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Augmented Lagrangean Relaxation and Decomposition Applied to the Short-Term Hydrothermal Coordination Problem

Mon, 10/29/2007 - 18:36 — admin
Publication TypeConference Paper
Year of Publication1999
AuthorsBeltran, C.; Heredia, F. J.
Conference Name19th IFIP TC7 Conference on System Modelling and Optimization
Conference Date12-16/07/1999
Conference LocationCambridge, U.K.
Type of WorkContributed oral presentation
Key Wordsaugmented lagrangian relaxation; generalized unit commitment; block coordinated descent method; auxiliary principle problem; research
AbstractThe problem dealt with is called the Short-Term Hydrothermal Coordination (SHTC) problem. The objective of this problem is the optimization of electrical production and distribution, considering a short-term planning horizon (from one day to one week). Hydraulic and thermal plants must be coordinated in order to satisfy the customer demand of electricity at the minimum cost and with a reliable service. The model for the STHC problem presented here considers the thermal system, the hydraulic system and the distribution network. Nowadays the Lagrangean Relaxation (LR) method is the most widespread procedure to solve the STHC problem. The initial Classical Lagrangean Relaxation (CLR) method was improved by the Augmented Lagrangean Relaxation (ALR) method, although recent advances in the multiplier updating for the CLR method (cutting plane, bundle methods, etc.) have brought this classical method back into fashion. Two main advantages of the ALR method over the CLR method: (1) the ALR method allows us to obtain a saddle-point even in cases where the CLR method presents a duality gap. The solution of the STHC problem by the CLR method usually yields an infeasible primal solution $x_k$ due to the duality gap, whereas in the ALR method a solution of the dual problem provides a feasible primal solution. (2) The second advantage is that, using the CLR method, the differentiability of the dual function cannot be ensured and therefore nondifferentiable methods must be applied in the CLR method. This difficulty can be overcome if an augmented Lagrangean is used, since the dual function $q_c$ is differentiable for an appropriate c. Thus, the multipliers can be updated using ``large steps''. The main weakness of the ALR method is that the quadratic terms introduced by the augmented Lagrangean are not separable. If we want to solve the STHC problem by decomposition, some methods, such as the Auxiliary Problem Principle, or, as in our case, the Block Coordinate Descent method, must be used. However, the CLR method gives a separable Lagrangean. The starting point is the paper by Batut and Renaud [1] and therefore we use Variable Duplication plus the Augmented Lagrangean Relaxation (ALR) method. The method used by Batut and Renaud is improved theoretically and practically. From the theoretical point of view, the conservative Auxiliary Problem Principle is replaced by the Block Coordinate Descent Method that shows to be faster. From the practical point of view, an effective software package designed to solve the Optimum Short-Term Hydrothermal Coordination Problem, is incorporated in order to speed up the whole algorithm. Several medium to large scale instances of this problem have been solved showing the applicability of the proposed procedure.
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NETFLOW93: Network Optimization, Theory and Practice

Mon, 10/29/2007 - 17:37 — admin
Publication TypeConference/School/Seminar attendance
Year of Publication1993
AuthorsF.-Javier Heredia
Event TypeConference
Conference OrganiserDipartimento di Informatica, Università di Pisa
Conference Dates3-7/10/1993
Conference LocationSan Miniato, Italy
Key Wordsoptimization; nonlinear network flows; research
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Large scale nonlinear network optimization with linear side constraints

Sun, 10/28/2007 - 20:44 — admin
Publication TypeConference Paper
Year of Publication1991
AuthorsHeredia, F. J.; Nabona, N.
Conference Name11th European Congress on Operations Research
Conference Date1991
Conference LocationAachen, Germany
Type of WorkContributed oral presentation
Key Wordsnonlinear network flows; linear side constraints; research
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Numerical implementation and computational results of nonlinear network optimization with linear side constraints

Sun, 10/28/2007 - 20:42 — admin
Publication TypeConference Paper
Year of Publication1991
AuthorsHeredia, F. J.; Nabona, N.
Conference Name15th IFIP Conference on System Modelling and Optimization
Conference Date1991
Conference LocationZurich, Switzerland
Type of WorkContributed oral presentation
Key Wordsnonlinear network flows; linear side constraints; research
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Optimum Short-Term Hydrothermal Scheduling with Spinning Reserve through Network Flows

Sun, 10/28/2007 - 19:47 — admin
Publication TypeConference Paper
Year of Publication1995
AuthorsHeredia, F. J.; Nabona, N.
Conference NameIEEE/Power Engineering Society Winter Meeting
Conference Date02/1995
Conference LocationNew York, EEUU
Type of WorkContributed oral presentation
Key Wordsnonlinear network flows; side constraints; power systems; short-term hydrothermal OPF; spinning reserve; research
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Network Model of Short-Term Optimal Hydrothermal Power Flow with Security Constraints

Sun, 10/28/2007 - 19:23 — admin
Publication TypeConference Paper
Year of Publication1995
AuthorsChiva, A.; Heredia, F.J.; Nabona, N.
Conference NameIEEE '95 Stockholm Power Tech
Series TitleInternational Symposium on Electric Power Engineering
Volume6, PS
Pagination67-73
Conference Date18-22/06/1995
PublisherRoyal Institute of Technology and IEEE Power Engineering Society
Conference LocationStockholm, Sweden
Type of WorkContributed oral presentation
Key Wordsresearch; nonlinear network flows; side constraints; power systems; short-term hydrothermal OPF; spinning reserve; transmission security contraints; research
URLClick Here
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Planificación Hidrotérmica a Corto Plazo. Optimización de un modelo acoplado de flujos no lineales en red

Sun, 10/28/2007 - 19:03 — admin
Publication TypeConference Paper
Year of Publication1997
AuthorsHeredia, F. J.; Nabona, N.
Conference NameXVIII Congreso Nacional de Estadística e Investigación Operativa
Conference Date11-14/03/1997
Conference LocationValència, Spain
Type of WorkContributed oral presentation
Key Wordsnonlinear network flows; side constraints; power systems; short-term hydrothermal OPF; research
AbstractEl Modelo Acoplado del problema de Planificación Hidrotérmica a Corto Plazo permite optimizar conjuntamente el sistema hidráulico, térmico y la red de transmisión mediante la resolución de un único problema de flujos no lineales en red con restricciones laterales. Este trabajo describe el modelo matemático, los resultados computacionales y las posibles extensiones del método.
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Nonlinear network flows with side constraints applied to short term hydrothermal coordination of electricity generation

Sun, 10/28/2007 - 18:50 — admin
Publication TypeConference Paper
Year of Publication1992
AuthorsHeredia, F. J.; Nabona, N.
Conference NameEuropean Conference on Numerical Methods in Engineering '92
Conference Date1992
Conference LocationBrussels, Belgium
Type of WorkContributed oral presentation
Key Wordsnonlinear network flows; side constraints; power systems; short-term hydrothermal OPF; research
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Nonlinear network flow problems with side constraints through projected Lagrangian methods

Sun, 10/28/2007 - 18:32 — admin
Publication TypeConference Paper
Year of Publication1997
AuthorsHeredia, F. J.
Conference NameEURO XV / INFORMS XXXIV Joint International Conference
Conference Date14-17/06/97
Conference LocationBarcelona, Spain
Type of WorkContributed oral presentation
Key Wordsnonlinear network flows; nonlinear side constraints; projected lagrangian methods; research
AbstractRecents numerical experiments show that the resolution of the Nonlinear network Flow problem with side Constraints (NFC) can be significantly sped up, when the side constraints are linear, by specialised codes based on a conjunction of primal partitioning techniques and active set methods. A natural extension of these methods one is to be used into a Projected Lagrangian Algorithm (PLA). A specialised (PLA) will solve the general (NFC) problem through the optimization of a sequence of (NFC) with linear side constraints, taking benefit of the efficiency of the linear side constraints codes. The description of this methodology will be presented together with the preliminary numerical results.
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Short-Term Hydrothermal Coordination by Augmented Lagrangean Relaxation: a new Multiplier Updating

Sun, 10/28/2007 - 18:21 — admin
Publication TypeConference Paper
Year of Publication1998
AuthorsBeltran, C.; Heredia, F. J.
Conference NameIX Congreso Latino-Iberoamericano de Investigación Operativa
Conference Date31-4/08/98
Conference LocationBuenos Aires, Argentina
Type of WorkContributed oral presentation
Key Wordsaugmented lagrangian relaxation; radar subgradient method; generalized unit commitment; research
AbstractAugmented Lagrangean Relaxation Method (ALRM) is one of the most powerfull technique to solve the Short­Term Hydrothermal Coordination Problem (STHC Problem ). A crucial step when using the ALR Method is the multipliers updating. In this paper we present an efficient new multiplier updating procedure: the Gradient Method with Radar Step. The method has been successfully tested solving large ­scale exemples of the STHC Problem
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