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Lagrangian relaxation

About: Lagrangian relaxation is a(n) research topic. Over the lifetime, 4244 publication(s) have been published within this topic receiving 124805 citation(s).

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Book
23 Sep 2014-

3,794 citations


Book
Colin R. Reeves1Institutions (1)
01 Jan 1993-
Abstract: Part 1 Introduction: combinatorial problems local and global optima heuristics. Part 2 Simulated annealing: the basic method enhancements and modifications applications conclusions. Part 3 Tabu search: the tabu framework broader aspects of intensification and diversification tabu search applications connections and conclusions. Part 4 Genetic algorithms: basic concepts a simple example extensions and modifications applications conclusions. Part 5 Artificial neural networks: neural networks combinatorial optimization problems the graph bisection problem the graph partition problem the travelling salesman problem scheduling problems deformable templates inequality constraints, the Knapsack problem summary. Part 6 Lagrangian relaxation: overview basic methodology Lagrangian heuristics and problem reduction determination of Lagrange multipliers dual ascent tree search applications conclusions. Part 7 Evaluation of heuristic performance: analytical methods empirical testing statistical inference conclusions.

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2,564 citations


Journal ArticleDOI
Marshall L. Fisher1Institutions (1)
01 Dec 2004-Management Science
TL;DR: This paper is a review of Lagrangian relaxation based on what has been learned in the last decade and has led to dramatically improved algorithms for a number of important problems in the areas of routing, location, scheduling, assignment and set covering.

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Abstract: (This article originally appeared in Management Science, January 1981, Volume 27, Number 1, pp. 1-18, published by The Institute of Management Sciences.) One of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints. Dualizing the side constraints produces a Lagrangian problem that is easy to solve and whose optimal value is a lower bound (for minimization problems) on the optimal value of the original problem. The Lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm. This approach has led to dramatically improved algorithms for a number of important problems in the areas of routing, location, scheduling, assignment and set covering. This paper is a review of Lagrangian relaxation based on what has been learned in the last decade.

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2,219 citations


Journal ArticleDOI
M. J. Box1Institutions (1)
TL;DR: A new method for finding the maximum of a general non-linear function of several variables within a constrained region is described, and shown to be efficient compared with existing methods when the required optimum lies on one or more constraints.

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Abstract: A new method for finding the maximum of a general non-linear function of several variables within a constrained region is described, and shown to be efficient compared with existing methods when the required optimum lies on one or more constraints. The efficacy of using effective constraints to eliminate variables is demonstrated, and a program to achieve this easily and automatically is described. Finally, the performance of the new method (the "Complex" method) with unconstrained problems, is compared with those of the Simplex method, from which it was evolved, and Rosenbrock's method.

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1,248 citations


Journal ArticleDOI
TL;DR: This paper presents a genetic algorithm (GA) solution to the unit commitment problem using the varying quality function technique and adding problem specific operators, satisfactory solutions to theunit commitment problem were obtained.

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Abstract: This paper presents a genetic algorithm (GA) solution to the unit commitment problem. GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms such as natural selection, genetic recombination and survival of the fittest. A simple GA algorithm implementation using the standard crossover and mutation operators could locate near optimal solutions but in most cases failed to converge to the optimal solution. However, using the varying quality function technique and adding problem specific operators, satisfactory solutions to the unit commitment problem were obtained. Test results for power systems of up to 100 units and comparisons with results obtained using Lagrangian relaxation and dynamic programming are also reported.

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1,092 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
2021119
2020128
2019121
2018127
2017187

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Topic's top 5 most impactful authors

Peter B. Luh

120 papers, 3.5K citations

Xuesong Zhou

23 papers, 1K citations

Tatsushi Nishi

20 papers, 263 citations

Krishna R. Pattipati

19 papers, 1.3K citations

Xiaoqi Yang

16 papers, 537 citations