arXiv subjects

Zdeněk Hanzálek

Publications and source records attributed to Zdeněk Hanzálek.

36 records · Page 2Linked to original sources

arXiv2024

Matheuristic Local Search for the Placement of Analog Integrated Circuits

The suboptimal physical design of the integrated circuits may not only increase the manufacturing costs due to the larger size of the chip but can also impact its performance by placing interconnected rectangular devices too far from each other. In the domain of Analog and Mixed-Signal Integrated Circuits (AMS ICs), placement automation is lacking behind its digital counterpart, mainly due to the variety of components and complex constraints the placement needs to satisfy. Integer Linear Programming (ILP) is a suitable approach to modeling the placement problem for AMS ICs. However, not even state-of-the-art solvers can create high-quality placements for large problem instances. In this paper, we study how to improve the results of our previous ILP model, first by introducing additional constraints and second by using matheuristics. Given the initial solution we obtain using our original ILP model, we use the solver to perform a local search. We try to improve the criterion by considering only a few spatially close rectangles while keeping the rest of the placement fixed. This local search approach enables us to significantly improve the quality of instances whose solution space we could not sufficiently explore before, even when the computation time reserved for the matheuristic is limited. Finally, we evaluate our revised approach on synthetically generated instances containing more than 200 independent rectangles and on real-life problems.

cs.OH↗

arXiv2024

Electrification of Transportation: A Hybrid Benders/SDDP Algorithm for Optimal Charging Station Trading

This paper examines the electrification of transportation as a response to environmental challenges caused by fossil fuels, exploring the potential of battery electric vehicles and hydrogen fuel cell vehicles as alternative solutions. However, a significant barrier to their widespread adoption is the limited availability of charging infrastructure. Therefore, this study proposes the development of comprehensive charging stations capable of accommodating both battery and hydrogen vehicles to address this challenge. The energy is purchased from the day-ahead and intraday auction-based electricity markets, where the electricity price is subject to uncertainty. Therefore, a two-stage stochastic programming model is formulated while the price scenarios are generated utilizing a k-means clustering algorithm. Given the complexity of the proposed model, an efficient solution approach is developed through the hybridization of the Benders decomposition algorithm and stochastic dual dynamic programming. In the Benders master problem, day-ahead bidding variables are determined, whereas the Benders sub-problem addresses intraday bidding and charging station scheduling variables, employing stochastic dual dynamic programming to tackle its intractability. Additionally, we transform the mixed integer linear program model of the second stage problem into a linear program, confirming its validity through KKT conditions. Our model provides practical insights for making informed decisions in electricity markets based on sequential auctions. While the bidding curves submitted to the day-ahead market remain unaffected by scenarios, those submitted to the intra-day market show dependence on fluctuations in day-ahead market prices.

math.OC↗

arXiv2024

Deep learning-driven scheduling algorithm for a single machine problem minimizing the total tardiness

In this paper, we investigate the use of the deep learning method for solving a well-known NP-hard single machine scheduling problem with the objective of minimizing the total tardiness. We propose a deep neural network that acts as a polynomial-time estimator of the criterion value used in a single-pass scheduling algorithm based on Lawler's decomposition and symmetric decomposition proposed by Della Croce et al. Essentially, the neural network guides the algorithm by estimating the best splitting of the problem into subproblems. The paper also describes a new method for generating the training data set, which speeds up the training dataset generation and reduces the average optimality gap of solutions. The experimental results show that our machine learning-driven approach can efficiently generalize information from the training phase to significantly larger instances. Even though the instances used in the training phase have from 75 to 100 jobs, the average optimality gap on instances with up to 800 jobs is 0.26%, which is almost five times less than the gap of the state-of-the-art heuristic.

math.OC↗

arXiv2023

Constraint Programming and Constructive Heuristics for Parallel Machine Scheduling with Sequence-Dependent Setups and Common Servers

This paper examines scheduling problem denoted as $P|seq, ser|C_{max}$ in Graham's notation; in other words, scheduling of tasks on parallel identical machines ($P$) with sequence-dependent setups ($seq$) each performed by one of the available servers ($ser$). The goal is to minimize the makespan ($C_{max}$). We propose a Constraint Programming (CP) model for finding the optimal solution and constructive heuristics suitable for large problem instances. These heuristics are also used to provide a feasible starting solution to the proposed CP model, significantly improving its efficiency. This combined approach constructs solutions for benchmark instances of up to 20 machines and 500 tasks in 10 seconds, with makespans 3-11.5% greater than the calculated lower bounds with a 5% average. The extensive experimental comparison also shows that our proposed approaches outperform the existing ones.

cs.GT↗

arXiv2022

Parallel Parking: Optimal Entry and Minimum Slot Dimensions

The problem of path planning for automated parking is usually presented as finding a collision-free path from initial to goal positions, where three out of four parking slot edges represent obstacles. We rethink the path planning problem for parallel parking by decomposing it into two independent parts. The topic of this paper is finding optimal parking slot entry positions. Path planning from initial to entry position is out of scope here. We show the relation between entry positions, parking slot dimensions, and the number of backward-forward direction changes. This information can be used as an input to optimize other parts of the automated parking process.

cs.RO↗

arXiv2020

Power of Pre-Processing: Production Scheduling with Variable Energy Pricing and Power-Saving States

This paper addresses a single machine scheduling problem with non-preemptive jobs to minimize the total electricity cost. Two latest trends in the area of the energy-aware scheduling are considered, namely the variable energy pricing and the power-saving states of a machine. Scheduling of the jobs and the machine states are considered jointly to achieve the highest possible savings. Although this problem has been previously addressed in the literature, the reported results of the state-of-the-art method show that the optimal solutions can be found only for instances with up to 35 jobs and 209 intervals within 3 hours of computation. We propose an elegant pre-processing technique called SPACES for computing the optimal switching of the machine states with respect to the energy costs. The optimal switchings are associated with the shortest paths in an interval-state graph that describes all possible transitions between the machine states in time. This idea allows us to implement efficient integer linear programming and constraint programming models of the problem while preserving the optimality. The efficiency of the models lies in the simplification of the optimal switching representation. The results of the experiments show that our approach outperforms the existing state-of-the-art exact method. On a set of benchmark instances with varying sizes and different state transition graphs, the proposed approach finds the optimal solutions even for the large instances with up to 190 jobs and 1277 intervals within an hour of computation.

cs.DS↗

arXiv2020

Multi-Variant Time Constrained FlexRay Static Segment Scheduling

The FlexRay bus is a modern standard used in the automotive industry.It offers deterministic message transmission with zero jitter while using time-triggered scheduling in the static segment. When several vehicle variants (i.e. different models and their versions) share the same signal, the car manufacturers require to schedule such signal at the same time in all vehicle variants. This requirement simplifies the signal traceability and diagnostics in different vehicle variants using the same platform and simplifies reuse of components and tools. In this paper, we propose a first fit based heuristic algorithm which creates the schedules for several vehicle variants at once, while transmitting a given signal at the same time in all the schedules. The scheduling algorithm also takes the time constraints as release dates and deadlines into account. Finally, different algorithm versions are compared on benchmark sets and low computational time demands are validated on large instances.

eess.SY↗

arXiv2020

Makespan minimization of Time-Triggered traffic on a TTEthernet network

The reliability of the increasing number of modern applications and systems strongly depends on interconnecting technology. Complex systems which usually need to exchange, among other things, multimedia data together with safety-related information, as in the automotive or avionic industry, for example, make demands on both the high bandwidth and the deterministic behavior of the communication. TTEthernet is a protocol that has been developed to face these requirements while providing the generous bandwidth of Ethernet up to 1\,Gbit/s and enhancing its determinism by the Time-Triggered message transmission which follows the predetermined schedule. Therefore, synthesizing a good schedule which meets all the real-time requirements is essential for the performance of the whole system. In this paper, we study the concept of creating the communication schedules for the Time-Triggered traffic while minimizing its makespan. The aim is to maximize the uninterrupted gap for remaining traffic classes in each integration cycle. The provided scheduling algorithm, based on the Resource-Constrained Project Scheduling Problem formulation and the load balancing heuristic, obtains near-optimal (within 15\% of non-tight lower bound) solutions in 5 minutes even for industrial sized instances. The universality of the provided method allows easily modify or extend the problem statement according to particular industrial demands. Finally, the studied concept of makespan minimization is justified through the concept of scheduling with porosity according to the worst-case delay analysis of Event-Triggered traffic.

cs.NI↗

arXiv2020

On Idle Energy Consumption Minimization in Production: Industrial Example and Mathematical Model

This paper, inspired by a real production process of steel hardening, investigates a scheduling problem to minimize the idle energy consumption of machines. The energy minimization is achieved by switching a machine to some power-saving mode when it is idle. For the steel hardening process, the mode of the machine (i.e., furnace) can be associated with its inner temperature. Contrary to the recent methods, which consider only a small number of machine modes, the temperature in the furnace can be changed continuously, and so an infinite number of the power-saving modes must be considered to achieve the highest possible savings. To model the machine modes efficiently, we use the concept of the energy function, which was originally introduced in the domain of embedded systems but has yet to take roots in the domain of production research. The energy function is illustrated with several application examples from the literature. Afterward, it is integrated into a mathematical model of a scheduling problem with parallel identical machines and jobs characterized by release times, deadlines, and processing times. Numerical experiments show that the proposed model outperforms a reference model adapted from the literature.

cs.CE↗

arXiv2020

Data-driven Algorithm for Scheduling with Total Tardiness

In this paper, we investigate the use of deep learning for solving a classical NP-Hard single machine scheduling problem where the criterion is to minimize the total tardiness. Instead of designing an end-to-end machine learning model, we utilize well known decomposition of the problem and we enhance it with a data-driven approach. We have designed a regressor containing a deep neural network that learns and predicts the criterion of a given set of jobs. The network acts as a polynomial-time estimator of the criterion that is used in a single-pass scheduling algorithm based on Lawler's decomposition theorem. Essentially, the regressor guides the algorithm to select the best position for each job. The experimental results show that our data-driven approach can efficiently generalize information from the training phase to significantly larger instances (up to 350 jobs) where it achieves an optimality gap of about 0.5%, which is four times less than the gap of the state-of-the-art NBR heuristic.

cs.AI↗

arXiv2020

Accelerated RRT* and its evaluation on Autonomous Parking

Finding a collision-free path for autonomous parking is usually performed by computing geometric equations, but the geometric approach may become unusable under challenging situations where space is highly constrained. We propose an algorithm based on Rapidly-Exploring Random Trees Star (RRT*), which works even in highly constrained environments and improvements to RRT*-based algorithm that accelerate computational time and decrease the final path cost. Our improved RRT* algorithm found a path for parallel parking maneuver in 95 % of cases in less than 0.15 seconds.

cs.RO↗

arXiv2019

Multi-Variant Scheduling of Critical Time-Triggered Communication in Incremental Development Process: Application to FlexRay

The portfolio of models offered by car manufacturing groups often includes many variants (i.e., different car models and their versions). With such diversity in car models, variant management becomes a formidable task. Thus, there is an effort to keep the variants as close as possible. This simple requirement forms a big challenge in the area of communication protocols. When several vehicle variants use the same signal, it is often required to simultaneously schedule such a signal in all vehicle variants. Furthermore, new vehicle variants are designed incrementally in such a way as to maintain backward compatibility with the older vehicles. Backward compatibility of time-triggered schedules reduces expenses relating to testing and fine-tuning of the components that interact with physical environment (e.g., electromagnetic compatibility issues). As this requirement provides for using the same platform, it simplifies signal traceability and diagnostics, across different vehicle variants, besides simplifying the reuse of components and tools. This paper proposes an efficient and robust heuristic algorithm, which creates the schedules for internal communication of new vehicle variants. The algorithm provides for variant management by ensuring compatibility among the new variants, besides preserving backward compatibility with the preceding vehicle variants. Based on the results of the proposed algorithm, the impact of maintaining compatibility among new variants and of preserving backward compatibility with the preceding variants on the scheduling procedure is examined and discussed. Thanks to the execution time of the algorithm, which is less than one second, the network parameters like the frame length and cycle duration are explored to find their best choice concerning the schedule feasibility.

eess.SY↗

arXiv2018

Roster Evaluation Based on Classifiers for the Nurse Rostering Problem

The personnel scheduling problem is a well-known NP-hard combinatorial problem. Due to the complexity of this problem and the size of the real-world instances, it is not possible to use exact methods, and thus heuristics, meta-heuristics, or hyper-heuristics must be employed. The majority of heuristic approaches are based on iterative search, where the quality of intermediate solutions must be calculated. Unfortunately, this is computationally highly expensive because these problems have many constraints and some are very complex. In this study, we propose a machine learning technique as a tool to accelerate the evaluation phase in heuristic approaches. The solution is based on a simple classifier, which is able to determine whether the changed solution (more precisely, the changed part of the solution) is better than the original or not. This decision is made much faster than a standard cost-oriented evaluation process. However, the classification process cannot guarantee 100% correctness. Therefore, our approach, which is illustrated using a tabu search algorithm in this study, includes a filtering mechanism, where the classifier rejects the majority of the potentially bad solutions and the remaining solutions are then evaluated in a standard manner. We also show how the boosting algorithms can improve the quality of the final solution compared with a simple classifier. We verified our proposed approach and premises, based on standard and real-world benchmark instances, to demonstrate the significant speedup obtained with comparable solution quality.

cs.AI↗

arXiv2018

Energy Optimization of Robotic Cells

This study focuses on the energy optimization of industrial robotic cells, which is essential for sustainable production in the long term. A holistic approach that considers a robotic cell as a whole toward minimizing energy consumption is proposed. The mathematical model, which takes into account various robot speeds, positions, power-saving modes, and alternative orders of operations, can be transformed into a mixed-integer linear programming formulation that is, however, suitable only for small instances. To optimize complex robotic cells, a hybrid heuristic accelerated by using multicore processors and the Gurobi simplex method for piecewise linear convex functions is implemented. The experimental results showed that the heuristic solved 93 % of instances with a solution quality close to a proven lower bound. Moreover, compared with the existing works, which typically address problems with three to four robots, this study solved real-size problem instances with up to 12 robots and considered more optimization aspects. The proposed algorithms were also applied on an existing robotic cell in Škoda Auto. The outcomes, based on simulations and measurements, indicate that, compared with the previous state (at maximal robot speeds and without deeper power-saving modes), the energy consumption can be reduced by about 20 % merely by optimizing the robot speeds and applying power-saving modes. All the software and generated datasets used in this research are publicly available.

cs.RO↗

arXiv2018

Using Two Independent Channels with Gateway for FlexRay Static Segment Scheduling

The FlexRay bus is a communication standard used in the automotive industry. It offers a deterministic message transmission in the static segment following a time-triggered schedule. Even if its bandwidth is ten times higher than the bandwidth of CAN, its throughput limits are going to be reached in high-class car models soon. A solution that could postpone this problem is to use an efficient scheduling algorithm that exploits both channels of the FlexRay. The significant and often neglected feature that can theoretically double the bandwidth is the possibility to use two independent communication channels that can intercommunicate through the gateway. In this paper, we propose a heuristic algorithm that decomposes the scheduling problem to the ECU-to-channel assignment subproblem which decides which channel the ECUs (Electronic Control Units) should be connected to and the channel scheduling subproblem which creates static segment communication schedules for both channels. The algorithm is able to create a schedule for cases where channels are configured in the independent mode as well as in the fault-tolerant mode or in cases where just part of the signals are fault-tolerant. Finally, the algorithm is evaluated on real data and synthesized data, and the relation between the portion of fault-tolerant signals and the number of allocated slots is presented.

eess.SY↗

arXiv2018

Algorithms for robust production scheduling with energy consumption limits

In this work, we consider a scheduling problem faced by production companies with large electricity consumption. Due to the contract with the electric utility, the production companies are obligated to comply with the total energy consumption limits in the specified time intervals (usually 15-minutes long), otherwise, the companies pay substantial penalty fees. Although it is possible to design production schedules that consider these limits as hard constraints, uncertainties occurring during the execution of the schedules are usually not taken into account. This may lead to situations in which the unexpected delays of the operations cause the violations of the energy consumption limits. Our goal is to design robust production schedules pro-actively guaranteeing that the energy consumption limits are not violated for the given set of uncertainty scenarios. We consider scheduling on one machine with release times of the operations and total tardiness as the objective function. To tackle this problem, we first propose a pseudo-polynomial algorithm for finding the optimal robust schedule for the given permutation of the operations. This algorithm is then utilised in three different algorithms for finding the optimal permutation: two exact (Branch-and-Bound and logic-based Benders decomposition) and one heuristic algorithm (tabu search). All the algorithms were experimentally evaluated on random instances with different sizes of the uncertainty scenarios set. Using the tabu search algorithm, we are able to solve large instances within one minute.

cs.DS↗

arXiv2018

Adaptive online scheduling of tasks with anytime property on heterogeneous resources

An acceptable response time of a server is an important aspect in many client-server applications; this is evident in situations in which the server is overloaded by many computationally intensive requests. In this work, we consider that the requests, or in this case tasks, generated by the clients are instances of optimization problems solved by anytime algorithms, i.e. the quality of the solution increases with the processing time of a task. These tasks are submitted to the server which schedules them to the available computational resources where the tasks are processed. To tackle the overload problem, we propose a scheduling algorithm which combines traditional scheduling approaches with a quality control heuristic which adjusts the requested quality of the solutions and thus changes the processing time of the tasks. Two efficient quality control heuristics are introduced: the first heuristic sets a global quality for all tasks, whereas the second heuristic sets the quality for each task independently. Moreover, in practice, the relationship between the processing time and the quality is not known a priori. Because it is crucial for scheduling algorithms to know at least the estimation of these relationships, we propose a general procedure for estimating these relationships using information obtained from the already executed tasks. Finally, the performance of the proposed scheduling algorithm is demonstrated on a real-world problem from the domain of personnel rostering with very good results.

cs.DC↗

arXiv2016

The triangle scheduling problem

This paper introduces a novel scheduling problem, where jobs occupy a triangular shape on the time line. This problem is motivated by scheduling jobs with different criticality levels. A measure is introduced, namely the binary tree ratio. It is shown that the greedy algorithm solves the problem to optimality when the binary tree ratio of the input instance is at most 2. We also show that the problem is unary NP-hard for instances with binary tree ratio strictly larger than 2, and provide a quasi polynomial time approximation scheme (QPTAS). The approximation ratio of Greedy on general instances is shown to be between 1.5 and 1.05.

cs.DS↗