We address the problem of scheduling non-preemptive jobs on identical parallel machines under a single renewable resource constraint, with the objective of minimizing the makespan. This setting captures relevant applications in energy-aware production planning, where energy usage must not exceed a fixed limit at any time. We introduce two mathematical formulations and propose an exact algorithm that integrates a branch-and-bound, advanced bounding techniques, and a constraint programming model. Extensive computational experiments on two benchmark sets from the literature show that the proposed approach outperforms existing exact methods, solving more instances to optimality and achieving consistently smaller optimality gaps within limited computation time. • We develop advanced bounds via column generation and metaheuristic based methods. • We introduce a new B&B with dynamic programming cuts and timetabling based pruning. • We present an exact algorithm using binary search with B&B, CP, and known methods. • We compare MILP and CP models for parallel machines with a single renewable resource. • We report superior computational results on two benchmark sets from the literature.

Constraint programming approaches for stochastic Resource-Constrained Project Scheduling Problem subject to disruptions

Classical scheduling problems such as Unrelated Parallel Machine Scheduling (UPMSP), Flexible Job Shop Scheduling (FJSP), and Resource-Constrained Project Scheduling (RCPSP) each capture important aspects of industrial scheduling, but real-world applications often require a combination of constraints from several of these formulations and additional requirements that are typically not supported in standard models. We propose a Generalized Parallel Machine Scheduling (GPMS) framework that, to the best of our knowledge, is the most general machine scheduling formulation to date and unifies machine eligibility with machine-dependent processing times, sequence- and machine-dependent setup times, rich temporal constraints, and secondary-resource constraints in a single formulation. Temporal constraints include machine calendars and precedence relations with min/max time lags and conditional machine eligibilities. Secondary resources are modeled with capacity calendars and pulse or step demands. To model and solve this generalized problem, we investigate a constraint programming approach and propose two CP models: a solver-agnostic high-level model and an interval-variable model. We also develop a randomized construction heuristic that finds feasible, high-quality schedules even for large and highly constrained instances; these schedules serve as warm starts for the interval-variable model. We evaluate 216 generated and 91 real-world instances, comparing the interval-variable model to the solver-agnostic model and to the construction heuristic. The warm-start interval-variable model attains the best objective on the majority of both generated and real-world instances, proves optimality for many small-to-medium instances, and finds near-optimal schedules for most industrial instances within a one-hour time limit. We release all models, code, and instances to support reproducible research.

Enhancing multi-agent deep reinforcement learning for flexible job-shop scheduling through constraint programming

Microplates are widely used for high-throughput experiments but are vulnerable to systematic plate effects. Careful placement of materials on a microplate can counteract them. While some tools exist, they often rely on randomization, are proprietary, and web-based, raising privacy concerns. PLAID and COMPD are two constraint programming (CP) models that produce higher quality layouts than randomization. However, they require MiniZinc and CP expertise, with no built-in visualization. MPLACE addresses these barriers as an open-source, Python-based GUI. MPLACE streamlines the workflow with both models by providing convenient data entry, multiple layout configurations, saving, loading, and visualization capabilities.

Mixed-integer linear programming and constraint programming formulations for solving the three-stage no-wait surgery scheduling problem

This paper introduces a novel algorithm for building run-time reconfigurable single constant multipliers based on addition/subtraction, fixed bit-shift, and multiplexing. An exhaustive exploration of a wide design space using a mix of constraint programming, depth-first search, and branch-and-prune techniques ensures that the architectures are optimal in terms of hardware cost within their model. In this work, detailed bit-level cost models, both for ASIC and for FPGA, are defined and validated against actual syntheses. Compared to the state of the art, the proposed approach enables much larger constant sets and also significantly improves the performance of the resulting architectures. An application to quantized neural network inference demonstrates a reduction in multiplier area with no degradation in delay or accuracy.

Iterated greedy algorithm with constraint programming for scheduling steelmaking-continuous casting process

This study tackles a complex parallel machine scheduling problem with unrelated machines, sequence-dependent setup times and total weighted tardiness minimization. To address the scalability and expertise limitations of exact and heuristic methods, the prompt-tuned large language model (LLM) application for intelligent dispatching (PLAID) is proposed as a framework that uses fine-tuned large language models to make sequential dispatching decisions. PLAID consists of three stages: generating training data with constraint programming, supervised fine-tuning and dispatching based on learned rules. Experiments on diverse instance sizes show that PLAID achieves competitive performance relative to dispatching rules, metaheuristics and exact approaches, while remaining robust and interpretable. Fine-tuned models such as GPT-4.1-Tuned and GPT-4.1-Nano-Tuned consistently reduce total weighted tardiness, demonstrating the benefit of domain-specific adaptation. Overall, PLAID provides both scalability and transparency, positioning fine-tuned LLMs as practical, human-centric tools for complex manufacturing scheduling.

Given polynomials f 0 , f 1 , …, f k the Ideal Membership Problem, IMP for short, asks if f 0 belongs to the ideal generated by f 1 , …, f k . In the search version of this problem, the task is to find a proof of this fact. The IMP is a well-known fundamental problem with numerous applications. For instance, it underlies many proof systems based on polynomials such as Nullstellensatz, Polynomial Calculus, and Sum-of-Squares. Although the IMP is in general intractable, in many important cases it can be efficiently solved. Mastrolilli [SODA’19] initiated a systematic study of IMPs for ideals arising from Constraint Satisfaction Problems (CSPs), parameterized by constraint languages, denoted IMP(Γ). The ultimate goal of this line of research is to classify all such IMPs accordingly to their complexity. Mastrolilli achieved this goal for IMPs arising from CSP(Γ) where Γ is a Boolean constraint language, while Bulatov and Rafiey [STOC’22] advanced these results to several cases of CSPs over finite domains. In this article, we consider IMPs arising from CSPs over “affine” constraint languages, in which constraints are subgroups (or their cosets) of direct products of Abelian groups. This kind of CSPs include systems of linear equations and are considered one of the most important types of tractable CSPs. Some special cases of the problem have been considered before by Bharathi and Mastrolilli [MFCS’21] for linear equations modulo 2, and by Bulatov and Rafiey [STOC’22] for systems of linear equations over GF ( p ), p prime. Here, we prove that if Γ is an affine constraint language then IMP(Γ) is solvable in polynomial time assuming the input polynomial has bounded degree.

Neuromorphic computing promises significant improvements in latency and energy efficiency for machine intelligence at the edge. However, its adoption in the IoT domain is still limited by the heterogeneity of the HW, the immaturity of the toolchains, and the poor reproducibility of experiments. The present paper sets out the inNuCE RI, a two-pillar facility composed of a physical inNuCE Lab and a cloud-based inNuCE HPP. The purpose of the inNuCE RI is to enable developers to prototype, evaluate and compare neuromorphic and conventional end-to-end digital solutions. From a methodological perspective, we formalize the adaptation of MLOps to event-driven sensing and brain-inspired computation as NMLOps. We illustrate how inNuCE RI instantiates NMLOps through containerized toolchains orchestrated with Kubernetes and Slurm-managed heterogeneous resources (neuromorphic chips, FPGAs, GPUs, MCUs). The approach is analyzed on representative AIoT use cases, including HAR, Braille reading, event-based gesture recognition, Hi-Co semantization of memories, navigation tracking, and constraint satisfaction problems. The development of inNuCE RI has been driven by the need to facilitate the transition from prototype (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in nuce</i>) to engineered AIoT systems for lower entry barriers and enforce reproducibility. This paves the way for future system-of-systems engineering.

Hierarchical planning and scheduling for bulk ports via network flow and deep reinforcement learning-guided constraint programming

Higher education has seen a significant increase in planning complexity with the proliferation of diverse course formats, limited classroom resources, elective choices across disciplines, and dynamically changing faculty availability. Conventional planning methods may lead to schedule conflicts, improper room utilization, inequitable faculty assignments, and time-consuming administrative processes. This research proposes a web-based, Smart Classroom &amp; Timetable Scheduler, an intelligent system that designs optimized, non-conflicting timetables using constraint-based modeling and optimization algorithms. The system's inputs and constraints outline the essential academic features, including classroom capacity, faculty availability, subject credit load, special fixed slots, and student batch combinations. The proposed framework uses Genetic Algorithm (GA) and Constraint Satisfaction Problem (CSP) techniques to design optimal schedules that minimize faculty workload imbalance and maximize classroom utilization. Several experimental scenarios showcase the reduced conflict, improved teaching load distribution, and flexible multi-department and multi-shift institutional support. This work gives a scalable and deployable solution for NEP 2020 that takes higher education institutions into the new paradigm of intelligent, automated academic planning.

The lecture scheduling process at the Information Systems Study Program of UIN Alauddin Makassar currently faces significant challenges due to the use of manual methods using spreadsheets. This conventional approach is highly susceptible to human errors, such as overlapping schedules for lecturers or rooms, is time-consuming, and lacks flexibility in handling sudden changes. This study aims to design and develop a web-based lecture scheduling information system by integrating the Unitime University Timetabling library to automate the process effectively and efficiently. The research methodology follows the Agile development model, which includes stages of requirement analysis, system design, implementation, and testing. The system utilizes the UniTime solver to model scheduling as a Constraint Satisfaction Problem (CSP), taking into account both hard constraints (e.g., no room conflicts) and soft constraints (e.g., lecturer preferences). System testing was conducted using Black Box Testing to validate functionalities and performance comparison testing to measure efficiency improvements. The results demonstrate that the developed system can generate a complete, conflict-free schedule in just 1 minute, compared to the 300 minutes required by manual methods. Furthermore, the system successfully eliminated 100% of detected potential scheduling conflicts. This research proves that integrating advanced scheduling libraries into modern web frameworks like Laravel provides a professional and highly efficient solution for academic management in higher education.

Constraint satisfaction problems usually exhibit a distinct satisfiability transition phenomenon under stochastic models, and an exact phase transition threshold has been strictly proven to exist especially in the RB model. Aiming at the difficulty in solving hard instances of the random binary model with growing domains (RB) near the phase transition region, this paper proposes a guided decimation algorithm based on asynchronous belief propagation with gradual perturbation (P-BP). On the basis of the asynchronous BP-guided decimation framework, the algorithm introduces a linear annealing perturbation mechanism, which enables the variable-to-constraint messages to transit smoothly from deterministic update to the style of Gibbs sampling. Meanwhile, in the late stage of decimation, the variable fixing strategy is changed from greedy selection to direct sampling from the marginal distribution, supplemented by an automatic restart strategy with a maximum of 3 restarts. These improvements retain the asynchronous update, damping factor and A/B/C edge processing rules of the original algorithm, while significantly enhancing the stochastic exploration capability and effectively alleviating the problems of message oscillation, local convergence and error propagation of fixed variables in the phase transition region. Research shows that the combination of gradual perturbation with late-stage probabilistic sampling and a restart mechanism provides an effective way to enhance the robustness of belief propagation-based algorithms for stochastic constraint satisfaction problems.

This study addresses the optimization of medical waste collection (MWC) in Ho Chi Minh City, Vietnam, where increasing waste volumes pose challenges for efficiency and sustainability. Using real-world operational data from Citenco, we formulate the problem as a capacitated vehicle routing problem (CVRP) with stochastic demand, solved through a combination of constraint programming and chance-constrained programming. The proposed model reduces total travel distance by 22%, travel time by 10%, and increases vehicle load utilization by 6%, while lowering the number of daily trips to treatment facilities. Sensitivity analysis confirms robustness under varying service levels and expanded coverage. These results provide evidence-based insights for policymakers and public waste management agencies, supporting sustainable decision-making in urban medical waste collection. • Medical waste collection is a challenging problem that can lead to hazardous impacts on environment. • Inefficiency in collecting route, which is also known as Waste Collection Vehicle Routing Problem, can be minimized by Chance-Constrained Programming. • Optimization model was developed to improve efficiency and test for robustness vs demand fluctuation. • Medical waste collection of Citenco Ltd., a major waste collector in Ho Chi Minh City, Vietnam, was optimized using the optimization model. • Sensitivity analysis for two scenarios, increased waste demand and increased collection points, were done.

This paper addresses the Tool Indexing Problem (TIP) with tool duplications, a critical optimisation problem in CNC turret operations where indexing time directly impacts production efficiency, particularly in high-volume manufacturing. The indexing problem has proven computationally challenging, and no highly effective exact formulations have been reported previously. We introduce two novel mathematical programming approaches: Integer Linear Programming (ILP) and, for the first time in the literature, a Constraint Programming (CP) formulation for the TIP with tool duplications. Additionally, we propose a new Iterated Greedy Search (IGS) metaheuristic designed to efficiently address large-scale problem instances resulting from the problem’s NP-hard nature. A comprehensive comparative analysis of benchmark instances shows that the CP formulation consistently outperforms the ILP model, especially for small- and medium-sized problems, making it the most effective exact approach reported to date. For larger problem sizes, the proposed IGS demonstrates slightly better performance than CP, surpassing all previously proposed heuristics in the literature. While CP remains an effective exact method across all problem scales, metaheuristics such as IGS continue to provide significant value by enabling the efficient solution of large-scale instances.

Managing academic class schedules and teaching assignments is a combinatorially complex problem that continues to challenge educational institutions worldwide.For school administrators, optimally assigning faculty to courses---while simultaneously balancing expertise, availability, and workload constraints---can require weeks of iterative trial and error.Although digital tools exist, many institutions still depend on fragmented spreadsheet-based processes.This paper presents a unified, web-based Integrated Timetable Scheduling and Faculty Workload Management System designed to address these challenges through formal Constraint Satisfaction Problem (CSP) modelling.The system leverages intelligent constraint enforcement, Minimum Remaining Value (MRV) heuristics, and forwardchecking search strategies to generate conflict-free, balanced timetables efficiently.A real-time dynamic substitution algorithm handles faculty absences automatically by identifying optimal replacements based on subject expertise and current workload.The system was implemented as a fully functional web application ---the Academic ERP ---and validated through both algorithmic simulation and live system testing.Experimental evaluations confirm that the system eliminates scheduling conflicts entirely, reduces workload variance by approximately 85%, and generates timetables in under ten seconds on standard institutional hardware.

The N-Queen problem is a classical combinatorial optimization and constraint satisfaction problem that involves placing N queens on an N × N chessboard such that no two queens threaten each other. Due to its exponential search space and increasing computational complexity with larger board sizes, the problem serves as an important benchmark for evaluating the efficiency of heuristic and metaheuristic optimization techniques. This study presents a comprehensive performance analysis of the Simulated Annealing (SA) optimization approach for solving the N-Queen problem across varying board dimensions. The proposed methodology models the N-Queen problem as an optimization task by defining an objective function that minimizes the number of conflicting queen pairs. Simulated Annealing is employed to iteratively explore the solution space, allowing probabilistic acceptance of suboptimal solutions to escape local minima. Key parameters, including initial temperature, cooling schedule, and termination criteria, are systematically tuned to evaluate their impact on convergence speed and solution quality. Experimental results demonstrate that the SA-based approach effectively finds valid solutions for large values of N with high success rates and reduced computational effort compared to exhaustive and deterministic methods. Performance metrics such as solution accuracy, convergence time, number of iterations, and conflict reduction rate are analyzed and discussed. The results indicate that Simulated Annealing offers a robust and scalable solution for the N-Queen problem, particularly for higher-dimensional instances where traditional methods become impractical. Overall, this study highlights the suitability of Simulated Annealing as an efficient metaheuristic for solving complex combinatorial optimization problems and provides insights into its performance characteristics when applied to the N-Queen problem.

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.