Nélio Henderson

A Metropolis algorithm combined with Hooke–Jeeves local search method applied to global optimization

Abstract A hybridization of a recently introduced Metropolis algorithm named the Particle Collision Algorithm (PCA) and the Hooke–Jeeves local search method is applied to a testbed of global optimization functions and to real-world chemical equilibrium nonlinear systems. The results obtained by this method, called HJPCA, are compared against those achieved by two state-of-the-art global optimization methods, C-GRASP and GLOBAL. HJPCA performs better than both algorithms, thus demonstrating its potential for other applications.

Simulation of single-phase multicomponent flow problems in gas reservoirs by Eulerian-Lagrangian techniques

Over the past two decades most discussions of the simulation of miscible displacement in porous media were related to incompressible flow problems; recently, however, attention has shifted to compressible problems. The first goal of this paper is the derivation of the governing equations (mathematical models) for a hierarchy of miscible isothermal displacements in porous media, starting from a very general single-phase, multicomponent, compressible flow problem; these models are then compared with previously proposed models. Next, we formulate an extension of the modified method of characteristics with adjusted advection to treat the transport and dispersion of the components of the miscible fluid; the fluid displacement must be coupled in a two-stage operator-splitting procedure with a pressure equation to define the Darcy velocity field required for transport and dispersion, with the outer stage incorporating an implicit solution of the nonlinear parabolic pressure equation and an inner stage for transport and diffussion in which the mass fraction equations are solved sequentially by first applying a globally conservative Eulerian–Lagrangian scheme to solve for transport, followed by a standard implicit procedure for including the diffusive effects. The third objective is a careful investigation of the underlying physics in compressible displacements in porous media through several high resolution numerical experiments. We consider real binary gas mixtures, with realistic thermodynamic correlations, in homogeneous and heterogeneous formations.

Applicability of the three-parameter Kozeny-Carman generalized equation to the description of viscous fingering in simulations of waterflood in heterogeneous porous media

We have developed a simulator for waterflood operations in oil reservoirs.The TPKCG equation was used to simulate heterogeneous porous media.New numerical results were generated from intensive simulations.We proved that the TPKCG equation is able to describe viscous fingers. This article discusses the applicability of the three-parameter Kozeny-Carman generalized equation to trigger immiscible viscous fingers and describe it in fractal heterogeneous porous media, during numerical simulations of waterflood operations in oil reservoirs. For that purpose, for the first time this equation was incorporated into a model that describes immiscible flows of incompressible two-phase fluids in porous media. Results were generated from intensive simulations, and viscous fingers were visualized graphically for three different well patterns, typical of oil fields: Line-Drive, Five-Spot and Inverted Five-Spot. Such results suggest that this generalization of the Kozeny-Carman equation can be used in numerical simulations of oil recovery processes susceptible to hydrodynamic instability phenomena.

The inverse distance weighted interpolation applied to a particular form of the path tubes Method

A simplified version of the inverse distance weighted interpolation formula was mathematically analyzed and employed in the context of a semi-Lagrangian scheme for the equation of advection. The scheme used is a particular formulation of Path Tubes method, a physically intuitive conservative method whose formulation is based on the theoretical foundations of the mechanics of continuous media, which uses the so-called Reynoldss transport theorem to establish judiciously its main property written on the basis of a conservative integral equation. The resulting algorithm is a five-point explicit semi-Lagrangian scheme for incompressible flow. From rigorous deductions based on the von Neumann stability analysis, it was proven that this explicit method is unconditionally stable. The present algorithm was evaluated using test problems that are prototypes of more sophisticated mathematical models commonly employed in the prediction of intensity variations of weather fronts. In addition, our methodology was compared against two other methods available in the literature. The proposed explicit semi-Lagrangian scheme was able to work with long time steps and proved to be accurate, non-oscillatory and non-diffusive.

Computation of Critical Points of Mixtures Using Particle Swarm Optimization with Low-Discrepancy Sequences

The prediction of critical points of thermodynamic systems is an important tool for modeling many high-pressure processes of theoretical and practical interest. In this article, the calculation of critical points of multicomponent mixtures is treated as a global minimization problem of a modified merit function associated with the criticality conditions obtained from the Gibbs tangent plane criterion, designed to discriminate the scale of the problem. The methodology used to solve the optimization problem is based on two versions of the particle swarm optimization (PSO), equipped with low-discrepancy sequences to prevent the sensitivity of the swarm with respect to the location of the initial population. To avoid a rapid decrease in the weight inertia, and to prevent stagnations near undesirable local minimizers, we present a modification of the PSO method, which uses different search cycles with the same inertia weight. This new version developed here is a fast and robust algorithm for solving the critical-point problem, via global optimization.

Testing population initialisation schemes for differential evolution applied to a nuclear reactor core design

In the process of nuclear core design, reactor cell parameters such as dimensions, enrichment and materials must be adjusted considering restrictions such as the average thermal flux, criticality and sub-moderation. This problem may be formulated using global optimisation methods in order to generate sets of design parameters to be analysed by programs that simulate the neutron interactions in the reactor core. This problem is highly multimodal, requiring techniques that overcome local optima, which can be done by promoting a greater populational diversity. An approach that has been overlooked is the selection of an initial set of solutions of the populational algorithms. In this work, we use the differential evolution algorithm to test two different generation schemes besides pseudorandom generation: pseudorandom generation followed by the application of opposition-based learning and the Sobol quasi-random generator. The results show the potential of each scheme for application in other nuclear science and engineering problems.

Prediction of Double Retrograde Vaporization by Hybrid Global-Local Optimization Using Fuzzy Clustering Means

Retrograde vaporization calculation is a hard problem, which possesses several solutions and demands a robust algorithm. In the present work, we solved the double retrograde vaporization problem by hybrid global-local optimization. In fact, we propose a new methodology that involves fuzzy clustering means together with Luus-Jaakola and Nelder-Mead algorithms. We applied the proposed methodology to solve the double retrograde vaporization problem for binary systems of methane + n-butane. For this mixture, the dew point curve exhibits an S-shape at temperatures slightly below the critical temperature of the more volatile component. This binary mixture was modeled using the original Peng-Robinson equation of state and the classical one-fluid van der Waals mixing rule.

Testing the topographical global initialization strategy in the framework of an unconstrained optimization method

In general, classical iterative algorithms for optimization, such as Newton-type methods, perform only local search around a given starting point. Such feature is an impediment to the direct use of these methods to global optimization problems, when good starting points are not available. To overcome this problem, in this work we equipped a Newton-type method with the topographical global initialization strategy, which was employed together with a new formula for its key parameter. The used local search algorithm is a quasi-Newton method with backtracking. In this approach, users provide initial sets, instead of starting points. Then, using points sampled in such initial sets (merely boxes in

Study of a Jacobian-free approach in the simulation of compressible fluid flows in porous media using a derivative-free spectral method

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