Bernd Dammann

A Branch and Bound Algorithm for a Class of Biobjective Mixed Integer Programs

Most real-world optimization problems are multiobjective by nature, involving noncomparable objectives. Many of these problems can be formulated in terms of a set of linear objective functions that should be simultaneously optimized over a class of linear constraints. Often there is the complicating factor that some of the variables are required to be integral. The resulting class of problems is named multiobjective mixed integer programming (MOMIP) problems. Solving these kinds of optimization problems exactly requires a method that can generate the whole set of nondominated points (the Pareto-optimal front). In this paper, we first give a survey of the newly developed branch and bound methods for solving MOMIP problems. After that, we propose a new branch and bound method for solving a subclass of MOMIP problems, where only two objectives are allowed, the integer variables are binary, and one of the two objectives has only integer variables. The proposed method is able to find the full set of nondominat...

High-performance small-scale solvers for linear Model Predictive Control

In Model Predictive Control (MPC), an optimization problem needs to be solved at each sampling time, and this has traditionally limited use of MPC to systems with slow dynamic. In recent years, there has been an increasing interest in the area of fast small-scale solvers for linear MPC, with the two main research areas of explicit MPC and tailored on-line MPC. State-of-the-art solvers in this second class can outperform optimized linear-algebra libraries (BLAS) only for very small problems, and do not explicitly exploit the hardware capabilities, relying on compilers for that. This approach can attain only a small fraction of the peak performance on modern processors. In our paper, we combine high-performance computing techniques with tailored solvers for MPC, and use the specific instruction sets of the target architectures. The resulting software (called HPMPC) can solve linear MPC problems 2 to 8 times faster than the current state-of-the-art solver for this class of problems, and the high-performance is maintained for MPC problems with up to a few hundred states.

A matlab framework for estimation of NLME models using stochastic differential equations

The non-linear mixed-effects model based on stochastic differential equations (SDEs) provides an attractive residual error model, that is able to handle serially correlated residuals typically arising from structural mis-specification of the true underlying model. The use of SDEs also opens up for new tools for model development and easily allows for tracking of unknown inputs and parameters over time. An algorithm for maximum likelihood estimation of the model has earlier been proposed, and the present paper presents the first general implementation of this algorithm. The implementation is done in Matlab and also demonstrates the use of parallel computing for improved estimation times. The use of the implementation is illustrated by two examples of application which focus on the ability of the model to estimate unknown inputs facilitated by the extension to SDEs. The first application is a deconvolution-type estimation of the insulin secretion rate based on a linear two-compartment model for C-peptide measurements. In the second application the model is extended to also give an estimate of the time varying liver extraction based on both C-peptide and insulin measurements.

Topology Optimization of Mass Distribution Problems in Stokes Flow

We consider topology optimization of mass distribution problems in 2D and 3D Stokes flow with the aim of designing devices that meet target outflow rates.

A mean-variance criterion for economic model predictive control of stochastic linear systems

Stochastic linear systems arise in a large number of control applications. This paper presents a mean-variance criterion for economic model predictive control (EMPC) of such systems. The system operating cost and its variance is approximated based on a Monte-Carlo approach. Using convex relaxation, the tractability of the resulting optimal control problem is addressed. We use a power management case study to compare different variations of the mean-variance strategy with EMPC based on the certainty equivalence principle. The certainty equivalence strategy is much more computationally efficient than the mean-variance strategies, but it does not account for the variance of the uncertain parameters. Open-loop simulations suggest that a single-stage mean-variance approach yields a significantly lower operating cost than the certainty equivalence strategy. In closed-loop, the single-stage formulation is overly conservative, which results in a high operating cost. For this case, a two-stage extension of the mean-variance approach provides the best trade-off between the expected cost and its variance. It is demonstrated that by using a constraint back-off technique in the specific case study, certainty equivalence EMPC can be modified to perform almost as well as the two-stage mean-variance formulation. Nevertheless, we argue that the mean-variance approach can be used both as a strategy for evaluating less computational demanding methods such as the certainty equivalence method, and as an individual control strategy when heuristics such as constraint back-off do not perform well.

A decomposition algorithm for Mean-Variance Economic Model Predictive Control of stochastic linear systems

This paper presents a decomposition algorithm for solving the optimal control problem (OCP) that arises in Mean-Variance Economic Model Predictive Control of stochastic linear systems. The algorithm applies the alternating direction method of multipliers to a reformulation of the OCP that decomposes into small independent subproblems. We test the decomposition algorithm using a simple power management case study, in which the OCP is formulated as a convex quadratic program. Simulations show that the decomposition algorithm scales linearly in the number of uncertainty scenarios. Moreover, a parallel implementation of the algorithm is several orders of magnitude faster than state-of-the-art convex quadratic programming algorithms, provided that the number of uncertainty scenarios is large.

Atomic scattering from an adsorbed monolayer solid with a helium beam that penetrates to the substrate

Diffraction and one-phonon inelastic scattering of a thermal energy helium atomic beam are evaluated in the situation that the target monolayer lattice is so dilated that the atomic beam penetrates to the interlayer region between the monolayer and the substrate. The scattering is simulated by propagating a wavepacket and including the effect of a feedback of the inelastic wave onto the diffracted wave, which represents a coherent re-absorption of the created phonons. Parameters are chosen to be representative of an observed p(1 × 1) commensurate monolayer solid of H2/NaCl(001) and a conjectured p(1 × 1) commensurate monolayer solid of H2/KCl(001). For the latter, there are cases where part of the incident beam is trapped in the interlayer region for times exceeding 50 ps, depending on the spacing between the monolayer and the substrate and on the angle of incidence. The feedback effect is large for cases of strong transient trapping.

Effect of vacancies and surfactants on the dynamics of ordering processes in multi-component systems

The dynamics of far-from-equilibrium ordering processes in multi-component systems, e.g. crystalline solids or fluid mixtures, that are being quenched in temperature is studied by computer-simulation techniques involving Monte Carlo (MC) as well as molecular dynamics (MD) methods. The systems are modeled by using simple two-dimensional statistical mechanical models such as multi-state Potts lattice models and models of particle systems interacting via Lennard-Jones-like potentials. The ordering dynamics is investigated under the conditions of both conservation and non-conservation of the order parameter as well as with and without the presence of additional ‘foreign’ components, such as vacancies and surfactants, that couple to the interfaces which develop during the ordering process. The present paper reviews recent progress in this field with an emphasis on a possible universal description of ordering dynamics.