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Journal articles on the topic 'Lagrangian Relaxation (LR)'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Zeynal, Hossein, Zuhaina Zakaria, and Ahmad Kor. "Improved Lagrangian relaxation generation decision-support in presence of electric vehicles." Indonesian Journal of Electrical Engineering and Computer Science 22, no. 1 (2021): 598–608. https://doi.org/10.11591/ijeecs.v22.i1.pp598-608.

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Decision making strategies for resources available in macro/micro scales have long been a critical argument. Among existing methods to address such a mixed-binary optimization model, Lagrangian relaxation (LR) found universal acceptance by many utilities, offering a fast and accurate answer. This paper aims at retrofitting the solution way of LR algorithm by dint of meta-heuristic cuckoo search algorithm (CSA). When integrating CSA into LR mechanism, a tighter duality gap is catered, representing more accurate feasible solution. The key performance of CSA exhibits a head start over other class

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Zeynal, Hossein, Zuhaina Zakaria, and Ahmad Kor. "Improved Lagrangian relaxation generation decision-support in presence of electric vehicles." Indonesian Journal of Electrical Engineering and Computer Science 22, no. 1 (2021): 598. http://dx.doi.org/10.11591/ijeecs.v22.i1.pp598-608.

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<p><span>Decision making strategies for resources available in macro/micro scales have long been a critical argument. Among existing methods to address such a mixed-binary optimization model, Lagrangian relaxation (LR) found universal acceptance by many utilities, offering a fast and accurate answer. This paper aims at retrofitting the solution way of LR algorithm by dint of meta-heuristic cuckoo search algorithm (CSA). When integrating CSA into LR mechanism, a tighter duality gap is catered, representing more accurate feasible solution. The key performance of CSA exhibits a head s

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3

Rodrigues, Rafael N., Edson L. da Silva, Erlon C. Finardi, and Fabricio Y. K. Takigawa. "Solving the Short-Term Scheduling Problem of Hydrothermal Systems via Lagrangian Relaxation and Augmented Lagrangian." Mathematical Problems in Engineering 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/856178.

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This paper addresses the short-term scheduling problem of hydrothermal power systems, which results in a large-scale mixed-integer nonlinear programming problem. The objective consists in minimizing the operation cost over a two-day horizon with a one-hour time resolution. To solve this difficult problem, a Lagrangian Relaxation (LR) based on variable splitting is designed where the resulting dual problem is solved by a Bundle method. Given that the LR usually fails to find a feasible solution, we use an inexact Augmented Lagrangian method to improve the quality of the solution supplied by the

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4

Hussin, S. M., M. Y. Hassan, L. Wu, M. P. Abdullah, N. Rosmin, and M. A. Ahmad. "Mixed Integer Linear Programming for Maintenance Scheduling in Power System Planning." Indonesian Journal of Electrical Engineering and Computer Science 11, no. 2 (2018): 607. http://dx.doi.org/10.11591/ijeecs.v11.i2.pp607-613.

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This paper discussed the merit of mixed-integer linear programming (MILP)-based approach against Lagrangian relaxation (LR)-based approach in solving generation and transmission maintenance scheduling problem. MILP provides a straightforward solution by formulating coupling constraints equations so that these sub-problems can be solved simultaneously without involving multipliers. In LR-based approach, generation and transmission maintenance scheduling, and security-constrained unit commitment have been solved individually and the integration was realized through a series of multipliers which

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S.M., Hussin, Hassan M.Y., Wu L., Abdullah M.P., Rosmin N., and Ahmad M.A. "Mixed Integer Linear Programming for Maintenance Scheduling in Power System Planning." Indonesian Journal of Electrical Engineering and Computer Science 11, no. 2 (2018): 607–13. https://doi.org/10.11591/ijeecs.v11.i2.pp607-613.

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This paper discussed the merit of mixed-integer linear programming (MILP)- based approach against Lagrangian relaxation (LR)-based approach in solving generation and transmission maintenance scheduling problem. MILP provides a straightforward solution by formulating coupling constraints equations so that these sub-problems can be solved simultaneously without involving multipliers. In LR-based approach, generation and transmission maintenance scheduling, and security-constrained unit commitment have been solved individually and the integration was realized through a series of multipliers which

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Rajamanickam, Subramani, and Vijayalakshmi C. "Design and Analysis of Lagrangian Algorithm for Power Flow System using Renewable Energy Resources." Indonesian Journal of Electrical Engineering and Computer Science 7, no. 2 (2017): 348. http://dx.doi.org/10.11591/ijeecs.v7.i2.pp348-355.

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This paper mainly deals with the implementation of an Lagrangian Relaxation (LR) technique through a Supervisory Control and Data Acquisition (SCADA) system. Maintaining Power Station is not an easy task which to achieve its demand such as regulating inputs monitoring energy losses. In this paper we have introduced novel SCADA based decentralized approach to minimize the loss of the system and optimize the total generation cost. Due to the nonlinearities of Electricity demand and scheduling time, the problem is not solvable with the usual optimization techniques. For getting appropriate soluti

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7

Filik, Ummuhan Basaran, and Mehmet Kurban. "Feasible Modified Subgradient Method for Solving the Thermal Unit Commitment Problem as a New Approach." Mathematical Problems in Engineering 2010 (2010): 1–11. http://dx.doi.org/10.1155/2010/159429.

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The Lagrangian relaxation- (LR-) based methods are commonly used to solve the thermal unit commitment (UC) problem which is an important subject in power system engineering. The main drawback of this group of methods is the difference between the dual and the primal solutions which gives some significant problems on the quality of the feasible solutions. In this paper, a new approach, feasible modified subgradient (F-MSG) method which does not require finding an unconstrained global minimum of the Lagrangian function and knowing an optimal value of the problem under consideration in order to u

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Wu, Hongyu, Qiaozhu Zhai, Xiaohong Guan, Feng Gao, and Hongxing Ye. "Security-Constrained Unit Commitment Based on a Realizable Energy Delivery Formulation." Mathematical Problems in Engineering 2012 (2012): 1–22. http://dx.doi.org/10.1155/2012/178193.

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Security-constrained unit commitment (SCUC) is an important tool for independent system operators in the day-ahead electric power market. A serious issue arises that the energy realizability of the staircase generation schedules obtained in traditional SCUC cannot be guaranteed. This paper focuses on addressing this issue, and the basic idea is to formulate the power output of thermal units as piecewise-linear function. All individual unit constraints and systemwide constraints are then reformulated. The new SCUC formulation is solved within the Lagrangian relaxation (LR) framework, in which a

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9

Zhang, Yungui, Huizhao Li, Xue Wang, and Yan Zeng. "A novel approach for solving multi-objective unit commitment based on decompositioncoordination." MATEC Web of Conferences 277 (2019): 03006. http://dx.doi.org/10.1051/matecconf/201927703006.

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Multi-objective unit commitment (MOUC) considers simultaneously both economic and environmental objectives, then finds the best trade off with respect to these objectives. This paper proposes a novel model for MOUC, and a decomposition coordination approach is presented to solve the model. The MOUC model considers environmental objective by introducing a novel penalty term, and it's a quantized term for preference of environmental objective, which could be a basis for carbon tax makers. The model is solved by a decomposition coordination approach, which decomposes the whole system into subsyst

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10

Hsiao, Chiu-Han, Frank Yeong-Sung Lin, Hao-Jyun Yang, et al. "Optimization-Based Approaches for Minimizing Deployment Costs for Wireless Sensor Networks with Bounded Estimation Errors." Sensors 21, no. 21 (2021): 7121. http://dx.doi.org/10.3390/s21217121.

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As wireless sensor networks have become more prevalent, data from sensors in daily life are constantly being recorded. Due to cost or energy consumption considerations, optimization-based approaches are proposed to reduce deployed sensors and yield results within the error tolerance. The correlation-aware method is also designed in a mathematical model that combines theoretical and practical perspectives. The sensor deployment strategies, including XGBoost, Pearson correlation, and Lagrangian Relaxation (LR), are determined to minimize deployment costs while maintaining estimation errors below

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11

Kurban, Mehmet, and Ümmühan Başaran Filik. "A Comparative Study of Three Different Mathematical Methods for Solving the Unit Commitment Problem." Mathematical Problems in Engineering 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/368024.

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The unit commitment (UC) problem which is an important subject in power system engineering is solved by using Lagragian relaxation (LR), penalty function (PF), and augmented Lagrangian penalty function (ALPF) methods due to their higher solution quality and faster computational time than metaheuristic approaches. This problem is considered to be a nonlinear programming-(NP-) hard problem because it is nonlinear, mixed-integer, and nonconvex. These three methods used for solving the problem are based on dual optimization techniques. ALPF method which combines the algorithmic aspects of both LR

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12

Lin, Frank Yeong-Sung, Chiu-Han Hsiao, Kuo-Chung Chu, and Yi-Heng Liu. "Minimum-Cost QoS-Constrained Deployment and Routing Policies for Wireless Relay Networks." Journal of Applied Mathematics 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/517846.

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With the continued evolution of wireless communication technology, relaying is one of the features proposed for the 4G LTE Advanced (LTE-A) system. The aim of relaying is to enhance both coverage and capacity. The idea of relays is not new, but relaying is being considered to ensure that the optimum performance is achieved to enable the expectations or good quality of service (QoS) of the users to be met while still keeping capital expenditure (CAPEX) within the budgeted bounds of operators. In this paper, we try to stand for an operator to propose a solution that determines where and how many

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13

Li, Hao, Zhengwu Wang, Shuiwang Chen, Weiyao Xu, Lu Hu, and Shuai Huang. "Integrated optimization of planning and operation of a shared automated electric vehicle system considering the trip selection and opportunity cost." Electronic Research Archive 32, no. 1 (2023): 41–71. http://dx.doi.org/10.3934/era.2024003.

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<abstract> <p>Shared autonomous electric vehicle systems (SAEVS) combine autonomous driving technology with shared electric vehicle services to provide advantages over traditional shared vehicle systems, including autonomous vehicle relocation and rapid response to user needs. In this study, we seek to enhance the operational efficiency and profitability of SAEVS by considering trip selection and the potential opportunity cost associated with unmet user demands. An integer linear programming (ILP) model is developed using a spatio-temporal state network to optimize the system desig

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14

Gopal, Kumar Parop, and Sambath M. "A hybrid multi-constraint lagrangian relaxation based aggregated cost based segment routing in qos aware software defined networks." Vietnam Journal of Science and Technology 63, no. 3 (2025): 576–93. https://doi.org/10.15625/2525-2518/19667.

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The rise of Software Defined Networking (SDN) increases routing flexibility and offers a more efficient method of balancing network flows. Because of the economic and technological challenges of shifting to a fully SDN-enabled network, the prevalent network design has been a hybrid SDN network architecture with partially deploying SDN switches in a traditional network. As the need for efficient and dependable network services in Software Defined Networks (SDNs) grows, guaranteeing Quality of Service (QoS) has become a significant concern. This study presents a new technique, "Hybrid Multi-cons

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15

Wu, Xinyu, Ruixiang Cheng, and Chuntian Cheng. "A Simplified Solution Method for End-of-Term Storage Energy Maximization Model of Cascaded Reservoirs." Energies 15, no. 12 (2022): 4503. http://dx.doi.org/10.3390/en15124503.

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In medium-term scheduling, the end-of-term storage energy maximization model is proposed to create conditions for the safety, stability and economic operation of the hydropower system after control term, which satisfies the system load demand undertaken by the cascaded system in a given scheduling period. This paper presents a simplified solution method based on the Lagrangian relaxation method (LR) to solve the end-of-term storage energy maximization model. The original Lagrange dual problem with multiple Lagrange multipliers is converted to that with only one Lagrange multiplier by an entrop

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16

Hsiao, Chiu-Han, Yean-Fu Wen, Frank Yeong-Sung Lin, et al. "An Optimization-Based Orchestrator for Resource Access and Operation Management in Sliced 5G Core Networks." Sensors 22, no. 1 (2021): 100. http://dx.doi.org/10.3390/s22010100.

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Network slicing is a promising technology that network operators can deploy the services by slices with heterogeneous quality of service (QoS) requirements. However, an orchestrator for network operation with efficient slice resource provisioning algorithms is essential. This work stands on Internet service provider (ISP) to design an orchestrator analyzing the critical influencing factors, namely access control, scheduling, and resource migration, to systematically evolve a sustainable network. The scalability and flexibility of resources are jointly considered. The resource management proble

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17

Aghdamigargari, Mehri, Sylvester Avane, Angelina Anani, and Sefiu O. Adewuyi. "Sustainability in Long-Term Surface Mine Planning: A Systematic Review of Operations Research Applications." Sustainability 16, no. 22 (2024): 9769. http://dx.doi.org/10.3390/su16229769.

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The mining industry, critical for global resource supply, has historically been linked to significant environmental degradation and social challenges, including habitat disruption, water and soil contamination, as well as fatalities. But recently, the industry has been undergoing a transformative change to meet evolving environmental and societal expectations. Operations Research (OR) provides essential tools and techniques to optimize decision-making processes in this context. This paper presents a comprehensive review of different OR methods and their applications in balancing economic, soci

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18

Başaran Filik, Ümmühan, and Mehmet Kurban. "Solving Unit Commitment Problem Using Modified Subgradient Method Combined with Simulated Annealing Algorithm." Mathematical Problems in Engineering 2010 (2010): 1–15. http://dx.doi.org/10.1155/2010/295645.

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This paper presents the solving unit commitment (UC) problem using Modified Subgradient Method (MSG) method combined with Simulated Annealing (SA) algorithm. UC problem is one of the important power system engineering hard-solving problems. The Lagrangian relaxation (LR) based methods are commonly used to solve the UC problem. The main disadvantage of this group of methods is the difference between the dual and the primal solution which gives some significant problems on the quality of the feasible solution. In this paper, MSG method which does not require any convexity and differentiability a

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19

Baghizadeh, Komeyl, Dominik Zimon, and Luay Jum’a. "Modeling and Optimization Sustainable Forest Supply Chain Considering Discount in Transportation System and Supplier Selection under Uncertainty." Forests 12, no. 8 (2021): 964. http://dx.doi.org/10.3390/f12080964.

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In recent decades, the forest industry has been growingly expanded due to economic conditions, climate changes, environmental and energy policies, and intense demand changes. Thus, appropriate planning is required to improve this industry. To achieve economic, social and environmental goals, a supply chain network is designed based on a multi-period and multi-product Mixed-Integer Non-Linear Programming (MINLP) model in which the objective is to maximize the profit, minimize detrimental environmental effects, improve social effects, and minimize the number of lost demands. In addition, to impr

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20

Sadeghi, Amir Hossein, Ziyuan Sun, Amirreza Sahebi-Fakhrabad, Hamid Arzani, and Robert Handfield. "A Mixed-Integer Linear Formulation for a Dynamic Modified Stochastic p-Median Problem in a Competitive Supply Chain Network Design." Logistics 7, no. 1 (2023): 14. http://dx.doi.org/10.3390/logistics7010014.

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Background: The Dynamic Modified Stochastic p-Median Problem (DMS-p-MP) is an important problem in supply chain network design, as it deals with the optimal location of facilities and the allocation of demand in a dynamic and uncertain environment. Methods: In this research paper, we propose a mixed-integer linear formulation for the DMS-p-MP, which captures the key features of the problem and allows for efficient solution methods. The DMS-p-MP adds two key features to the classical problem: (1) it considers the dynamic nature of the problem, where the demand is uncertain and changes over time

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21

R., Subramani* C. Vijayalakshmi. "IMPLEMENTATION OF NON-LINEAR MULTI OBJECTIVE OPTIMIZATION FOR ENERGY MANAGEMENT SYSTEMS." Global Journal of Engineering Science and Research Management 4, no. 7 (2017): 35–43. https://doi.org/10.5281/zenodo.824967.

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This paper mainly deals with the development of an energy management of the platform using a SCADA (Supervisory Control and Data Acquisition) system. A predictive controller is implemented above the centralized SCADA platform. The distribution net-works have been focused by a Monitor, Control and maintain equipment in the sub stations to reduce the operating cost. This re-search proposes a new energy management model is that enables a flexible and also efficient operation of various power plants. The Distribution Control Centre (DCC) is being monitored and controlled by SCADA systems and the D

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22

Feng, Xiaoming, and Yuan Liao. "Unit Commitment by Structure Based Solution and Efficient Lagrangian Relaxation." International Journal of Emerging Electric Power Systems 11, no. 1 (2010). http://dx.doi.org/10.2202/1553-779x.2328.

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Lagrangian relaxation (LR) is one of the most promising approaches for solving power system unit commitment (UC) problems by means of decomposition. There are several technical challenges in developing an effective LR solution. The first is to devise an efficient dual optimization procedure. The second is to have a quick and reliable procedure for removing residual violations in the relaxed constraints. The third is to make the solution algorithm less dependent of problem domain knowledge to improve solution portability. This paper presents a general algorithm that depends only on the formal s

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23

Fattahi, Parviz, and Mehdi Tanhatalab. "Stochastic inventory-routing problem with lateral transshipment for perishable product." Journal of Modelling in Management ahead-of-print, ahead-of-print (2021). http://dx.doi.org/10.1108/jm2-09-2019-0230.

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Purpose This study aims to design a supply chain network in an uncertain environment while exists two options for distribution of the perishable product and production lot-sizing is concerned. Design/methodology/approach Owing to the complexity of the mathematical model, a solution approach based on a Lagrangian relaxation (LR) heuristic is developed which provides good-quality upper and lower bounds. Findings The model output is discussed through various examples. The introduction of some enhancements and using some heuristics results in better outputs in the solution procedure. Practical imp

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