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arXiv 2024年

作者： Ma, Tingchen Ou, Yongsheng Xu, Sheng The Shenzhen Institute of Advanced Technology Chinese Academy of Sciences Shenzhen518055 China The Shenzhen College of Advanced Technology University of Chinese Academy of Sciences Shenzhen518055 China The Guangdong Provincial Key Lab of Robotics and Intelligent System Shenzhen Institute of Advanced Technology Chinese Academy of Sciences Shenzhen518055 China

The Bundle Adjustment (BA) algorithm is a widely used nonlinear optimization technique in the backend of Simultaneous Localization and Mapping (SLAM) systems. By leveraging the co-view relationships of landmarks from multiple perspectives, it constructs a joint estimation model for both poses and landmarks, enabling the system to generate refined maps and reduce front-end localization errors. However, applying BA to LiDAR data presents unique challenges due to the large volume of 3D points typically present in point clouds, making robust and accurate model solving more complex. In this work, we propose a novel mean square group metric (MSGM). This metric applies mean square transformation to uniformly process the measurement of plane landmarks from a single perspective. The transformed metric ensures scale interpretability while avoiding the time-consuming point-by-point calculations. By integrating a robust kernel function, the metrics involved in the BA model are reweighted, enhancing the robustness of the solution process. On the basis of the proposed robust LiDAR BA model, we derived an explicit second-order estimator (RSO-BA). This estimator employs analytical formulas for Hessian and gradient calculations, ensuring the precision of the BA solution. We evaluated the proposed RSO-BA estimator against existing implicit second-order and explicit approximate second-order estimators using the publicly available datasets. The experimental results demonstrate that the RSO-BA estimator outperforms its counterparts regarding registration accuracy and robustness, particularly in large-scale or complex unstructured environments. Copyright © 2024, The Authors. All rights reserved.

关键词： nonlinear programming

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An integrated reliable four-level supply chain with multi-stage products under shortage and stochastic constraints

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE-OPERATIONS & LOGISTICS 2023年第1期10卷 Article: 1958023页

作者： Gharaei, Abolfazl Amjadian, Alireza Shavandi, Ali Univ Toronto Fac Engn Dept Mech & Ind Engn 5 Kings Coll Rd Toronto ON M5S 3G8 Canada Kharazmi Univ Fac Engn Dept Ind Engn Tehran Iran Sharif Univ Technol Fac Engn Dept Ind Engn Tehran Iran

In this paper, we design and optimise an integrated four-level Supply Chain (SC), which contains a supplier, a producer, a wholesaler and multiple retailers. The levels cooperate to make an Integrated SC (ISC) so that the inventory cost is minimised and the reliability is maximised, simultaneously. The model is constrained by real stochastic constraints on total space, number of orders, procurement cost, shortage cost, setup cost and production capacity. An Lp-Metric function converts the reliability function and cost function into a single-objective function to optimise the number of stockpiles and period lengths. The designed ISC is a large-scale nonlinear programming (NLP) and hard to solve by generic methods. Accordingly, two algorithms, entitled 'Sequential Quadratic programming (SQP)' and 'Interior Point (IP)' with super-linear convergence rates are applied for finding the optimum solution. The performance of proposed algorithms is compared based on optimality criteria. Findings showed that the obtained solutions by SQP algorithm have better performance than IP algorithm in terms of optimality error and solution quality. However, the number of taken iterations by IP is less than SQP algorithm. Finally, the result of sensitivity analyses confirmed the excellent performance of the presented methods for solving the large-scale NLP models.

关键词： Reliability supply chain integration inventory nonlinear programming Sequential Quadratic programming (SQP) Interior Point (IP)

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Direct Shooting Method for Numerical Optimal Control: A Modified Transcription Approach

arXiv

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arXiv 2024年

作者： Tang, Jiawei Zhong, Yuxing Wang, Pengyu Chen, Xingzhou Wu, Shuang Shi, Ling The Department of Electronic and Computer Engineering Hong Kong University of Science and Technology Clear Water Bay Hong Kong Shenzhen Key Laboratory of Robotics Perception and Intelligence The Department of Electronic and Electrical Engineering Southern University of Science and Technology Shenzhen China The Noah’s Ark Lab Huawei Canada

Direct shooting is an efficient method to solve numerical optimal control. It utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control problem making the problem solvable by nonlinear programming solvers. However, conventional direct shooting raises a contradictory dynamics issue when using an augmented state to handle high-order systems. This paper fills the research gap by considering the direct shooting method for high-order systems. We derive the modified Euler and Runge-Kutta-4 methods to transcribe the system dynamics constraint directly. Additionally, we provide the global error upper bounds of our proposed methods. A set of benchmark optimal control problems shows that our methods provide more accurate solutions than existing approaches. © 2024, CC BY.

关键词： nonlinear programming

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Partial-to-Partial Shape Matching with Geometric Consistency

arXiv

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arXiv 2024年

作者： Ehm, Viktoria Gao, Maolin Roetzer, Paul Eisenberger, Marvin Cremers, Daniel Bernard, Florian Technical University of Munich Germany Munich Center for Machine Learning Germany University of Bonn Germany

Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. A prominent challenge are partial-to-partial shape matching settings, which occur when the shapes to match are only observed incompletely (e.g. from 3D scanning). Although partial-to-partial matching is a highly relevant setting in practice, it is rarely explored. Our work bridges the gap between existing (rather artificial) 3D full shape matching and partial-to-partial real-world settings by exploiting geometric consistency as a strong constraint. We demonstrate that it is indeed possible to solve this challenging problem in a variety of settings. For the first time, we achieve geometric consistency for partial-to-partial matching, which is realized by a novel integer non-linear program formalism building on triangle product spaces, along with a new pruning algorithm based on linear integer programming. Further, we generate a new inter-class dataset for partial-to-partial shape-matching. We show that our method outperforms current SOTA methods on both an established intra-class dataset and our novel inter-class dataset. The code of this work is publicly available1 Copyright © 2024, The Authors. All rights reserved.

关键词： nonlinear programming

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Insights on the Cenozoic Tectonic Evolution and Heat Sources in the Eastern Tibet Plateau Revealed by Magnetotelluric Imaging

SSRN

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SSRN 2024年

作者： Ji, Leizhe Jin, Sheng Ye, Gaofeng Sun, Xiaolei Wei, Wenbo Qi, Jialin School of Geophysics and Information Technology China University of Geosciences Beijing100083 China Key Laboratory of Intraplate Volcanoes and Earthquakes China University of Geosciences Beijing Ministry of Education Beijing100083 China Land Resources Exploration Center of Hebei Bureau of Geology and Mineral Exploration and Development Shijiazhuang050081 China

The continued collision of the Indian and Asian continents has formed the Himalayas and Tibetan Plateau through various deformation processes. The uplift and deformation are also accompanied by extensive geothermal activity. However, the geodynamic mechanism is still unclear and debated on the rigid-block extrusion model and the mid-lower crustal flow model. To address this challenge, we obtained a 3D resistivity model in the eastern Tibetan Plateau using a nonlinear conjugate gradient method based on the Magnetotelluric sounding data. Two low-resistivity anomalies (C1 and C2) are identified in the Ganzi-Litang suture and near the Xianshuihe fault, isolated by the crustal high-resistivity body and an upper mantle medium-resistivity body. We propose that the low-resistivity C1 is caused by the re-activation of the Ganzi-Litang suture, and the low-resistivity C2 can be interpreted as partial melting due to the upwelling of mantle material. Our resistivity model, combined with other geological and geophysical evidences, supports the stepwise uplift propagation style in the eastern Tibetan Plateau, suggesting the tectonic evolution is dominated by the pre-existing lithospheric structural weak zone in the early stage, the late-stage crust deformation is controlled by the mid-lower crustal flow and upwelling of lithospheric mantle material. Furthermore, the Eastern Tibetan Plateau Geothermal Belt (ETGB) can be divided into two types of geothermal belts, each with distinct deep heat source mechanisms, and the thermal channels of the ETGB are unified and controlled by the northwest deep faults in the eastern Tibetan Plateau. © 2024, The Authors. All rights reserved.

关键词： nonlinear programming

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Particle swarm optimization solving nonlinear programming problems in power system

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2nd International Conference on Opto-Electronics Engineering and Materials Research, OEMR 2013

作者： Kang, Li Li, Xiao-Guang Department of Electrical Engineering and Automation Luoyang Institute of Science and Technology Luoyang 471023 China

ISBN: (纸本)9783037857731

In order to improve the control capability of the power system voltage stability and to enhance spatial and temporal coordination of voltage control means, it is essential to establish the model of emergency voltage control that can globally mobilize reactive power support and voltage control potential. Focus on the long-term voltage stability of power system, the paper introduce nonlinear programming into emergency voltage control, settle the problem that how to establish the model of emergency voltage control. Based on detailed models of power system, the receding optimization model of long-term voltage stability control is established under framework of model predictive control. In order to improve the computational efficiency and reduce feedback delays, nonlinear programming sensitivity algorithm is proposed to solve receding optimization model. The proposed method can improve computational efficiency significantly which creates the condition for the emergency voltage control application to large-scale systems. © (2013) Trans Tech Publications, Switzerland.

关键词： nonlinear programming

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Energy Management Strategies for Wt-Pv-Bess Hybrid Ac/Dc Microgrid in Multi-Layer Caged Poultry Farm

SSRN

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SSRN 2024年

作者： Wu, Jiewen Li, Junxiang Liu, Zijun Business School University of Shanghai for Science and Technology Shanghai China School of Intelligent Emergency Management University of Shanghai for Science and Technology Shanghai China

To optimize land resource utilization and reduce raising costs, multi-layer cage systems have been increasingly adopted by chicken farms and are widely regarded as having promising development prospects. However, certain drawbacks of these systems remain evident. The centralized use of ventilation fans increases the harmonic components in individual chicken houses, which can compromise the reliability of not only individual chicken houses but also the entire electrical system. Moreover, as farms are typically located in remote areas, external power grids often experience outages due to various factors. Manually starting standby diesel generators during such outages can lead to hypoxia in chickens during the transition. Additionally, current chicken houses rely entirely on traditional external energy supplies, which are associated with high carbon emissions and do not align with the low-carbon development goals of the farming industry. To address these issues, this paper proposes an AC/DC hybrid microgrid system and corresponding energy management strategies. These include smooth switching strategy for transitions between grid-connected and off-grid modes, pre-synchronization control strategy, grid-connected energy management strategy based on electricity pricing, and nonlinear optimization strategy designed for multi-peak power tracking in photovoltaic generation. Finally, the effectiveness of the AC/DC hybrid microgrid proposed in the article is demonstrated by simulating and analyzing several cases from on-grid, off-grid, and on-off-grid aspects, which provides valuable insights for advancing the development of smart, low-carbon livestock farming. © 2024, The Authors. All rights reserved.

关键词： nonlinear programming

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A Graph-based Adversarial Imitation Learning Framework for Reliable & Realtime Fleet Scheduling in Urban Air Mobility

arXiv

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arXiv 2024年

作者： Poddar, Prithvi Paul, Steve Chowdhury, Souma Department of Mechanical and Aerospace Engineering University at Buffalo University at Buffalo BuffaloNY14260 United States Department of Mechanical and Aerospace Engineering Center for Embodied Autonomy and Robotics University at Buffalo University at Buffalo BuffaloNY14260 United States

The advent of Urban Air Mobility (UAM) presents the scope for a transformative shift in the domain of urban transportation. However, its widespread adoption and economic viability depends in part on the ability to optimally schedule the fleet of aircraft across vertiports in a UAM network, under uncertainties attributed to airspace congestion, changing weather conditions, and varying demands. This paper presents a comprehensive optimization formulation of the fleet scheduling problem, while also identifying the need for alternate solution approaches, since directly solving the resulting integer nonlinear programming problem is computationally prohibitive for daily fleet scheduling. Previous work has shown the effectiveness of using (graph) reinforcement learning (RL) approaches to train real-time executable policy models for fleet scheduling. However, such policies can often be brittle on out-of-distribution scenarios or edge cases. Moreover, training performance also deteriorates as the complexity (e.g., number of constraints) of the problem increases. To address these issues, this paper presents an imitation learning approach where the RL-based policy exploits expert demonstrations yielded by solving the exact optimization using a Genetic Algorithm. The policy model comprises Graph Neural Network (GNN) based encoders that embed the space of vertiports and aircraft, Transformer networks to encode demand, passenger fare, and transport cost profiles, and a Multi-head attention (MHA) based decoder. Expert demonstrations are used through the Generative Adversarial Imitation Learning (GAIL) algorithm. Interfaced with a UAM simulation environment involving 8 vertiports and 40 aircrafts, in terms of the daily profits earned reward, the new imitative approach achieves better mean performance and remarkable improvement in the case of unseen worst-case scenarios, compared to pure RL results. Copyright © 2024, The Authors. All rights reserved.

关键词： nonlinear programming

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Alleviating Range Anxiety: Developing Optimal Speed Profile for Electric Car Driver

SSRN

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SSRN 2024年

作者： Atmaca, Erkan Istanbul University-Cerrahpaşa Faculty of Engineering Electrical and Electronics Engineering Department Avcılar Istanbul34320 Turkey

We propose a solution to the eco-driving problem by framing it as a non-linear optimization problem in space domain. The only decision variables involved are speeds, which are determined at discrete points along a predefined route. Our formulation offers flexibility, allowing the objective function to prioritize either time minimization or energy minimization. This formulation facilitates a rapid solution through both the sequential programming or interior-point method embedded in a commercial software. Given the battery's limited energy capacity and the powerful torque capabilities of the propulsion force, the resulting solution predominantly converges to a nearly constant speed with minor fluctuations, suggesting an average target speed customized for each road section. While sharp corners may induce interruptions on this speed, it can serve as a reference or target speed, easily adhered to by human drivers. This approach has the potential to alleviate range anxiety. © 2024, The Authors. All rights reserved.

关键词： nonlinear programming

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Real-time Safety Index Adaptation for Parameter-varying Systems via Determinant Gradient Ascend

arXiv

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arXiv 2024年

作者： Chen, Rui Zhao, Weiye Liu, Ruixuan Zhang, Weiyang Liu, Changliu Carnegie Mellon University PittsburghPA United States University of Michigan Ann ArborMI United States

Safety Index Synthesis (SIS) is critical for deriving safe control laws. Recent works propose to synthesize a safety index (SI) via nonlinear programming and derive a safe control law such that the system 1) achieves forward invariant (FI) with some safe set and 2) guarantees finite time convergence (FTC) to that safe set. However, real-world system dynamics can vary during run-time, making the control law infeasible and invalidating the initial SI. Since the full SIS nonlinear programming is computationally expensive, it is infeasible to re-synthesize the SI each time the dynamics are perturbed. To address that, this paper proposes an efficient approach to adapting the SI to varying system dynamics and maintaining the feasibility of the safe control law. The proposed method leverages determinant gradient ascend and derives a closed-form update to safety index parameters, enabling real-time adaptation performance. A numerical study validates the effectiveness of our approach. Copyright © 2024, The Authors. All rights reserved.

关键词： nonlinear programming

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