In this work we address the Quadratic Minimum Spanning Tree Problem (QMSTP) known to be NP-hard. Given a complete graph, the QMSTP consists of determining a minimum spanning tree (MST) considering interaction costs between pairs of edges to be modelled. A Lagrangian relaxation procedure is devised and an efficient local search algorithm with tabu thresholding is developed. Computational experim...

We propose a new algorithm for unit commitment that employs a Lagrange relaxation technique with a new augmentation of the Lagrangian. The new augmentation involves a duplication of variables that allows relaxation of the coupling between generator timespanning constraints and system-wide instantaneous constraints. This framework allows the possibility of committing units that are required for ...

We propose a new algorithm for unit commitment that employs a Lagrange relaxation technique with a new augmentation of the Lagrangian. The new augmentation involves a duplication of variables that allows relaxation of the coupling between generator timespanning constraints and system-wide instantaneous constraints. This framework allows the possibility of committing units that are required for ...

This paper proposes a new approach based on augmented Lagrangian relaxation for short term generation scheduling problem with transmission and environmental constraints. In this method, the system constraints, e.g. load demand, spinning reserve, transmission capacity and environmental constraints, are relaxed by using Lagrangian multipliers, and quadratic penalty terms associated with system lo...

Solution oscillations, often caused by identical solutions to the homogeneous subproblems, constitute a severe and inherent disadvantage in applying Lagrangian relaxation based methods to resource scheduling problems with discrete decision variables. In this paper, the solution oscillations caused by homogeneous subproblems in the Lagrangian relaxation framework are identified and analyzed. Bas...

This paper is devoted to the numerical resolution of unit-commitment problems. More precisely we present the French model optimizing the daily production of electricity. Its resolution is done is two phases: first a Lagrangian relaxation solves the dual to find a lower bound; it also gives a primal relaxed solution. The latter is used in the second phase for a heuristic resolution based on a pr...

We consider the two-level uncapacitated facility location problem with singleassignment constraints (TUFLP-S), a problem that arises in industrial applications in freight transportation and telecommunications. We present a new Lagrangian relaxation approach for the TUFLP-S, based on solving a single-level uncapacitated facility location problem (UFLP) as the Lagrangian subproblem. We also devel...

The Lagrangian relaxation strategy (or dualization) is one of the most important methodologies of optimization for solving structured large-scale mathematical programming problems. The line search procedure is very often encountered in solving the dual problem by using some ascent algorithm, such as a bundle algorithm, or an interior point algorithm, etc.. The existing line search methods, for ...

This paper presents an algorithm to obtain near optimal solutions for the Steiner tree problem in graphs. It is based on a Lagrangian relaxation of a multi-commodity flow formulation of the problem. An extension of the subgradient algorithm, the volume algorithm, has been used to obtain lower bounds and to estimate primal solutions. It was possible to solve several difficult instances from the ...

Maximum a posteriori (MAP) inference is one of the fundamental inference tasks in graphical models. MAP inference is in general NP-hard, making approximate methods of interest for many problems. One successful class of approximate inference algorithms is based on linear programming (LP) relaxations. The augmented Lagrangian method can be used to overcome a lack of strict convexity in LP relaxat...