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Master Problem (master + problem)

Distribution by Scientific Domains

Mathematics and Statistics	42%
Engineering	28%

Selected Abstracts

Optimal methodology for distribution systems reconfiguration based on OPF and solved by decomposition technique

EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 6 2010
H. M. Khodr
Abstract This paper presents a new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach. The objective minimizes power losses, balancing load among feeders and subject to constraints: capacity limit of branches, minimum and maximum power limits of substations or distributed generators, minimum deviation of bus voltages and radial optimal operation of networks. The Generalized Benders decomposition algorithm is applied to solve the problem. The formulation can be embedded under two stages; the first one is the Master problem and is formulated as a mixed integer non-linear programming problem. This stage determines the radial topology of the distribution network. The second stage is the Slave problem and is formulated as a non-linear programming problem. This stage is used to determine the feasibility of the Master problem solution by means of an OPF and provides information to formulate the linear Benders cuts that connect both problems. The model is programmed in GAMS. The effectiveness of the proposal is demonstrated through two examples extracted from the literature. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Augmented Lagrangian coordination for distributed optimal design in MDO

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2008
S. Tosserams
Abstract Quite a number of coordination methods have been proposed for the distributed optimal design of large-scale systems consisting of a number of interacting subsystems. Several coordination methods are known to have numerical convergence difficulties that can be explained theoretically. The methods for which convergence proofs are available have mostly been developed for so-called quasi-separable problems (i.e. problems with individual subsystems coupled only through a set of linking variables, not through constraints and/or objectives). In this paper, we present a new coordination approach for multidisciplinary design optimization problems with linking variables as well as coupling objectives and constraints. Two formulation variants are presented, offering a large degree of freedom in tailoring the coordination algorithm to the design problem at hand. The first, centralized variant introduces a master problem to coordinate coupling of the subsystems. The second, distributed variant coordinates coupling directly between subsystems. Our coordination approach employs an augmented Lagrangian penalty relaxation in combination with a block coordinate descent method. The proposed coordination algorithms can be shown to converge to Karush,Kuhn,Tucker points of the original problem by using the existing convergence results. We illustrate the flexibility of the proposed approach by showing that the analytical target cascading method of Kim et al. (J. Mech. Design-ASME 2003; 125(3):475,480) and the augmented Lagrangian method for quasi-separable problems of Tosserams et al. (Struct. Multidisciplinary Opt. 2007, to appear) are subclasses of the proposed formulations. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Optimal carbon source switching strategy for the production of PHA copolymers

AICHE JOURNAL, Issue 3 2001
Nikolaos V. Mantzaris
During polymerization in a nongrowing cell population of Ralstonia eutropha, alternating between two different carbon sources (fructose and fructose/valeric acid) could lead to the production of block copolymers consisting of blocks of homo-poly-3-hydroxybutyrate (PHB) and polyhydroxybutyrate-co-valerate (PHBV) copolymer. The problem of finding the optimal number of carbon source switches and corresponding switching times that maximize the final concentration of diblock copolymers (PHB-PHBV and PHBV-PHB) was addressed. It was mathematically formulated in the mixed-integer nonlinear programming (MINLP) framework, which allows the decomposition of the original problem into the primal and master problems. The primal problem corresponds to the original problem for a fixed number of carbon source switches, whereas the master problem consists of finding the number of carbon source switches that maximizes the optimum solutions of all possible primal problems. The global optimum was obtained for 39 carbon source switches. It corresponds to a mass fraction of 50.6% of final diblock copolymer concentration over the final total polymer concentration. [source]

A nested benders decomposition approach for telecommunication network planning

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 6 2010
Joe Naoum-Sawaya
Abstract Despite its ability to result in more effective network plans, the telecommunication network planning problem with signal-to-interference ratio constraints gained less attention than the power-based one because of its complexity. In this article, we provide an exact solution method for this class of problems that combines combinatorial Benders decomposition, classical Benders decomposition, and valid cuts in a nested way. Combinatorial Benders decomposition is first applied, leading to a binary master problem and a mixed integer subproblem. The subproblem is then decomposed using classical Benders decomposition. The algorithm is enhanced using valid cuts that are generated at the classical Benders subproblem and are added to the combinatorial Benders master problem. The valid cuts proved efficient in reducing the number of times the combinatorial Benders master problem is solved and in reducing the overall computational time. More than 120 instances of the W-CDMA network planning problem ranging from 20 demand points and 10 base stations to 140 demand points and 30 base stations are solved to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010 [source]

Shortest-path network interdiction,

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2002
Eitan Israeli
Abstract We study the problem of interdicting the arcs in a network in order to maximize the shortest s,t path length. "Interdiction" is an attack on an arc that destroys the arc or increases its effective length; there is a limited interdiction budget. We formulate this bilevel, max,min problem as a mixed-integer program (MIP), which can be solved directly, but we develop more efficient decomposition algorithms. One algorithm enhances Benders decomposition by adding generalized integer cutting planes, called "supervalid inequalities" (SVIs), to the master problem. A second algorithm exploits a unique set-covering master problem. Computational results demonstrate orders-of-magnitude improvements of the decomposition algorithms over direct solution of the MIP and show that SVIs also help solve the original MIP faster. Published 2002 Wiley Periodicals, Inc. [source]