Rainer E. Burkard

QAPLIB – A Quadratic Assignment ProblemLibrary

A collection of electronically available data instances for the QuadraticAssignment Problem is described. For each instance, we provide detailedinformation, indicating whether or not the problem is solved to optimality. Ifnot, we supply the best known bounds for the problem. Moreover we surveyavailable software and describe recent dissertations related to the QuadraticAssignment Problem.

A thermodynamically motivated simulation procedure for combinatorial optimization problems

Abstract Exchange algorithms are an important class of heuristics for hard combinatorial optimization problems as, e.g., salesman problems or quadratic assignment problems. In Kirkpatricks and Cernys exchange algorithms for the travelling salesman problem and placement problem they propose to perform an exchange not only if the objective function value decreases by this exchange, but also in certain cases if the objective function value increases. An exchange increasing the objective function value is performed stochastically depending on the size of the increment. Computational tests with quadratic assignment problems revealed an excellent behaviour in such an approach. Suboptimal solutions differing 1–2% from the best known solutions are obtained by a simple program in short time. By starting this program several times with different starting values all known minimal objective function values were reached. Thus this approach is well suited also for smaller computers and leads in short time to acceptable solutions.

QAPLIB-A quadratic assignment problem library

Abstract After a short introduction into quadratic assignment problems we give a library of problem instances for the quadratic assignment problem. The examples are listed y authors in alphabetical order.

Quadratic Assignment Problems

Abstract This paper surveys quadratic assignment problems (QAP). At first several applications of this problem class are described and mathematical formulations of QAPs are given. Then some exact solution methods and good heuristics are outlined. Their computational behaviour is illustrated by numerical results. Further recent results on the asymptotic probabilistic behaviour of QAPs are outlined.

Perspectives of Monge properties in optimization

Abstract An m × n matrix C is called Monge matrix if c ij + c rs ⩽ c is + c rj for all 1 ⩽ i r ⩽ m , 1 ⩽ j s ⩽ n . In this paper we present a survey on Monge matrices and related Monge properties and their role in combinatorial optimization. Specifically, we deal with the following three main topics: (i) fundamental combinatorial properties of Monge structures, (ii) applications of Monge properties to optimization problems and (iii) recognition of Monge properties.

Assignment Problems: Revised Reprint

This book provides a comprehensive treatment of assignment problems from their conceptual beginnings in the 1920s through present-day theoretical, algorithmic, and practical developments. The authors have organized the book into 10 self-contained chapters to make it easy for readers to use the specific chapters of interest to them without having to read the book linearly. The topics covered include bipartite matching algorithms, linear assignment problems, quadratic assignment problems, multi-index assignment problems, and many variations of these problems. Exercises in the form of numerical examples provide readers with a method of self-study or students with homework problems, and an associated webpage offers applets that readers can use to execute some of the basic algorithms as well as links to computer codes that are available online. Audience: Assignment Problems is a useful tool for researchers, practitioners, and graduate students. Researchers will benefit from the detailed exposition of theory and algorithms related to assignment problems, including the basic linear sum assignment problem and its many variations. Practitioners will learn about practical applications of the methods, the performance of exact and heuristic algorithms, and software options. This book also can serve as a text for advanced courses in discrete mathematics, integer programming, combinatorial optimization, and algorithmic computer science. Contents: Preface; Chapter 1: Introduction; Chapter 2: Theoretical Foundations; Chapter 3: Bipartite Matching Algorithms; Chapter 4: Linear Sum Assignment Problem; Chapter 5: Further Results on the Linear Sum Assignment Problem; Chapter 6: Other Types of Linear Assignment Problems; Chapter 7: Quadratic Assignment Problems: Formulations and Bounds; Chapter 8: Quadratic Assignment Problems: Algorithms; Chapter 9: Other Types of Quadratic Assignment Problems; Chapter 10: Multi-index Assignment Problems; Bibliography; Author Index; Subject Index

The Quickest Flow Problem

AbstractConsider a network

Well-Solvable Special Cases of the Traveling Salesman Problem: A Survey

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