Modeling, Simulation and Optimization of Complex Processes

We present a new method for solving multivalued variational inequalities, where the underlying function is upper semicontinuous and satisfies a certain generalized monotone assumption. First, we construct an appropriate hyperplane which separates the current iterative point from the solution set. Then the next iterate is obtained as the projection of the current iterate onto the intersection of the feasible set with the halfspace containing the solution set. We also analyze the global convergence of the algorithm under minimal assumptions.

The paper discusses the use of the Huber estimator for parameter estimation problems which are constrained by a system of ordinary differential equations. In particular, a local and global convergence analysis for the estimation with the Huber estimator is given. For comparison, numerical results are given for an estimation with this estimator and both l ₁ estimation and the least squares approach for a parameter estimation problem for a chemical process.

The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem that has a natural formulation as a Mixed Integer Quadratically Constrained Program. This MIQCP is closely related to the Quadratic Assignment Problem and, as far as we know, has not received any attention yet. We show in this article that such a formulation has interesting theoretical properties. Its QP relaxation produces, in particular, the first known nontrivial lower bound on the number of shuntings. In our experiments, it also outperformed alternative integer linear models computationally. The strengthening technique that raises the lower bound might also be useful for other combinatorial optimization problems.

Ticket pricing in public transport usually takes a welfare maximization point of view. Such an approach, however, does not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and integer programming. An application to pricing railway tickets for the intercity network of the Netherlands is presented. The results demonstrate that prices that are much fairer than standard ones can be computed in this way.

Recently we proposed a domain decomposition method (DDM) for solving a Dirichlet problem for a second order elliptic equation, where differently from other DDMs, the value of the normal derivative on an interface is updated from iteration to iteration. In this paper we develop a method for solving strongly mixed boundary value problems (BVPs), where boundary conditions are of different type on different sides of a rectangle and the transmission of boundary conditions occurs not only in vertices but also in one or several inner points of a side of the rectangle. Such mixed problems often arise in mechanics and physics. Our method reduces these strongly mixed BVPs to sequences of weakly mixed problems for the Poisson equation in the sense that on each side of the rectangle there is given only one type of boundary condition, which are easily solved by a program package, constructed recently by Vu (see [13]). The detailed investigation of the convergence of the method for a model problem is carried out. After that the method is applied to a problem of semiconductors. The convergence of the method is proved and numerical experiments confirm the efficiency of the method.

In a housing-based outsourcing model, the database server is the client’s property and the outsourcing service provider only provides physical security of machines and data, and monitors (and if necessary restores) the operating condition of the server. Soft security-related aspects (e.g., DBMS security breaches) are the client’s responsibility. This is a non-trivial task for most of the clients.In this paper, we propose an extensible architecture for detecting, monitoring and preventing database security breaches in a housing-based outsourcing model. The architecture can help in dealing with both outsider and insider threats. It is well suited for the detection of both predefined and potential security breaches. Our solution to the database security breach detection is based on the well-known pentesting- and version checking-based techniques in network and operation systems security. The architecture features visual monitoring and secure auditing w.r.t. all database user activities in real time. Moreover, it also supports automatic prevention techniques if security risks are established w.r.t. the found security breaches.

This paper proposes real-time sequential convex programming (RTSCP), a method for solving a sequence of nonlinear optimization problems depending on an online parameter. We provide a contraction estimate for the proposed method and, as a byproduct, a new proof of the local convergence of sequential convex programming. The approach is illustrated by an example where RTSCP is applied to nonlinear model predictive control.

Pricing and hedging of higher order derivatives such as multidimensional (up to 100 underlying assets) European and first generation exotic options represent mathematically complex and computationally intensive problems. Grid computing promises to give the capability to handle such intense computations. With several Grid middleware solutions available for gridifying traditional applications, it is cumbersome to select an ideal candidate, to develop financial applications, that can cope up with time critical computational demand for complex pricing requests. In this paper we present SuperQuant Financial Benchmark Suite to evaluate and quantify the overhead imposed by a Grid middleware on throughput of the system and turnaround times for computation. This approach is a step towards producing a middleware independent, reproducible, comparable, self-sufficient and fair performance analysis of Grid middlewares. The result of such a performance analysis can be used by middleware vendors to find the bottlenecks and problems in their design and implementation of the system and by financial application developers to verify the implementation of their financial algorithms. In this paper we explain the motivation and the details of the proposed benchmark suite. As a proof of concept, we utilize the benchmarks in an International Grid Programming contest and demonstrate the result of initial experiments.

We present a dimension adaptive sparse grid combination technique for the machine learning problem of regression. A function over a d-dimensional space, which assumedly describes the relationship between the features and the response variable, is reconstructed using a linear combination of partial functions; these may depend only on a subset of all features. The partial functions, which are piecewise multilinear, are adaptively chosen during the computational procedure. This approach (approximately) identifies the anova-decomposition of the underlying problem. We introduce two new localized criteria, one inspired by residual estimators based on a hierarchical subspace decomposition, for the dimension adaptive grid choice and investigate their performance on real data.

In biological applications, features are extracted from microscopy images of cells and are used for automated classification. Usually, a huge number of images has to be analyzed so that computing the features takes several weeks or months. Hence, there is a demand to speed up the computation by orders of magnitude. This paper extends previous results of the computation of co-occurrence matrices and Haralick texture features, as used for analyzing images of cells, by general-purpose graphics processing units (GPUs). New GPUs include more cores (480 stream processors) and their architecture enables several new capabilities (namely, computing capabilities). With the new capabilities (by atomic functions) we further parallelize the computation of the co-occurrence matrices. The visually profiling tool was used to find the most critical bottlenecks which we investigated and improved. Changes in the implementation like using more threads, avoiding costly barrier synchronizations, a better handling with divergent branches, and a reorganization of the thread tasks yielded the desired performance boost. The computing time of the features for one image with around 200 cells is compared to the original software version as a reference, to our first CUDA version with computing capability v1.0 and to our improved CUDA version with computing capability v1.3. With the latest CUDA version we obtained an improvement of 1.4 to the previous CUDA version, computed on the same GPU (gForce GTX 280). In total, we achieved a speedup of 930 with the most recent GPU (gForce GTX 480, Fermi) compared to the original CPU version and a speedup of 1.8 compared to the older GPU with the optimized CUDA version.

Two-dimensional steady free-surface flows over an obstacle are considered. The fluid is assumed to be inviscid and incompressible; and the flow is irrotational. Both gravity and surface tension are included in the dynamic boundary condition. Far upstream, the flow is assumed to be uniform. Triangular obstruction is located at the channel bottom as positive bump or negative bump (dip). This problem has been investigated by many researchers, such as Forbes [5], Shen [8], and Dias and Vanden-Broeck [2], to seek for new types of solutions. In this paper, the fully nonlinear problem is formulated by using a boundary integral equation technique. The resulting integrodifferential equations are solved iteratively by using Newton’s method. When surface tension is neglected, a new solution type of subcritical flow is proposed, the so-called drag-free solution. Furthermore, solutions of flows over a dip in the bottom are also presented. When surface tension is included, there is an additional parameter in the problem known as the Bond number B. In addition, the weakly nonlinear problem is investigated and compared with the fully nonlinear results. Finally, solution diagrams for all flow regimes are presented on the (F,hob)-plane for which F is the Froude number and hob is the dimensionless height of the obstacle.

Human cells contain 46 chromosomes with a total length of about 5 cm beads-ona- string type of nucleosomal fibre, called chromatin. Packaging this into a nucleus of typically 5–20 μm diameter requires extensive compatification. This packaging cannot be random, as considerable evidence has been gathered that chromatin folding is closely related to local genome function. However, the different levels of compactification are ill understood and not easily accessible by experiments.

A novel method is presented for identification of a generalized bilinear system with nonlinear terms consisting of the product of the state vector and the coupling force variables. The identification process requires a series of pulse response experiments from input values of various pulse duration for coupling force variables. It also requires experiments with multiple inputs rather than one single input at a time. The resulting identified system matrices represent the input–output map of the generalized bilinear system. A simple example is given to illustrate the concept of the identification method.

This paper presents a computationally efficient version of the Eigensystem Realization Algorithm (ERA) to model the dynamics of large-domain acoustic propagation from High Performance Computing (HPC) data. This adaptation of the ERA permits hundreds of thousands of output signals to be handled at a time. Once the ERA-derived reduced-order models are obtained, they can be used for future simulation of the propagation accurately without having to go back to the HPC model. Computations that take hours on a massively parallel high performance computer can now be carried out in minutes on a laptop computer.

In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems typically arise from the convexification of integer control decisions. We treat this problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using an SQP method. Concerning the solution of the quadratic subproblems we present a factorization of the QP’s KKT system, based on a combined null-space range-space approach exploiting the problem’s block sparse structure. We demonstrate the merit of this approach for a vehicle control problem in which the integer gear decision is convexified.

An inverse problem for the steady vector transfer equation for polarized radiation is studied. For this problem, an attenuation factor is found from a given solution of the equation at a medium boundary. An approach is propounded to solve the inverse problem by using special external radiative sources. A formula is proposed which relates the Radon transform of an attenuation factor to a solution of the equation at the medium boundary. Numerical experiments show that the proposed reconstruction algorithm for the polarized-radiation transfer equation has an advantage over the similar method for the scalar case.

We study a Dirichlet boundary control problem of the Poisson equation where the Dirichlet control is considered in the energy space H ^1∕2(Γ). Both, finite and boundary element approximations of the minimal solution are presented. We state the unique solvability of both approaches, as well as the stability and error estimates. The numerical example is in good agreement with the theoretical results.

Modern nasal surgery aims at improving airways for healthy, comfortable breathing. Presently available measurements are not sufficient to describe optimized shapes, particle transport and flow. Computational Fluid Dynamics (CFD), particularly Large Eddy simulation (LES), might help to understand flow details and define standards. However, the human nose flow is challenging state-of-the-art CFD methods. It is generally not as clear and as well investigated as technical flows where CFD has originally been developed for. The challenging aspects are: First, the geometrical complexity of the nasal airways is much higher. Thin, long channels exist with multiple junctions and separations, 3-dimensionally contorted, requiring high resolution. Second, flow conditions are an interaction of several physical phenomena and tend to challenge numerical schemes in terms of viscosity, Reynolds number, Mach number, wall roughness, turbulence, heat transfer, humidity, fluid-tissue interaction etc. Third, only few validable experimental data of sufficient accuracy are available. Dealing with humans, either no standardized measurement conditions exist due to the bodies’ uniqueness or standard measurement procedures of engineering type cannot be applied. This causes a lack of comparability, limiting conclusions for surgery. Within this contribution, exemplary flow simulations through a real nose geometry under average conditions will be shown using a MPICH-parallelized, compressible Navier–Stokes scheme. The emphasis is on investigating fast, small-scale flow fluctuations near the regio olfactoria. The intention is to present a first step and to show in which direction developments must turn in order to perform reliable simulations. A 3D compressible CFD research code will be used, which is developed at the Institute of Fluid Machinery, University of Karlsruhe, Germany.

Congestion control is a distributed algorithm to share network bandwidth among competing users on the Internet. In the common case, quick response time for mice traffic (HTTP traffic) is desired when mixed with elephant traffic (FTP traffic). The current approach using loss-based with Additive Increase, Multiplicative Decrease (AIMD) is too greedy and eventually, most of the network bandwidth would be consumed by elephant traffic. As a result, it causes longer response time for mice traffic because there is no room left at the routers. MaxNet is a new TCP congestion control architecture using an explicit signal to control transmission rate at the source node. In this paper, we show that MaxNet can control well the queue length at routers and therefore the response time to HTTP traffic is several times faster than with TCP Reno/RED.

This paper introduces a superstable state-space representation suitable for modeling short-duration wave propagation dynamics in large domain. The true system dimensions and the number of output nodes can be extremely large, yet one is only interested in the propagation dynamics during a relatively short time duration. The superstable model can be interpreted as a finite-time version of the standard state-space model that is equivalent to the unit pulse response model. The state-space format of the model allows to user to take advantage of extensive state-space based tools that are widely available for simulation, model reduction, dynamic inversion, Kalman filtering, etc. The practical utility of the new representation is demonstrated in modeling the acoustic propagation of a sound source in a complex city center environment.

In this work we describe a fast solution algorithm for the time dependent Navier–Stokes equations in the regime of moderate Reynolds numbers. Special to this approach is the underlying discretization: both for spatial and temporal discretization we apply higher order Galerkin methods. In space, standard Taylor-Hood like elements on quadrilateral or hexahedral meshes are used. For time discretization, we employ discontinuous Galerkin methods. This combination of Galerkin discretizations in space and time allows for a consistent variational space-time formulation of the Navier Stokes equations. This brings along the benefit of a well defined adjoint problem to be used for optimization methods based on the Euler-Lagrange approach and for adjoint error estimation methods. Special care is given to the solution of the algebraic systems. Higher order discontinuous Galerkin formulations in time ask for a coupled treatment of multiple solution states. By an approximative factorization of the system matrices we can reduce the complex system to a multi-step method employing only standard backward Euler like time steps.

The ongoing efforts to develop an in-house Euler solver on a multi-block structured grid using the finite volume method are briefly presented in this paper. The flux through the control volume’s surface is computed using Roe’s scheme and extended to second order using the MUSCL approach. The steady state solution is determined using a time-marching approach with a modified Runge–Kutta scheme in the core. The acceleration of convergence to a steady solution is realized using a preconditioned multigrid method, a highly efficient method making explicit schemes such as the Runge–Kutta scheme competitive compared to implicit schemes. The numerical results clearly demonstrate the capability of the developed Euler solver to handle complex configurations and the superior efficiency of the preconditioned multigrid method.

We consider planning problems of flexible chemical batch processes paying special attention to uncertainties in problem data. The optimization problems are formulated as two-stage stochastic mixed-integer models in which some of the decisions (first-stage) have to be made under uncertainty and the remaining decisions (second-stage) can be made after the realization of the uncertain parameters. The uncertain model parameters are represented by a finite set of scenarios. The risk conscious planning problem under uncertainty is solved by a stage decomposition approach using a multi-objective evolutionary algorithm which optimizes the expected scenario costs and the risk criterion with respect to the first-stage decisions. The second-stage scenario decisions are handled by mathematical programming. Results from numerical experiments for a multi-product batch plant are presented.

A concise treatment of isogeometric analysis with particular emphasis on the relation to isoparametric finite elements is given. Besides preserving the exact geometry, this relatively new extension of the finite element method possesses the attractive feature of offering increased smoothness of the basis functions in the Galerkin projection. Such a property is particularly beneficial for stress analysis in linear elasticity problems, which is demonstrated by means of a 3D simulation example.

Two different hierarchical levels of algorithmic differentiation are compared: the traditional approach and a higher-level approach where matrix operations are considered to be atomic. More explicitly: It is discussed how computer programs that consist of matrix operations (e.g. matrix inversion) can be evaluated in univariate Taylor polynomial arithmetic. Formulas suitable for the reverse mode are also shown. The advantages of the higher-level approach are discussed, followed by an experimental runtime comparison.

Optimal control theory has been studied for use in developing valve trains in engines to minimize vibration and wear. Previous works have concentrated on the optimization of the cam lobe profile using an ideal linear spring model for the valve spring. The ideal linear spring model cannot capture the variations in spring stiffness that occur at high speeds due to the internal spring dynamics. By using a multiple-mass lumped-parameter spring, greater accuracy may be obtained in simulation. In addition, such a model allows for the introduction of spring pitch to be included as an additional optimization parameter. In this paper, a simple multi-mass variable pitch spring model is developed to be used in valve pitch optimization as well as cam profile optimization.