Progress in Combinatorial Optimization


Book Description

Progress in Combinatorial Optimization provides information pertinent to the fundamental aspects of combinatorial optimization. This book discusses how to determine whether or not a particular structure exists. Organized into 21 chapters, this book begins with an overview of a polar characterization of facets of polyhedra obtained by lifting facets of lower dimensional polyhedra. This text then discusses how to obtain bounds on the value of the objective in a graph partitioning problem in terms of spectral information about the graph. Other chapters consider the notion of a triangulation of an oriented matroid and show that oriented matroid triangulation yield triangulations of the underlying polytopes. This book discusses as well the selected results and problems on perfect ad imperfect graphs. The final chapter deals with the weighted parity problem for gammoids, which can be reduced to the weighted graphic matching problem. This book is a valuable resource for mathematicians and research workers.




Advances In Combinatorial Optimization: Linear Programming Formulations Of The Traveling Salesman And Other Hard Combinatorial Optimization Problems


Book Description

Combinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research/management science, artificial intelligence, machine learning, and software engineering.Advances in Combinatorial Optimization presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the 'traveling salesman problem' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the 'vertex coloring problem' (VCP)). This work also represents a proof of the equality of the complexity classes 'P' (polynomial time) and 'NP' (nondeterministic polynomial time), and makes a contribution to the theory and application of 'extended formulations' (EFs).On a whole, Advances in Combinatorial Optimization offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general.




Progress in Combinatorial Optimization


Book Description

This book presents recent developments and new trends in Combinatorial Optimization. Combinatorial Optimization is an active research area that has applications in many domains such as communications, network design, VLSI, scheduling, production, computational biology. In the past years, new results and major advances have been seen in many areas including computational complexity, approximation algorithms, cutting-plane based methods and submodularity function minimization. More efficient and powerful methods have been developed for approaching real-worlds problems, and new concepts and theoritical results have been introduced.




Efficient Approximation and Online Algorithms


Book Description

This book provides a good opportunity for computer science practitioners and researchers to get in sync with current state-of-the-art and future trends in the field of combinatorial optimization and online algorithms. Recent advances in this area are presented focusing on the design of efficient approximation and on-line algorithms. One central idea in the book is to use a linear program relaxation of the problem, randomization and rounding techniques.




Combinatorial Optimization


Book Description

There have been significant developments in the theory and practice of combinatorial optimization in the last 15 years. This progress has been evidenced by a continuously increasing number of international and local conferences, books and papers in this area. This book is also another contribution to this burgeoning area of operations research and optimization. This volume contains the contributions of the participants of the recent NATO Ad vanced Study Institute, New Frontiers in the Theory and Practice of Combinatorial Op timization, which was held at the campus of Bilkent University, in Ankara, Turkey, July 16-29, 1990. In this conference, we brought many prominent researchers and young and promising scientists together to discuss current and future trends in the theory and prac tice of combinatorial optimization. The Bilkent campus was an excellent environment for such an undertaking. Being outside of Ankara, the capital of Turkey, Bilkent University gave the participants a great opportunity for exchanging ideas and discussing new theories and applications without much distraction. One of the primary goals of NATO ASIs is to bring together a group of scientists and research scientists primarily from the NATO countries for the dissemination of ad vanced scientific knowledge and the promotion of international contacts among scientists. We believe that we accomplished this mission very successfully by bringing together 15 prominent lecturers and 45 promising young scientists from 12 countries, in a university environment for 14 days of intense lectures, presentations and discussions.




Combinatorial Optimization


Book Description

From the reviews: "About 30 years ago, when I was a student, the first book on combinatorial optimization came out referred to as "the Lawler" simply. I think that now, with this volume Springer has landed a coup: "The Schrijver". The box is offered for less than 90.- EURO, which to my opinion is one of the best deals after the introduction of this currency." OR-Spectrum




Recent Advances in Evolutionary Computation for Combinatorial Optimization


Book Description

This cutting-edge volume presents recent advances in the area of metaheuristic combinatorial optimisation, with a special focus on evolutionary computation methods. Moreover, it addresses local search methods and hybrid approaches.




Industrial Applications of Combinatorial Optimization


Book Description

Industries rely more and more on advanced technology. Accelerated computer evolution makes large-scale computation practical. Many enterprises are be ginning to benefit from more efficient allocation of resources and more effective planning, scheduling, manufacturing, and distribution by adopting state-of-the art decision support systems. Academics increasingly emphasize application driven research. All these forces have moved optimization from a pure class room and textbook terminology to an accepted tool in today's business world. This book chronicles and describes applications of combinatorial optimization in industry. A wide range of applications is included: manpower planning • production planning • job sequencing and scheduling • manufacturing layout design • facility planning • vehicle scheduling and routing • retail seasonal planning • I! space shuttle scheduling, and telecommunication network design . • The applications covered in this book comprise a representative set of industry sectors including electronics, airlines, manufacturing, tobacco, retail, telecom munication, defense, and livestock. These examples should encourage opera tions researchers and applied mathematicians by pointing out how the impor tance and practicality of optimization is starting to be realized by the manage ment of various organizations and how some pioneering developments in this field are beginning to bear fruit.




Nonlinear Combinatorial Optimization


Book Description

Graduate students and researchers in applied mathematics, optimization, engineering, computer science, and management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization. Nonlinear combinatorial optimization is a new research area within combinatorial optimization and includes numerous applications to technological developments, such as wireless communication, cloud computing, data science, and social networks. Theoretical developments including discrete Newton methods, primal-dual methods with convex relaxation, submodular optimization, discrete DC program, along with several applications are discussed and explored in this book through articles by leading experts.




Introduction to Combinatorial Optimization


Book Description

Introductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields. There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems. Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization. Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, such as greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer. Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.