Filtern
Dokumenttyp
- Artikel (7)
- Konferenzbeitrag (3)
- ZIB-Report (3)
Sprache
- Englisch (13)
Gehört zur Bibliographie
- nein (13)
Schlagworte
- VLSI-Design (1)
- computational complexity (1)
- facet classification (1)
- polyhedral structure (1)
- quadratic 0/1 optimization (1)
- symmetry (1)
Institut
Quadratic 0/1 Optimization and a Decomposition Approach for the Placement of Electronic Circuits.
(1992)
The placement in the layout design of electronic circiuts consists of finding a non- overlapping assignment of rectangular cells to positions on the chip so what wireability is guaranteed and certain technical constraints are met.This problem can be modelled as a quadratic 0/1- program subject to linear constraints. We will present a decomposition approach to the placement problem and give results about $NP$-hardness and the existence of $\varepsilon$-approximative algorithms for the involved optimization problems. A graphtheoretic formulation of these problems will enable us to develop approximative algorithms. Finally we will present details of the implementation of our approach and compare it to industrial state of the art placement routines. {\bf Keywords:} Quadratic 0/1 optimization, Computational Complexity, VLSI-Design.
A Branch & Cut Algorithm for the Asymmetric Traveling Salesman Problem with Precedence Constraints
(1997)
In this paper we consider a variant of the classical ATSP, namely the asymmetric Hamiltonian path problem (or equivalently ATSP) with precedence constraints. In this problem precedences among the nodes are present, stating that a certain node has to precede others in any feasible sequence. This problem occurs as a basic model in scheduling and routing and has a wide range of applications varying from helicopter routing[Timlin89], sequencing in flexible manufacturing [AscheuerEscuderoGroetschelStoer90,AscheuerEscuderoGroetschelStoer93], to stacker crane routing in an automatic storage system[Ascheuer95]. We give an integer programming model and summarize known classes of valid inequalities. We describe in detail the implementation of a branch&-cut algorithm and give computational results on real world instances and benchmark problems from TSPLIB. The results we achieve indicate that our implementation outperforms other implementations found in the literature. Real world instances up to 174 nodes could be solved to optimality within a few minutes of CPU-time. As a side product we obtained a branch&cut-algorithm for the ATSP. All instances in TSPLIB could be solved to optimality in a reasonable amount of computing time.
An application of combinatorial optimization to statistical physics and circuit layout design
(1988)
The target visitation problem (TVP) is concerned with finding a route to visit a set of targets starting from and returning to some base. In addition to the distance traveled a tour
is evaluated by taking also preferences into account which
address the sequence in which the targets are visited. The
problem thus is a combination of two well-known combinato-
rial optimization problems: the traveling salesman and the
linear ordering problem. In this paper we present several
possible IP-Models for this problem and compared them to
their usability for branch-and-cut approaches.
Usually complete linear descriptions of polytopes consist of
an enormous number of facet-defining inequalities already
for very small problem sizes. In this paper, we describe a method
for dividing the inequalities into equivalence classes without resorting to a normal form. Within each
class, facets are related by certain symmetries and it is sufficient
to list one representative of each class to give a complete
picture of the structural properties of a polytope. We propose an algorithm
for the classification and illustrate its efficiency on a broad range of combinatorial optimization problems including the Traveling Salesman and the Linear Ordering Problem.