arXiv subjects

Zdeněk Hanzálek

Publications and source records attributed to Zdeněk Hanzálek.

At least 19 recordsLinked to original sources

arXiv2026

Resource-constrained Project Scheduling with Time-of-Use Energy Tariffs and Machine States: A Logic-based Benders Decomposition Approach

In this paper, we investigate the Resource-Constrained Project Scheduling Problem (RCPSP) with Time-of-Use (TOU) energy tariffs and machine states, a variant of RCPSP for production scheduling, where energy price is part of the criteria and one highly energy-demanding machine can be in one of the following three states: proc, idle, or off. The problem involves scheduling all tasks, respecting precedence constraints and resource limitations, while minimizing the combination of the overall makespan and the Total Energy Cost (TEC), which varies according to the TOU tariffs, which can take negative values. We propose two novel approaches to solve it: a monolithic Constraint Programming (CP) approach and a Logic-Based Benders Decomposition (LBBD) approach. The latter combines a master problem handling the energy cost solved using Integer Linear Programming (ILP) with a subproblem handling the RCPSP, resolved using CP. Both approaches outperform the monolithic compact ILP counterpart, but the LBBD significantly outperforms the monolithic CP in most cases, especially when the makespan criterion is not included in the objective function, solving to optimality instances with up to 480 tasks. Finally, we propose a way to generalize our LBBD approach to other problems sharing similar characteristics, and applied it to various problems, such as an RCPSP with blocking times & total weighted tardiness criterion, or a flexible job shop.

math.OC↗

arXiv2026

Schedulable Job-Level Dependencies for Cause-Effect Chains via Graph Neural Networks

Modern automotive software architectures comprise large sets of mixed-criticality functions executing on shared multi-core platforms with strict real-time and end-to-end timing requirements. Sensor-to-actuator data propagation in such systems is typically expressed via cause-effect chains with worst-case data-age budgets. Job-level dependencies (JLDs) have been introduced to provide a schedule-agnostic mechanism for bounding the data age independently of the underlying scheduler. The state-of-the-art methods for synthesizing JLDs, however, do not check whether the produced JLDs are enforceable under a concrete scheduling policy or jointly schedulable at the system level. In this paper we propose the first machine-learning-based JLD synthesis method, built around a two-level Graph Neural Network with temperature-controlled sampling that learns the structural patterns connecting cause-effect chain configurations to their JLD solutions. Since learned outputs may not be correct by construction, we embed the GNN in a novel Generate-and-Verify architecture in which a safe DP data-age checker, together with a per-chain EDF feasibility checker and a system-level demand-bound test, accept or reject each candidate. We show that the ML-based generator substantially outperforms the original greedy heuristic while achieving orders-of-magnitude lower synthesis time, demonstrating that learned structural priors can effectively replace exponential propagation-tree enumeration on this class of real-time scheduling problems.

cs.SE↗

arXiv2026

Hierarchical Rectangle Packing Solved by Multi-Level Recursive Logic-based Benders Decomposition

We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are not fixed, and the packing is inherently hierarchical: each item is either a rectangle or a block occurrence, whose dimensions are a solution of another packing problem. This recursive structure reflects real-world scenarios in which components, boxes, or modules must be packed within higher-level containers. We formally define the problem and propose exact formulations in Mixed-Integer Linear Programming and Constraint Programming. Given the computational difficulty of solving complex packing instances directly, we propose decomposition heuristics. First, we implement an existing Bottom-Up baseline method that solves subblocks before combining them at higher levels. Building upon this, we introduce a novel multilevel Logic-based Benders Decomposition method. This heuristic method dynamically refines block dimension constraints, eliminating the need for manual selection of candidate widths or aspect ratios. Experiments on synthetic instances with up to seven hierarchy levels, 80 items per block, and limited computation time show that the proposed decomposition significantly outperforms both monolithic formulations and the Bottom-Up method in terms of solution quality and scalability.

cs.CG↗

arXiv2026

Integrated packing, placement, scheduling, and routing of personalized production: a pharmaceutical Industry 4.0 use-case with a planar transport system

The recent emergence of planar transport systems necessitates re-evaluation of Flexible Manufacturing Systems (FMS) to address the simultaneous scheduling of internal logistics and production operations. By operating on a tile-based planar grid, these systems allow independent movers full two-dimensional freedom, mitigating inefficiencies inherent to traditional sequential lines. This paper applies a planar FMS framework to a real-world use case in the pharmaceutical industry: the automated production of personalized drugs. Implementing this system requires solving optimization problems at both tactical and operational levels. The tactical level involves decisions regarding production line layout and the positioning of drug dispensers. A Mixed-Integer Quadratic Programming model is utilized for the packing problem to exploit drug co-occurrence patterns found in historical patient data. Subsequently, we solve the placement problem - a bi-level problem combining an assignment problem with Shortest Hamiltonian paths with neighborhoods - to arrange dispensers in a layout minimizing expected travel distances. The operational level is encountered daily, scheduling individual movers to process new orders as quickly as possible. This scheduling problem is formulated using Constraint Programming, modeling movers as reservoir resources to ensure order completeness, complemented by a routing phase using an iterative conflict-resolution mechanism and DAG-based reasoning to convert schedules into conflict-free paths. Evaluation using real-world prescription data for 40 drugs shows the framework scales efficiently across several layout topologies for up to 500 orders, with schedules that are highly effective and computationally tractable for daily operations.

math.OC↗

arXiv2026

Periodic Scheduling of Grouped Time-Triggered Signals on a Single Resource

Time-triggered messages are of crucial importance in modern communication networks. Offline-generated schedules, which specify start times for periodic messages, enable us to achieve deterministic behavior in critical applications. In automotive and avionics domains, so-called signals (measurements and commands) are periodically generated and communicated (via messages) among sensors, controllers, and actuators. However, the message contains not only the useful signal data, but also necessary metadata, e.g., message ID. Metadata is stored as a header or tail and extends the message size; when the signal is very short (as it often is in applications), sending each in a separate message is inefficient. Thus, several signals are grouped into a single message, depending on their periodicity and length, and sent with just one header. Such an approach increases the utilization of the communication resource (link or bus), since less bandwidth is wasted on headers (Kuaban et al. 2021). However, grouping the signals into messages is complicated. The maximum size of the message (including the metadata) is finite, since longer messages have a lower probability of successful delivery. Also, longer messages are less flexible for scheduling in a periodic setting. This is similar to the work of Huan et al. (2019), where the compromise between energy efficiency and latency for IoT devices was investigated. In this paper, we study the fundamental problem of grouping time-triggered signals into messages and periodic scheduling of messages on a single resource.

cs.NI↗

arXiv2025

Fast Resource Management Algorithm for Passive Surveillance Systems

Passive surveillance systems (PSS) detect and track objects that emit electromagnetic signals from hundreds of kilometers away. These systems have a limited number of receivers and can only observe a fraction of the frequencies of interest simultaneously. To improve its behavior, we propose the ResourceTune algorithm, which iteratively constructs optimized schedules to determine which frequencies each receiver should observe at a given time step. The algorithm's main component is the optimization of receiver configurations using a left-right heuristic combined with linear programming. Our approach is unique because, unlike others, we focus on optimizing available resources and observed frequencies, which was never done before. We experimentally compared the proposed algorithm with a greedy and the state-of-the-art method for construction of PSS schedules. In most of the considered scenarios, ResourceTune outperformed both algorithms, and in the most extreme case, its objective value was more than 2.7 times better than the values reached by other methods.

cs.OH↗

arXiv2025

A batch production scheduling problem in a reconfigurable hybrid manufacturing-remanufacturing system

In recent years, remanufacturing of End-of-Life (EOL) products has been adopted by manufacturing sectors as a competent practice to enhance their sustainability and market share. Due to the mass customization of products and high volatility of market, processing of new products and remanufacturing of EOLs in the same shared facility, namely Hybrid Manufacturing-Remanufacturing System (HMRS), is a mean to keep such production efficient. Accordingly, customized production capabilities are required to increase flexibility, which can be effectively provided under the Reconfigurable Manufacturing System (RMS) paradigm. Despite the advantages of utilizing RMS technologies in HMRSs, production management of such systems suffers excessive complexity. Hence, this study concentrates on the production scheduling of an HMRS consisting of non-identical parallel reconfigurable machines where the orders can be grouped into batches. In this regard, Mixed-Integer Linear Programming (MILP) and Constraint Programming (CP) models are devised to formulate the problem. Furthermore, a computationally efficient solution method is developed based on a Logic-based Benders Decomposition (LBBD) approach. The warm start technique is also implemented by providing a decent initial solution to the MILP model. Computational experiments attest to the LBBD method's superiority over the MILP, CP, and warm-started MILP models by obtaining an average gap of about 2%, besides it yields actionable managerial insights for scheduling in HMRSs.

cs.CE↗

arXiv2025

Reinforcement Learning for Search Tree Size Minimization in Constraint Programming: New Results on Scheduling Benchmarks

Failure-Directed Search (FDS) is a significant complete generic search algorithm used in Constraint Programming (CP) to efficiently explore the search space, proven particularly effective on scheduling problems. This paper analyzes FDS's properties, showing that minimizing the size of its search tree guided by ranked branching decisions is closely related to the Multi-armed bandit (MAB) problem. Building on this insight, MAB reinforcement learning algorithms are applied to FDS, extended with problem-specific refinements and parameter tuning, and evaluated on the two most fundamental scheduling problems, the Job Shop Scheduling Problem (JSSP) and Resource-Constrained Project Scheduling Problem (RCPSP). The resulting enhanced FDS, using the best extended MAB algorithm and configuration, performs 1.7 times faster on the JSSP and 2.1 times faster on the RCPSP benchmarks compared to the original implementation in a new solver called OptalCP, while also being 3.5 times faster on the JSSP and 2.1 times faster on the RCPSP benchmarks than the current state-of-the-art FDS algorithm in IBM CP Optimizer 22.1. Furthermore, using only a 900-second time limit per instance, the enhanced FDS improved the existing state-of-the-art lower bounds of 78 of 84 JSSP and 226 of 393 RCPSP standard open benchmark instances while also completely closing a few of them.

cs.LG↗

arXiv2025

Improving Rapidly-exploring Random Trees algorithm for Automated Parking in Real-world Scenarios

Automated parking is a self-driving feature that has been in cars for several years. Parking assistants in currently sold cars fail to park in more complex real-world scenarios and require the driver to move the car to an expected starting position before the assistant is activated. We overcome these limitations by proposing a planning algorithm consisting of two stages: (1) a geometric planner for maneuvering inside the parking slot and (2) a Rapidly-exploring Random Trees (RRT)-based planner that finds a collision-free path from the initial position to the slot entry. Evaluation of computational experiments demonstrates that improvements over commonly used RRT extensions reduce the parking path cost by 21 % and reduce the computation time by 79.5 %. The suitability of the algorithm for real-world parking scenarios was verified in physical experiments with Porsche Cayenne.

cs.RO↗

arXiv2025

A first look at ROS 2 applications written in asynchronous Rust

The increasing popularity of the Rust programming language in building robotic applications using the Robot Operating System (ROS 2) raises questions about its real-time execution capabilities, particularly when employing asynchronous programming. Existing real-time scheduling and response-time analysis techniques for ROS 2 focus on applications written in C++ and do not address the unique execution models and challenges presented by Rust's asynchronous programming paradigm. In this paper, we analyze the execution model of R2R -- an asynchronous Rust ROS 2 bindings and various asynchronous Rust runtimes, comparing them with the execution model of C++ ROS 2 applications. We propose a structured approach for R2R applications aimed at deterministic real-time operation involving thread prioritization and callback-to-thread mapping schemes. Our experimental evaluation based on measuring end-to-end latencies of a synthetic application shows that the proposed approach is effective and outperforms other evaluated configurations. A more complex autonomous driving case study demonstrates its practical applicability. Overall, the experimental results indicate that our proposed structure achieves bounded response times for time-critical tasks. This paves the way for future work to adapt existing or develop new response-time analysis techniques for R2R applications using our structure.

cs.SE↗

arXiv2025

Thermal Modeling and Optimal Allocation of Avionics Safety-critical Tasks on Heterogeneous MPSoCs

Multi-Processor Systems-on-Chip (MPSoC) can deliver high performance needed in many industrial domains, including aerospace. However, their high power consumption, combined with avionics safety standards, brings new thermal management challenges. This paper investigates techniques for offline thermal-aware allocation of periodic tasks on heterogeneous MPSoCs running at a fixed clock frequency, as required in avionics. The goal is to find the assignment of tasks to (i) cores and (ii) temporal isolation windows while minimizing the MPSoC temperature. To achieve that, we propose and analyze three power models, and integrate them within several novel optimization approaches based on heuristics, a black-box optimizer, and Integer Linear Programming (ILP). We perform the experimental evaluation on three popular MPSoC platforms (NXP i.MX8QM MEK, NXP i.MX8QM Ixora, NVIDIA TX2) and observe a difference of up to 5.5°C among the tested methods (corresponding to a 22% reduction w.r.t. the ambient temperature). We also show that our method, integrating the empirical power model with the ILP, outperforms the other methods on all tested platforms.

cs.SE↗

arXiv2025

Periodic Chains Scheduling on Dedicated Resources -- A Crucial Problem in Time-Sensitive Networks

Periodic messages transfer data from sensors to actuators in cars, planes, and complex production machines. When considering a given routing, the unicast message starts at its source and goes over several dedicated resources to reach its destination. Such unicast message can be represented as a chain of point-to-point communications. Thus, the scheduling of the periodic chains is a principal problem in time-triggered Ethernet, like IEEE 802.1Qbv Time-Sensitive Networks. This paper studies a strongly NP-hard periodic scheduling problem with harmonic periods, task chains, and dedicated resources. We analyze the problem on several levels of generality and complexity and provide the corresponding proofs. We describe a solution methodology to find a feasible schedule that minimizes the chains' degeneracy related to start-to-end latency normalized in the number of periods. We use the local search with the first fit scheduling heuristic, which we warm-start with a constraint programming model. This notably improves the schedulability of instances with up to 100% utilization and thousands (and more) of tasks, with high-quality solutions found in minutes. An efficient constraint programming matheuristic significantly reduces the degeneracy of the found schedules even further. The method is evaluated on sets of industrial-, avionic-, and automotive-inspired instances.

cs.NI↗

arXiv2025

Green Scheduling with Time-of-Use Tariffs and Machine States: Optimizing Energy Cost via Branch-and-Bound and Bin Packing Strategies

This paper presents a branch-and-bound algorithm, enhanced with bin packing strategies, for scheduling under variable energy pricing and power-saving states. The proposed algorithm addresses the 1,TOU|states|TEC problem, which involves scheduling jobs to minimize total energy cost (TEC) while considering time-of-use (TOU) electricity prices and different machine states (e.g., processing, idle, off). Key innovations include instance pre-processing for rapid lower bound calculations, a novel branching scheme combined with initializations, a block-finding primal heuristic, and a tighter lower bound for jobs with non-coprime processing times. These enhancements result in an efficient algorithm capable of solving benchmark instances with real energy prices with 200 jobs more than 100 times faster than existing state-of-the-art methods.

math.OC↗

arXiv2025

Packing-Inspired Algorithms for Periodic Scheduling Problems with Harmonic Periods

We tackle the problem of non-preemptive periodic scheduling with a harmonic set of periods. Problems of this kind arise within domains of periodic manufacturing and maintenance, and also during the design of industrial, automotive, and avionics communication protocols, where efficient scheduling of messages is crucial for the performance of a time-triggered network. We consider the decision variant of the periodic scheduling problem on a single highly-utilized machine. We first prove a bijection between periodic scheduling and a particular (so-called height-divisible) 2D packing of rectangles. We formulate the problem using Constraint Programming and compare it with equivalent state-of-the-art Integer Linear Programming formulation, showing the former's superiority on difficult instances. Furthermore, we develop a packing-inspired first fit heuristic, which we compare with methods described in the literature. We justify our proposed methods on synthetically generated problem instances inspired by the communication of messages on one channel.

cs.DS↗

arXiv2025

A matheuristic approach for an integrated lot-sizing and scheduling problem with a period-based learning effect

This research investigates a multi-product capacitated lot-sizing and scheduling problem incorporating a novel learning effect, namely the period-based learning effect. This is inspired by a real case in a core analysis laboratory under a job shop setting. Accordingly, a Mixed-Integer Linear Programming (MILP) model is extended based on the big-bucket formulation, optimizing the total tardiness and overtime costs. Given the complexity of the problem, a cutting plane method is employed to simplify the model. Afterward, three matheuristic methods based on the rolling horizon approach are devised, incorporating two lower bounds and a local search heuristic. Furthermore, a post-processing approach is implemented to incorporate lot-streaming possibility. Computational experiments demonstrate: 1) the simplified model performs effectively in terms of both solution quality and computational time; and 2) although the model encounters challenges with large-scale instances, the proposed matheuristic methods achieve satisfactory outcomes; and 3) it can be inferred that the complexity of the models and solution methods are independent of the learning effect; however, the value of learning effect may impact the performance of the lower bounds; 4) in manufacturing settings, where the lot-streaming is possible, incorporating post-processing can drastically improve the objective function; 5) the impact of the period-based learning effect in the results is significant, and the model's sensitivity to time-based parameters (e.g., learning rate) is more than cost-based ones (e.g., tardiness cost).

math.OC↗

arXiv2024

Low Fidelity Digital Twin for Automated Driving Systems: Use Cases and Automatic Generation

Automated driving systems are an integral part of the automotive industry. Tools such as Robot Operating System and simulators support their development. However, in the end, the developers must test their algorithms on a real vehicle. To better observe the difference between reality and simulation--the reality gap--digital twin technology offers real-time communication between the real vehicle and its model. We present low fidelity digital twin generator and describe situations where automatic generation is preferable to high fidelity simulation. We validated our approach of generating a virtual environment with a vehicle model by replaying the data recorded from the real vehicle.

cs.RO↗

arXiv2024

POMDP-Based Trajectory Planning for On-Ramp Highway Merging

This paper addresses the trajectory planning problem for automated vehicle on-ramp highway merging. To tackle this challenge, we extend our previous work on trajectory planning at unsignalized intersections using Partially Observable Markov Decision Processes (POMDPs). The method utilizes the Adaptive Belief Tree (ABT) algorithm, an approximate sampling-based approach to solve POMDPs efficiently. We outline the POMDP formulation process, beginning with discretizing the highway topology to reduce problem complexity. Additionally, we describe the dynamics and measurement models used to predict future states and establish the relationship between available noisy measurements and predictions. Building on our previous work, the dynamics model is expanded to account for lateral movements necessary for lane changes during the merging process. We also define the reward function, which serves as the primary mechanism for specifying the desired behavior of the automated vehicle, combining multiple goals such as avoiding collisions or maintaining appropriate velocity. Our simulation results, conducted on three scenarios based on real-life traffic data from German highways, demonstrate the method's ability to generate safe, collision-free, and efficient merging trajectories. This work shows the versatility of this POMDP-based approach in tackling various automated driving problems.

cs.RO↗

arXiv2024

Automated Placement of Analog Integrated Circuits using Priority-based Constructive Heuristic

This paper presents a heuristic approach for solving the placement of Analog and Mixed-Signal Integrated Circuits. Placement is a crucial step in the physical design of integrated circuits. During this step, designers choose the position and variant of each circuit device. We focus on the specific class of analog placement, which requires so-called pockets, their possible merging, and parametrizable minimum distances between devices, which are features mostly omitted in recent research and literature. We formulate the problem using Integer Linear Programming and propose a priority-based constructive heuristic inspired by algorithms for the Facility Layout Problem. Our solution minimizes the perimeter of the circuit's bounding box and the approximated wire length. Multiple variants of the devices with different dimensions are considered. Furthermore, we model constraints crucial for the placement problem, such as symmetry groups and blockage areas. Our outlined improvements make the heuristic suitable to handle complex rules of placement. With a search guided either by a Genetic Algorithm or a Covariance Matrix Adaptation Evolution Strategy, we show the quality of the proposed method on both synthetically generated and real-life industrial instances accompanied by manually created designs. Furthermore, we apply reinforcement learning to control the hyper-parameters of the genetic algorithm. Synthetic instances with more than 200 devices demonstrate that our method can tackle problems more complex than typical industry examples. We also compare our method with results achieved by contemporary state-of-the-art methods on the MCNC and GSRC datasets.

cs.NE↗