Theoretical Aspects of Local Search

Local search has been applied successfully to a diverse collection of optimization problems. It's appreciated for its basic conceptual foundation, its general applicability, and its power to serve as a source for new search paradigms. The typical characteristics of combinatorial optimization problems to which local search can be applied, its relation to complexity theory, and the combination with randomized search features have led to a wealth of interesting theoretical results. However, these results are scattered throughout the literature.

This is the first book that presents a large collection of theoretical results in a consistent manner, thus providing the reader with a coherent overview of the achievements obtained so far, but also serving as a source of inspiration for the development of novel results in the challenging field of local search.

From the reviews:

"This book focuses on theoretical aspects, in mainly three areas: performance guarantees, time complexity, asymptotic convergence. ... Throughout the authors avoid excessive and unnecessary formalism which leads to a style that makes even the more technical proofs quite easily readable. The book is suitable for a postgraduate course on the theory of local search. With its collection of results concerning the theoretical aspects of local search it is a most welcome addition to the literature on the topic." (Matthias Ehrgott, Zentralblatt MATH, Vol. 1130 (8), 2008)

"The book gives a nice overview of theoretical results obtained for some local search algorithms used to solve combinatorial optimization problems. ... The book is written for students from graduate level and for interested scholars working on related fields of science and engineering. ... it can be recommended as an introductory textbook as well. ... The authors did a good job in selecting the material, and the presentation is also nice. The book can be well recommended to the interested reader." (Tibor Csendes, Siam Review, Vol. 50 (3), 2008)

"Theoretical Aspects of Local Search focuses on local search for combinatorial optimization problems. ... This book provides deep theoretical analysis; it includes many theorems and proofs and some examples. Each chapter has bibliographical notes and exercises. I recommend it to students and researchers who ... are interested in the theoretical aspects of local search." (Julius Žilinskas, Interfaces, Vol. 38 (3), 2008)

"The book focuses on three main topics: performance guarantees, investigations of time complexity, and asymptotic convergence studies in the case where a probabilistic iteration mechanism is applied. ... Overall, this book brings to its readers many fresh ideas in the field of local search. ... The book is very well written, and authored by well-known researchers involved in the field. ... the book will be very useful for researchers, students, and engineers involved in optimization." (Patrick Siarry, ACM Computing Reviews, Vol. 49 (5), 2008)

"As the title of the book indicates, the authors focus on the theoretical aspects of local search. ... I can recommend the book to readers who are interested in such an introduction. The book should be particularly interesting for students who already know the basic concepts in complexity theory and are eager to see what these (and related) concepts are good for in the world of local search." (Hans-Ulrich Simon, Mathematical Reviews, Issue 2009 g)

“The authors of the book under review are in an excellent position to write a very different account. ... clearly aimed at advanced undergraduate students, although the blurb mentions ‘researchers and graduate students’ as the intended audience. ... the book provides a concise and easily understandable introduction to the basics of local search, an important concept in the design of heuristics. ... it is well-suited for a term-long course on heuristic design for theoretically-inclined undergraduates and first-year graduate students.” (Jakub Mareček, SIGACT News, Vol. 40 (2), 2009)