Michael Armbruster

LP and SDP branch-and-cut algorithms for the minimum graph bisection problem: a computational comparison

While semidefinite relaxations are known to deliver good approximations for combinatorial optimization problems like graph bisection, their practical scope is mostly associated with small dense instances. For large sparse instances, cutting plane techniques are considered the method of choice. These are also applicable for semidefinite relaxations via the spectral bundle method, which allows to exploit structural properties like sparsity. In order to evaluate the relative strengths of linear and semidefinite approaches for large sparse instances, we set up a common branch-and-cut framework for linear and semidefinite relaxations of the minimum graph bisection problem. It incorporates separation algorithms for valid inequalities of the bisection cut polytope described in a recent study by the authors. While the problem specific cuts help to strengthen the linear relaxation significantly, the semidefinite bound profits much more from separating the cycle inequalities of the cut polytope on a slightly enlarged support. Extensive numerical experiments show that this semidefinite branch-and-cut approach without problem specific cuts is a superior choice to the classical simplex approach exploiting bisection specific inequalities on a clear majority of our large sparse test instances from VLSI design and numerical optimization.

A comparative study of linear and semidefinite branch-and-cut methods for solving the minimum graph bisection problem

Semidefinite relaxations are known to deliver good approximations for combinatorial optimization problems like graph bisection. Using the spectral bundle method it is possible to exploit structural properties of the underlying problem and to apply, even to sparse large scale instances, cutting plane methods, probably the most successful technique in linear programming. We set up a common branch-and-cut framework for linear and semidefinite relaxations of the minimum graph bisection problem. It incorporates separation algorithms for valid inequalities presented in the recent study [2] of the facial structure of the associated polytope. Extensive numerical experiments show that the semidefinite branch-and-cut approach outperforms the classical simplex approach on a clear majority of the sparse large scale test instances. On instances from compiler design the simplex approach is faster.

Duo duplex drive-by-wire computer system

Abstract The integration of drive-by-wire systems into the future generations of vehicles requires a reliable and safe processing of the drivers input requests. Many approaches presented in the last years apply specialised control units as well as communication systems not available in high quantities. This results in cost-intensive systems and increasing developmental periods, which proves to be harmful in the highly competitive automotive sector. Therefore, this article describes a safety relevant controller composed of commercial-off-the-shelf components designed for automotive applications. The article explains the hardware structure consisting of four electronic control units (ECU), connected via the controller area network, constituting a duo duplex system. To stop the communication of faulty ECUs an additional hardware unit is included in the controller system—the so-called BUSPWR block. Beside the hardware a detailed description of the redundancy management is given, which is the software operating the redundant controller. Safety relevant software components have to meet requirements of high software quality standards. For this reason the last part of the article concentrates on the software development process and its supporting tool chain. The application of automated code generation for safety relevant drive-by-wire systems is discussed in detail.

Redundancy Management for Drive-by-Wire Computer Systems

The integration of drive-by-wire systems into the future generations of vehicles requires a reliable and safe processing of the driver’s input requests. Many approaches presented in the last years apply specialized control units as well as communication systems not available in high quantities. This results in cost-intensive systems and increasing developmental periods, which proves to be harmful in the highly competitive automotive sector. Therefore this article describes a safety relevant control system composed of commercial-off-the-shelf (COTS) components designed for automotive applications. The paper explains the hardware structure consisting of four electronic control units (ECU), connected via CAN, which constitute a duo duplex system. Furthermore a detailed description of the redundancy management is given, which is the software operating the redundant computer system. Safety relevant software components have to meet requirements of high software quality standards. For this reason the last part of the paper concentrates on the software development process and its supporting tool chain. The application of automated code generation for safety relevant drive-by-wire systems is discussed in detail.

On the Graph Bisection Cut Polytope

Given a graph

LP-based Genetic Algorithm for the Minimum Graph Bisection Problem

G=(V,E)

X-by-Wire Plattform — Konzept und Auslegung

with node weights

Aircraft controlling device, has decision unit provided to decide execution of security-critical control function on microcomputers and/or control units due to comparison of output data of microcomputers

\varphi_v \in \mathbb{N}\cup\{0\}

Affordable X-By-Wire technology based on an innovative, scalable E/E platform-concept

,

Hybrid Genetic Algorithm Within Branch-and-Cut for the Minimum Graph Bisection Problem

v\in V