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Lagrangian relaxation

About: Lagrangian relaxation is a research topic. Over the lifetime, 4244 publications have been published within this topic receiving 124805 citations.


Papers
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Journal ArticleDOI
TL;DR: An algorithm for solving stochastic integer programming problems with recourse, based on a dual decomposition scheme and Lagrangian relaxation, which can be applied to multi-stage problems with mixed-integer variables in each time stage.

526 citations

Journal ArticleDOI
TL;DR: The works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC are reviewed to help transform research advances into real-world applications.
Abstract: Optimization models have been widely used in the power industry to aid the decision-making process of scheduling and dispatching electric power generation resources, a process known as unit commitment (UC). Since UC’s birth, there have been two major waves of revolution on UC research and real life practice. The first wave has made mixed integer programming stand out from the early solution and modeling approaches for deterministic UC, such as priority list, dynamic programming, and Lagrangian relaxation. With the high penetration of renewable energy, increasing deregulation of the electricity industry, and growing demands on system reliability, the next wave is focused on transitioning from traditional deterministic approaches to stochastic optimization for unit commitment. Since the literature has grown rapidly in the past several years, this paper is to review the works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC. Relevant lines of future research are also discussed to help transform research advances into real-world applications.

519 citations

Journal ArticleDOI
TL;DR: For Air Products and Chemicals, Inc., inventory management of industrial gases at customer locations is integrated with vehicle scheduling and dispatching, and the system has been saving between 6% to 10% of operating costs.
Abstract: For Air Products and Chemicals, Inc., inventory management of industrial gases at customer locations is integrated with vehicle scheduling and dispatching. Their advanced decision support system includes on-line data entry functions, customer usage forecasting, a time/distance network with a shortest path algorithm to compute intercustomer travel times and distances, a mathematical optimization module to produce daily delivery schedules, and an interactive schedule change interface. The optimization module uses a sophisticated Lagrangian relaxation algorithm to solve mixed integer programs with up to 800,000 variables and 200,000 constraints to near optimality. The system, first implemented in October, 1981, has been saving between 6% to 10% of operating costs.

492 citations

Journal ArticleDOI
TL;DR: Numerical results show that the feature of easy implementation, better convergence, and highly near-optimal solution to the UC problem can be achieved by the proposed Lagrangian relaxation and genetic algorithms (LRGA).
Abstract: This paper presents an application of a combined genetic algorithms (GAs) and Lagrangian relaxation (LR) method for the unit commitment (UC) problem. Genetic algorithms (GAs) are a general purpose optimization technique based on principle of natural selection and natural genetics. The Lagrangian relaxation (LR) method provides a fast solution but it may suffer from numerical convergence and solution quality problems. The proposed Lagrangian relaxation and genetic algorithms (LRGA) incorporates genetic algorithms into Lagrangian relaxation method to update the Lagrangian multipliers and improve the performance of Lagrangian relaxation method in solving combinatorial optimization problems such as the UC problem. Numerical results on two cases including a system of 100 units and comparisons with results obtained using Lagrangian relaxation (LR) and genetic algorithms (GAs), show that the feature of easy implementation, better convergence, and highly near-optimal solution to the UC problem can be achieved by the LRGA.

488 citations

Journal ArticleDOI
TL;DR: A view of the progress and understanding that has been achieved during the last eight years about Lagrangian functions and its relevance to practical algorithms is given.
Abstract: Lagrangian functions are the basis of many of the more successful methods for nonlinear constraints in optimization calculations. Sometimes they are used in conjunction with linear approximations to the constraints and sometimes penalty terms are included to allow the use of algorithms for unconstrained optimization. Much has been discovered about these techniques during the last eight years and this paper gives a view of the progress and understanding that has been achieved and its relevance to practical algorithms. A particular method is recommended that seems to be more powerful than the author believed to be possible at the beginning of 1976.

486 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202373
2022169
2021127
2020129
2019122
2018127