42 research outputs found

### ABACUS - A Branch-And-CUt System, Version 2.0, User's Guide and Reference Manual

ABACUS is a C++ framework for the implementation of branch-and-cut algorithms, branch-and-price algorithms, and their combination for linear mixed integer and combinatorial optimization problems. This manual explains the installation, the design, and the usage of the framework. Both the basic steps and advanced features are discussed. The reference manual describes all classes together with all members that are relevant for the user

### A Simple TSP-Solver: An ABACUS Tutorial

This CWEB program shows how a branch-and-cut algorithm for the traveling salesman problem (TSP) can be implemented with the software framework ABACUS. The intention of this program is not the practically efficient solution of TSPs but to show basic and some advanced features of ABACUS

### Introduction to ABACUS - A branch-and-cut System

The software system ABACUS is an object-oriented framework for the implementation of branch-and-cut and branch-and-price algorithms. This paper shows the basics of its application to combinatorial and mixed integer optimization problems

### Computing Delaunay-Triangulations in Manhatten and Maximum Metric

Delaunay-Triangulations (the duals of Voronoi Diagrams) are well known to be structures that contain a lot of neighborhood-information about a given (finite) set of points in the plane. Many algorithms rely on efficient procedures to compute them in practical applications, yet the textbook descriptions usually only treat the case of Euclidean metric. We modify one of the algorithms known for the Euclidean case (the incremental algorithm of Ohya, Iri, and Murota) to become suitable for a more general class of ''Delaunay Triangulations'' including those for the Manhattan and Maximum metrics. We give a detailed description of this algorithm that makes it (rather) easy to write a computer program for the calculation of Delaunay Triangulations for these metrics. We give computational results for our own implementation of the algorithm

### Provably good solutions for the traveling salesman problem

The determination of true optimum solutions of combinatorial optimization problems is seldomly required in practical applications. The majority of users of optimization software would be satisfied with solutions of guaranteed quality in the sense that it can be proven that the given solution is at most a few percent off an optimum solution. This paper presents a general framework for practical problem solving with emphasis on this aspect. A detailed discussion along with a report about extensive computational experiments is given for the traveling salesman problem

### Practical Performance of Efficient Minimum Cut Algorithms

In the late eighties and early nineties, three major exciting new developments (and some ramifications) in the computation of minimum capacity cuts occurred and these developments motivated us to evaluate the old and new methods experimentally. We provide a brief overview of the most important algorithms for the minimum capacity cut problem and compare these methods both on problem instances from the literature and on problem instances originating from the solution of the traveling salesman problem by branch-and-cut