Combinatorial Optimization for Undergraduates

ISBN-13: 9781461395133 / Angielski / Miękka / 2012 / 228 str.

L. R. Foulds

Opis

The major purpose of this book is to introduce the main concepts of discrete optimization problems which have a finite number of feasible solutions. Following common practice, we term this topic combinatorial optimization. There are now a number of excellent graduate-level textbooks on combina- torial optimization. However, there does not seem to exist an undergraduate text in this area. This book is designed to fill this need. The book is intended for undergraduates in mathematics, engineering, business, or the physical or social sciences. It may also be useful as a reference text for practising engineers and scientists. The writing of this book was inspired through the experience of the author in teaching the material to undergraduate students in operations research, engineering, business, and mathematics at the University of Canterbury, New Zealand. This experience has confirmed the suspicion that it is often wise to adopt the following approach when teaching material of the nature contained in this book. When introducing a new topic, begin with a numerical problem which the students can readily understand; develop a solution technique by using it on this problem; then go on to general problems. This philosophy has been adopted throughout the book. The emphasis is on plausibility and clarity rather than rigor, although rigorous arguments have been used when they contribute to the understanding of the mechanics of an algorithm.

Spis treści

One: Techniques.- 0 Introduction to the Techniques of Combinatorial Optimization.- 0.1. The General Problem.- 0.2. Important Combinatorial Optimization Problems.- 0.3. The Fundamental Algorithm, Efficiency and the Digital Computer.- 1 Linear Programming and Extensions.- 1.1. An Introduction to Linear Programming.- 1.2. The Transportation Problem.- 1.3. The Assignment Problem.- 2 Solution Techniques.- 2.1. Integer Programming.- 2.2. Dynamic Programming.- 2.3. Complexity.- 2.4. Heuristic Problem Solving.- 3 Optimization on Graphs and Networks.- 3.1. Minimal Spanning Trees.- 3.2. Shortest Paths.- 3.3. The Maximum-Flow Problem.- 3.4. The Minimum-Cost-Flow Problem.- 3.5. Activity Networks.- Two: Applications.- 4 Some Applications of Combinatorial Optimization Techniques.- 4.1. Facilities Layout.- 4.2. The Traveling Salesman Problem.- 4.3. The Vehicle Scheduling Problem.- 4.4. Car Pooling.- 4.5. Evolutionary Tree Construction.- 5 Appendix.- 5.1. Linear Algebra.- 5.2. Graph Theory.- Further Reading.