Practical Computation Time Research Articles

Efficient Formulations for 1-SVM and their Application to Recommendation Tasks

The present paper proposes new approaches for recommendation tasks based on one-class support vector machines (1-SVMs) with graph kernels generated from a Laplacian matrix. We introduce new formulations for the 1-SVM that can manipulate graph kernels quite efficiently. We demonstrate that the proposed formulations fully utilize the sparse structure of the Laplacian matrix, which enables the proposed approaches to be applied to recommendation tasks having a large number of customers and products in practical computational times. Results of various numericalexperiments demonstrating the high performance of the proposed approaches are presented.

Towards Real-Time Global Localization in Dynamic Unstructured Environments

Global localization is the problem in which a mobile robot has to estimate the self-position with respect to an a priori given map as it navigates without using any a priori knowledge of the initial self-position. Previous studies on global localization mainly focused on static environments, where the a priori map is almost correct. On the other hand, in dynamic environments, there are several sources of computational complexity. For example, not only the self-position but also the map should be estimated due to the map errors. The main contribution of this paper is to address such computational complexity by decomposing our global localization problem into two smaller subproblems, and solving the subproblems in a practical computation time. Also, we demonstrate the robustness and the efficiency of the proposed method in various large and complex environments.

Optimal H infinity PD Controller Design for Flexible Spacecraft by Branch and Bound Algorithm

This paper proposes optimization of the PD controller gains by minimizing H infinity norm for flexible spacecraft attitude control. Solving the problem is known to be difficult because it is described by a bilinear matrix inequality (BMI) that cannot be transformed into linear matrix inequalities (LMIs). In order to solve it within practical computation time, we revise the branch and bound algorithm and incorporate the quantization of the variable domains. The ETS-VI mathematical model is used to demonstrate its ability.

Application of a Genetic Algorithm to the Optimization of Rate Constants in Chemical Kinetic Models for Combustion Simulation of HCCI Engines

For numerically predicting the combustion processes in homogeneous charge compression ignition (HCCI) engines, practical chemical kinetic models have been explored. A genetic algorithm (GA) has been applied to the optimization of the rate constants in detailed chemical kinetic models, and a detailed kinetic model (592 reactions) for gasoline reference fuels with arbitrary octane number between 60 and 100 has been obtained from the detailed reaction schemes for iso-octane and n-heptane proposed by Golovitchev. The ignition timing in a gasoline HCCI engine has been predicted reasonably well by zero-dimensional simulation using the CHEMKIN code with this detailed kinetic model. An original reduced reaction scheme (45 reactions) for dimethyl ether (DME) has been derived from Curran’s detailed scheme, and the combustion process in a DME HCCI engine has been predicted reasonably well in a practical computation time by three-dimensional simulation using the authors’ GTT code, which has been linked to the CHEMKIN subroutines with the proposed reaction scheme and also has adopted a modified eddy dissipation combustion model.

Efficient Calculation of Resolution and Covariance for Penalized-Likelihood Reconstruction in Fully 3-D SPECT

Resolution and covariance predictors have been derived previously for penalized-likelihood estimators. These predictors can provide accurate approximations to the local resolution properties and covariance functions for tomographic systems given a good estimate of the mean measurements. Although these predictors may be evaluated iteratively, circulant approximations are often made for practical computation times. However, when numerous evaluations are made repeatedly (as in penalty design or calculation of variance images), these predictors still require large amounts of computing time. In Stayman and Fessler (2000), we discussed methods for precomputing a large portion of the predictor for shift-invariant system geometries. In this paper, we generalize the efficient procedure discussed in Stayman and Fessler (2000) to shift-variant single photon emission computed tomography (SPECT) systems. This generalization relies on a new attenuation approximation and several observations on the symmetries in SPECT systems. These new general procedures apply to both two-dimensional and fully three-dimensional (3-D) SPECT models, that may be either precomputed and stored, or written in procedural form. We demonstrate the high accuracy of the predictions based on these methods using a simulated anthropomorphic phantom and fully 3-D SPECT system. The evaluation of these predictors requires significantly less computation time than traditional prediction techniques, once the system geometry specific precomputations have been made.

Solving Truck Delivery Problems Using Integrated Evaluation Criteria Based on Neighborhood Degree and Evolutionary Algorithm

To solve a real-world truck delivery and dispatch problem (TDDP) that involves multiple mutually conflicting objectives, such as running and loading costs, a concept of neighborhood degree (ND) and an integrated evaluation criteria (IEC) of the solution based on ND are proposed. The IEC makes the weight setting easier than by using conventional methods. To find a high-quality solution to a TDDP in practical computational time, an evolutionary algorithm is proposed. It involves 3 components: (i) a simulated annealing (SA)-based method for finding an optimal or a suboptimal route for each vehicle; (ii) an evolutionary computation (EC)-based method for finding an optimal schedule for a group of vehicles; and (iii) threshold-based evolutionary operations, utilizing the ND concept. The TDDP viewed from real-world application is formulated and the proposed algorithm is implemented on a personal computer using C++. The proposed algorithm is evaluated in 2 experiments involving real-world data representative of the TDDP, and applied to food product delivery to a chain of 46 convenience stores in Saitama Prefecture. In the 2 experiments, our proposed algorithm resulted in a better schedule (with 80%-90% shorter computational time) than a schedule produced by an expert. By incorporating application-specific evaluation criteria, the proposed algorithm is applied to problems such as home-delivery of parcels or mail, and to problems of multidepot delivery and dispatch.

Finding all solutions of piecewise-linear resistive circuits using the simplex method

Recently, an efficient algorithm was proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using the simplex method, which could solve a problem where the number of PWL resistors is 200 and the number of linear regions is 10/sup 200/. In this work, an improved version of this algorithm is proposed, which can be applied to a broader class of PWL resistive circuits and could solve problems where the number of PWL resistors is 500 and the number of linear regions is 10/sup 500/ in practical computation time.

Finding all solutions of nonlinear equations using the dual simplex method

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time.

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

AbstractAn efficient algorithm is proposed for finding all solutions of piecewise‐linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for non‐existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. However, this algorithm requires a very large number of pivotings because the simplex method is applied on many regions. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of large‐scale problems, including those where the number of variables is 300 and the number of linear regions is 10300, in practical computation time. Copyright © 2002 John Wiley & Sons, Ltd.

FINDING ALL SOLUTIONS OF SYSTEMS OF NONLINEAR EQUATIONS USING THE DUAL SIMPLEX METHOD

An efficient algorithm is proposed for finding all solutions of nonlinear equations using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations in a given region. In the conventional LP test, the system of nonlinear equations is transformed into an LP problem, to which the simplex method is applied. However, although the LP test is very powerful, it requires many pivotings for each region. In this paper, we use the dual simplex method in the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm can find all solutions of systems of 200 nonlinear equations in practical computation time.

A fast, simple and versatile algorithm to fill the depressions of digital elevation models

The usual numerical methods for removing the depressions of a Digital Elevation Model (DEM) gradually fill the depressions and merge the embedded ones. These methods are complex to implement and need large computation time, particularly when the DEM contains a high proportion of random noise. A new method is presented here. It is innovative because, instead of gradually filling the depressions, it first inundates the surface with a thick layer of water and then removes the excess water. The algorithm is simple to understand and to implement, requiring only a few tens of code lines. It is much faster than usual algorithms. Moreover, this method is versatile: depressions can be replaced with a surface either strictly horizontal, or slightly sloping. The first option is used for the calculation of depression storage capacity and the second one for drainage network extraction. The method is fully detailed and a pseudo-code is provided. Its practical computation time, evaluated on generated fractal surfaces, is asymptotically proportional to N 1.2 where N is the number of grid points. The theoretical computation time is asymptotically proportional to N 1.5 in all cases, with the exception of some exotic ones with no practical interest. By contrast, existing methods have a computation time asymptotically proportional to N 2. Applications are done for both generated and measured surfaces with 256 cells to 6.2 million cells.

Finding all solutions of piecewise‐linear circuits by using linear programming

AbstractAn efficient algorithm is proposed for finding all solutions of piecewise‐linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations of the form Pg(x) + Qx – s = 0 in a given region. In the LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. In this paper, it is shown that the LP test can be performed very efficiently mostly by Phase II of the simplex method. Using the proposed techniques, the number of pivotings in the LP test becomes much smaller, which makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of relatively large scale circuits (including those where the number of variables is 200 and the number of linear regions is 10200) in practical computation time. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(7): 1–11, 2001

Performance evaluation of the LP test algorithm for finding all solutions of piecewise-linear resistive circuits

In this letter, the performance of the LP test algorithm, which is an algorithm for finding all solutions of piecewise-linear resistive circuits, is evaluated by numerical experiments. It is shown that the algorithm could find all solutions of large-scale problems (including those where the number of variables is 200-300 and the number of linear regions is 10 200 -10 300 ) in practical computation time.

Small molecule penetrant diffusion in aromatic polyesters: a molecular dynamics simulation study

Molecular dynamics (MD) simulations have been used to study diffusion of methane in three highly impermeable aromatic polyesters that are good barrier materials. These are amorphous poly(ethylene terephthalate) (PET) and poly(ethylene 2,6-naphthalene dicarboxylate) (PEN), and the nematic mesophase of the thermotropic liquid crystalline copolyester (LCP) of p-hydroxy benzoic acid (HBA) and 2,6 hydroxy naphthoic acid (HNA). Diffusion coefficients were determined in the temperature ranges of 450–625 K for PET, 500–625 for PEN, 425–530 K for the LCP, where values are large enough to be accessible to MD in practical computation times. Extrapolation, via Arrhenius plots, of the coefficients to near room temperature gave good agreement with experimental data in that region. This was found even though the glass transition temperatures ( T g) of PET (350 K) and PEN (390 K) lie in the intervening temperature range. This finding confirms previous observations that a low temperature hopping regime for small penetrants sets in on cooling well before the T g of the host. Analysis of diffusant trajectories in terms of diffusive jump size distribution also shows that the low temperature hopping regime remains in place over the temperature range studied in these low diffusion coefficient polymers. Correlation of diffusion coefficients with free volume was examined. The LCP, even though diffusion there is highly anisotropic, is found to lie on a correlation found previously for five other polymers studied via MD. However, PET and PEN fail badly and are found to diffuse much more slowly than inferred from free volume vs diffusion coefficient behavior in the other polymers.

Hierarchical modelling of textile composite materials and structures by the homogenization method

For the simulation of mechanical behaviours of textile composite materials and structures, a novel hierarchical modelling technique is proposed. Not only the global deformation but also the stresses at multiscales are analysed precisely. Four-level hierarchy is defined for the textile composites such as woven and knitted fabric composites. The stresses at the mesostructure, which is a periodic unit cell of textile composite materials consisting of fibre bundles and matrix, can be evaluated accurately by the homogenization method and finite-element mesh superposition technique. The latter technique makes it possible to overlay arbitrary local fine mesh on the global rough mesh. Anisotropic damage mechanics is also utilized for strength evaluation at the mesoscale. Three-dimensional modelling of the mesostructure of woven and knitted fabric composite materials is shown. Localization analysis has been carried out within practical computational time and cost by the proposed hierarchical modelling.

A timing-driven floorplanning algorithm with the Elmore delay model for building block layout

This paper presents a timing-driven floorplanning algorithm for building block layout. As the interconnection delay model, the proposed algorithm adopts the Elmore delay model. The algorithm consists of two phases. In the first phase, a timing-driven topological arrangement of blocks is generated with the resolution of overlap among blocks using nonlinear programming under the timing constraints. In the second one, the algorithm performs floorplan sizing which determines the sizes and the shapes of blocks based on the topological arrangement obtained in the first phase so as to minimize the chip area, and obtains a legal floorplan. This phase is based on the topological constraint manipulation. Through the experimental results, the proposed algorithm can produce results without any timing violations within a practical computation time.

A method to extract three-dimensional objects from three-dimensional NMR image data.

A method to extract shapes of bubble polyhedra from three-dimensional nuclear magnetic resonance image data of foam has been developed. The method consists of four steps: first, to compute series of maximum intensity projection images from the three-dimensional NMR image data of foam to visualize the network structure of the bubble edges; second, to measure the three-dimensional coordinates of vertices of the bubble polyhedra interactively on a CRT using the series of MIP images to obtain polyhedral edges; third, to construct polyhedral faces from the assembly of the edge data; and fourth, to construct bubble polyhedra from the assembly of the face data. The algorithm for construction of polygons and polyhedra is based on the selection of polygons or polyhedra from an enormous number of possible combinations of edges or faces under some simple selection rules. Since the computation time for the selection increased exponentially with the number of the edge data, a 'partial volume sweeping' method in which a cubic region which could accommodate any bubble polyhedron was swept over the three-dimensional image area, was developed to reduce the computation time. By using this method, it was demonstrated that the shapes of many bubble polyhedra could be extracted automatically from the assembly of the edge data within a practical computation time.

Analysis method for light scattering from magnetic materials by the three‐dimensional boundary element method

AbstractTo analyze the light scattered from a magneto‐optical disk, a method is proposed for calculating the light scattered from a magnetic material with grooves. The model used is divided by an infinite boundary between the free space or an isotropic dielectric and an isotropic magnetic material. By using the relative permittivity of the isotropic magnetic materiel, the governing equation for the magnetic material is derived from Maxwell's equations. The three‐dimensional boundary element method is applied to this equation. The boundary element equation for free space or an isotropic dielectric material is the one in which the boundary element method is applied to a general Helmholtz equation. The one in the magnetic material is obtained by adding the volume integral in the magnetic material to the general equation. If boundary elements are large, the integral in the magnetic material near the boundary is evaluated at too small a value. The numerical results oscillate with only the foregoing method. To resolve this problem with taking practical memory size and computation time into consideration, an attenuating term is added to Green's function used in the integration in the magnetic material. With the method proposed, the optical scattering from a magnetic material can now be analyzed.

A Monte Carlo Variance Reduction Approach for Non-Boltzmann Tallies

Quantities that depend on the collective effects of groups of particles cannot be obtained from the standard Boltzmann transport equation. Monte Carlo estimates of these quantities are called non-Boltzmann tallies and have become increasingly important recently. Standard Monte Carlo variance reduction techniques were designed for tallies based on individual particles rather than groups of particles. Experience with non-Boltzmann tallies and analog Monte Carlo has demonstrated the severe limitations of analog Monte Carlo for many non-Boltzmann tallies. In fact, many calculations absolutely require variance reduction methods to achieve practical computation times. A description is given of how variance reduction techniques can be applied when non-Boltzmann estimates are desired.

Whole Core Calculations of Power Reactors by Use of Monte Carlo Method.

Abstract Whole core calculations have been performed for a commercial size PWR and a prototype LMFBR by using vectorized Monte Carlo codes. Geometries of cores were precisely represented in a pin by pin model. The calculated parameters were k eff, control rod worth, power distribution and so on. Both multigroup and continuous energy models were used and the accuracy of multigroup approximation was evaluated through the comparison of both results. One million neutron histories were tracked to considerably reduce variances. It was demonstrated that the high speed vectorized codes could calculate k eff, assembly power and some reactivity worths within practical computation time. For pin power and small reactivity worth calculations, the order of 10 million histories would be necessary. It would be difficult for the conventional scalar code to solve such large scale problems while the present codes consumed computation time less than 30 min for a PWR and 1 hour for an LMFBR. Required number of histories to achieve target design accuracy were estimated for those neutronic parameters.