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A Unifying Complexity-Certification Framework for Branch-and-Bound Algorithms for Mixed-Integer Linear and Quadratic Programming

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arXiv 2025年

作者： Shoja, Shamisa Arnström, Daniel Axehill, Daniel Division of Automatic Control Department of Electrical Engineering Linköping University Sweden Division of Systems and Control Department of Information Technology Uppsala University Sweden

In model predictive control (MPC) for hybrid systems, solving optimization problems efficiently and with guarantees on worst-case computational complexity is critical, particularly in real-time applications. These optimization problems often take the form of mixed-integer linear programs (MILPs) or mixed-integer quadratic programs (MIQPs) that depend on system parameters. A common approach for solving such problems is the branch-and-bound (B&B) method. This paper extends existing complexity certification methods by presenting a unified complexity-certification framework for B&B-based MILP and MIQP solvers, specifically for the family of multi-parametric MILP and MIQP problems that arise in, e.g., hybrid MPC applications. The framework provides guarantees on worst-case computational metrics, including the maximum number of iterations or relaxations B&B algorithms require to reach optimality. It systematically accounts for different branching and node selection strategies, as well as heuristics integrated into B&B, ensuring a comprehensive certification framework. By offering theoretical guarantees and practical insights for solver customization, the proposed framework enhances the reliability of B&B for real-time application. The usefulness of the proposed framework is demonstrated through numerical experiments on both random MILPs and MIQPs, as well as on MIQPs arising from a hybrid MPC problem. © 2025, CC BY.

关键词： Mixed-integer linear programming

Parallel Domain-Decomposition Algorithms for Complexity Certification of Branch-and-Bound Algorithms for Mixed-Integer Linear and Quadratic Programming

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arXiv 2025年

When implementing model predictive control (MPC) for hybrid systems with a linear or a quadratic performance measure, a mixed-integer linear program (MILP) or a mixed-integer quadratic program (MIQP) needs to be solved, respectively, at each sampling instant. Recent work has introduced the possibility to certify the computational complexity of branch-and-bound (B&B) algorithms when solving MILP and MIQP problems formulated as multi-parametric MILPs (mp-MILPs) and mp-MIQPs. Such a framework allows for computing the worst-case computational complexity of standard B&B-based MILP and MIQP solvers, quantified by metrics such as the total number of LP/QP iterations and B&B nodes. These results are highly relevant for real-time hybrid MPC applications. In this paper, we extend this framework by developing parallel, domain-decomposition versions of the previously proposed algorithm, allowing it to scale to larger problem sizes and enable the use of high-performance computing (HPC) resources. Furthermore, to reduce peak memory consumption, we introduce two modifications to the existing (serial) complexity certification framework, integrating them into the proposed parallel algorithms. Numerical experiments show that the parallel algorithms significantly reduce computation time while maintaining the correctness of the original framework. © 2025, CC BY.

关键词： Mixed-integer linear programming

Modeling and Simulation of Pollution Removal Efficiency in Activated Sludge Wastewater Treatment Processes

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Modeling and Simulation of Pollution Removal Efficiency in A...

IEEE SSD International Multi-Conference on systems, Signals and Devices

作者： Sameh Chattaoui Raja Jarray Soufiene Bouallègue Research Laboratory in Automatic Control (LARA) National Engineering School of Tunis National Higher Engineering School of Tunis Tunis Tunisia Research Laboratory in Automatic Control (LARA) National Engineering School of Tunis High Institute of Industrial Systems of Gabès Gabès Tunisia

ISBN: (数字)9798331542726

ISBN: (纸本)9798331542733

Water pollution is a growing challenge for the environment and ecosystems, necessitating management of Wastewater Treatment Plants (WWTPs). Modeling the dynamical behaviors of these complex systems significantly affects the control and prediction performance. This study compares the performance of three widely used Activated Sludge Models (ASM1, ASM2, and ASM3) in removing key pollutants, mainly including Chemical Oxygen Demand (COD), Biochemical Oxygen Demand (BOD5), Total Suspended Solids (TSS), Total Nitrogen (TN), and Hydrogen potential (pH). Each model of the activated sludge process incorporates unique representation of biological and chemical processes like nitrification, denitrification, and phosphorus removal. The results demonstrate significant differences in the models' stability, sensitivity, and effectiveness under varied operational conditions. The ASM3 benchmark consistently performs well in extreme scenarios, ASM1 shows strong stability, and ASM2 balances efficiency and reliability. These findings provide actionable insights for optimizing WWTP's operations, guiding model selection based on specific treatment objectives.

关键词： Analytical models Oxygen Sensitivity Purification Biological system modeling Predictive models Stability analysis Wastewater treatment Sludge treatment Context modeling

Driver Behaviour Soft-Sensor based on Neurofuzzy systems and Weighted Projection on Principal Components

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arXiv 2025年

作者： Escaño, Juan Manuel Ridao-Olivar, Miguel A. Ierardi, Carmelina Sánchez, Adolfo J. Rouzbehi, Kumars Department of Systems Engineering and Automatic Control Universidad de Sevilla Sevilla41092 Spain Department of Engineering Universidad Loyola Andalucía Sevilla41704 Spain

This work has as main objective the development of a soft-sensor to classify, in real time, the behaviors of drivers when they are at the controls of a vehicle. Efficient classification of drivers’ behavior while driving, using only the measurements of the sensors already incorporated in the vehicles and without the need to add extra hardware (smart phones, cameras, etc.), is a challenge. The main advantage of using only the data center signals of modern vehicles is economical. The classification of the driving behavior and the warning to the driver of dangerous behaviors without the need to add extra hardware (and their software) to the vehicle, would allow the direct integration of these classifiers into the current vehicles without incurring a greater cost in the manufacture of the vehicles and therefore be an added value. In this work, the classification is obtained based only on speed, acceleration and inertial measurements which are already present in many modern vehicles. The proposed algorithm is based on a structure made by several Neurofuzzy systems with the combination of projected data in components of various Principal Component Analysis. A comparison with several types of classical classifying algorithms has been made. © 2025, CC BY.

关键词： Smartphones

TCIP: Transformed Colour Intensity Profiles analysis for fault detection in power line insulators

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Multimedia Tools and Applications 2025年第8期84卷 4503-4534页

作者： Tomaszewski, Michal Gasz, Rafal Kasana, Singara Singh Osuchowski, Jakub Singh, Simranjit Zator, Slawomir Department of Computer Science Faculty of Electrical Engineering Automatic Control and Informatics Opole University of Technology Prószkowska 76 Opole45-758 Poland Department of Computer Science and Information Technology Central University of Haryana Haryana Mahendergarh123031 India Department of Information Technology Dr B. R. Ambedkar National Institute of Technology Punjab Jalandhar India Department of Safety Engineering and Technical Systems Faculty of Production Engineering and Logistics Opole University of Technology Prószkowska 76 Opole45-758 Poland

In response to the escalating demand for electricity, the aging process and inherent failures in power lines have become unavoidable challenges in their operational integrity. This research addresses the imperative need for a robust method to detect damage in power insulator disc images, introducing a novel feature extraction technique grounded in color intensity profile transformation and ensemble learning. For the purposes of the research, a specific dataset was developed based on publicly available images of power insulators. The collection consists of 9232 images of insulator discs which included 2184 images of damaged discs. The discernible damages include breakages and burnouts. Two distinct analysis variants were employed. In the first variant (V1), two classification groups were selected: disc with damages and disc without damages. In the second variant (V2), three classification groups were selected: discs without damage, broken discs, and burnout discs. The described research was divided into two successive stages. In the first of them (S1), the transformed color intensity profiles for the prepared data set were built and various machine learning models for their classification were trained and evaluated. In the next stage (S2), previously developed, highest efficient machine learning models, were used to make the detection of various damaged types of overhead line insulator discs. For the first stage of research high-performance results and a high value of the F1 score parameters were obtained (F1 score = 0.999 for the first variant (S1V1) and F1 score = 0.992 for the second variant (S1V2). In the second stage of research and the first variant (S2V1), the highest result of the F1 score was 0.932 and for the second variant (S2V2) F1 score was 0.930. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

关键词： Feature extraction

Design of a Navigation Function for a Polyhedral World 16th

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Design of a Navigation Function for a Polyhedral World

16th APCA International Conference on automatic control and Soft Computing, controlO 2024

作者： Nicu, Theodor-Gabriel Stoican, Florin Ioan, Daniel Prodan, Ionela Department of Automatic Control and Systems Engineering Romania National University of Science and Technology "Politehnica" Bucharest 313 Splaiul Independenţei Bucharest060042 Romania Univ. Grenoble Alpes Grenoble INP Institute of Engineering and Management LCIS Valence26000 France

ISBN: (纸本)9783031817236

This work pertains to the generation of navigation functions for obstacle avoidance and target tracking. One initially defines a so-called spherical world which can be further mapped into many other different topologies using a series of diffeomorphic transformations. This specific configuration further allows one to exploit the main advantages of the sum function approach with respect to the obstacle collision avoidance capabilities of an agent, sum function which is used in order to induce an effective navigation function judging not only from computational perspective, but also from the local minima point of view. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Topology

CONVERGENCE ANALYSIS OF LINEARIZED q PENALTY METHODS FOR NONCONVEX OPTIMIZATION WITH NONLINEAR EQUALITY CONSTRAINTS

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arXiv 2025年

作者： El Bourkhissi, Lahcen Necoara, Ion Department of Automatic Control and Systems Engineering National University of Science and Technology Politehnica Bucharest Romania Department of Automatic Control and Systems Engineering National University of Science and Technology Politehnica Bucharest Bucharest060042 Romania Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy Bucharest050711 Romania

In this paper, we consider nonconvex optimization problems with nonlinear equality constraints. We assume that the objective function and the functional constraints are locally smooth. To solve this problem, we introduce a linearized q penalty based method, where q ∈ (1, 2] is the parameter defining the norm used in the construction of the penalty function. Our method involves linearizing the objective function and functional constraints in a Gauss-Newton fashion at the current iteration in the penalty formulation and introduces a quadratic regularization. This approach yields an easily solvable subproblem, whose solution becomes the next iterate. By using a novel dynamic rule for the choice of the regularization parameter, we establish that the iterates of our method converge to an ǫ-first-order solution in O(1/ǫ2+(q−1)/q) outer iterations. Finally, we put theory into practice and evaluate the performance of the proposed algorithm by making numerical comparisons with existing methods from literature. © 2025, CC BY.

关键词： Numerical methods

Low production cost virtual modelling and control laboratories for chemical engineering students

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IFAC-PapersOnLine 2016年第6期49卷 230-235页

作者： Rossiter, J.A. Department of Automatic Control and Systems Engineering University of Sheffield SheffieldS1 3JD United Kingdom

This paper gives a brief review of work on virtual and remote laboratories along with a critique of their strengths and weaknesses. This is used as a motivation for a proposed method for producing virtual laboratories which, while relatively crude in comparison with professional alternatives, are much cheaper and faster to produce and thus can be created using the skill set and time of normal academics. Some examples and the coding processes are demonstrated. © 2016

关键词： Cost engineering Laboratories Chemical engineering students Coding process Independent learning Modelling and controls Production cost Remote laboratories Student engagement Virtual laboratories

Path Planning for Autonomous Underwater Vehicles in Complex Environments Based on a PRM* Algorithm

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Path Planning for Autonomous Underwater Vehicles in Complex ...

IEEE SSD International Multi-Conference on systems, Signals and Devices

作者： Ali Arifi Raja Jarray Soufiene Bouallègue Research Laboratory in Automatic Control (LARA) of National Engineering School of Tunis National Engineering School of Gabès University of Gabès Gabès Tunisia Research Laboratory in Automatic Control (LARA) of National Engineering School of Tunis High Institute of Industrial Systems of Gabès Gabès Tunisia

ISBN: (数字)9798331542726

ISBN: (纸本)9798331542733

This paper proposes a Probabilistic Roadmap (PRM) planner for Autonomous Underwater Vehicles (AUVs) navigating in complex 3D environments. An improved version of PRM algorithms, called PRM*, is introduced to improve the capabilities of nodes specification, edges construction, and graph creation. For implementation, a pseudo-code for the proposed PRM* planner is provided. Numerical simulations are performed in different scenarios with increasing number of static obstacles and complexity. Evaluations of the generated collision-free paths are carried out using the Straight-Line Rate (SLR) and Computational Time (CT) metrics. Analyses and comparisons are performed to validate the significance and superiority of the proposed PRM* planner. Demonstrative results show that the PRM* algorithm outperforms the ordinary PRM one in terms of path compactness, smoothness, and collision avoidance.

关键词： Autonomous underwater vehicles Three-dimensional displays Navigation Probabilistic logic Numerical simulation Path planning Complexity theory Collision avoidance Vehicle dynamics Robots