock occurrences. Second, an industrial case study in an aerospace manufacturing firm validates the practical applicability of the approach by retrospectively comparing the CP model against an existing commercial scheduler. The results underscore that the integrated framework not only enhances scheduling performance through improved workload control but also provides a more stable operational environment.