8 resultados para Branch and Bound algorithms

em SAPIENTIA - Universidade do Algarve - Portugal


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Discrete optimization problems are very difficult to solve, even if the dimention is small. For most of them the problem of finding an ε-approximate solution is already NP-hard. The branch-and-bound algorithms are the most used algorithms for solving exactly this sort of problems.

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Discrete optimization problems are very difficult to solve, even if the dimantion is small. For most of them the problem of finding an ε-approximate solution is already NP-hard.

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Tese dout., Matemática, Investigação Operacional, Universidade do Algarve, 2009

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This talk addresses the problem of controlling a heating ventilating and air conditioning system with the purpose of achieving a desired thermal comfort level and energy savings. The formulation uses the thermal comfort, assessed using the predicted mean vote (PMV) index, as a restriction and minimises the energy spent to comply with it. This results in the maintenance of thermal comfort and on the minimisation of energy, which in most operating conditions are conflicting goals requiring some sort of optimisation method to find appropriate solutions over time. In this work a discrete model based predictive control methodology is applied to the problem. It consists of three major components: the predictive models, implemented by radial basis function neural networks identifed by means of a multi-objective genetic algorithm [1]; the cost function that will be optimised to minimise energy consumption and provide adequate thermal comfort; and finally the optimisation method, in this case a discrete branch and bound approach. Each component will be described, with a special emphasis on a fast and accurate computation of the PMV indices [2]. Experimental results obtained within different rooms in a building of the University of Algarve will be presented, both in summer [3] and winter [4] conditions, demonstrating the feasibility and performance of the approach. Energy savings resulting from the application of the method are estimated to be greater than 50%.

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One of the crucial problems of fuzzy rule modeling is how to find an optimal or at least a quasi-optimal rule base fro a certain system. In most applications there is no human expert available, or, the result of a human expert's decision is too much subjective and is not reproducible, thus some automatic method to determine the fuzzy rule base must be deployed.

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Neural networks and genetic algorithms have been in the past successfully applied, separately, to controller turning problems. In this paper we propose to combine its joint use, by exploiting the nonlinear mapping capabilites of neural networks to model objective functions, and to use them to supply their values to a genetic algorithm which performs on-line minimization.

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Novel method of controller (PID) autotuning, involving neural networks and genetic algorithms: to employ neural networks to map the identification measures and controller parameters to objective functions, adapt these models on-line; to employ the genetic algorithm to perform on-line minimization.

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A new electrochemical methodology to study labile trace metal/natural organic matter complexation at low concentration levels in natural waters is presented. This methodology consists of three steps: (i) an estimation of the complex diffusion coefficient (DML), (ii) determination at low pH of the total metal concentration initially present in the sample, (iii) a metal titration at the desired pH. The free and bound metal concentrations are determined for each point of the titration and modeled with the non-ideal competitive adsorption (NICA-Donnan) model in order to obtain the binding parameters. In this methodology, it is recommended to determine the hydrodynamic transport parameter, α, for each set of hydrodynamic conditions used in the voltammetric measurements. The methodology was tested using two fractions of natural organic matter (NOM) isolated from the Loire river, namely the hydrophobic organic matter (HPO) and the transphilic organic matter (TPI), and a well characterized fulvic acid (Laurentian fulvic acid, LFA). The complex diffusion coefficients obtained at pH 5 were 0.4 ± 0.2 for Pb and Cu/HPO, 1.8 ± 0.2 for Pb/TPI and (0.612 ± 0.009) × 10−10 m2 s−1 for Pb/LFA. NICA-Donnan parameters for lead binding were obtained for the HPO and TPI fractions. The new lead/LFA results were successfully predicted using parameters derived in our previous work.