Advances In Combinatorial Optimization Linear Programming Formulations Of The Traveling Salesman And Other Hard Combinatorial Optimization Problems
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Advances In Combinatorial Optimization: Linear Programming Formulations Of The Traveling Salesman And Other Hard Combinatorial Optimization Problems
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.
Advances in Bio-inspired Computing for Combinatorial Optimization Problems
Author: Camelia-Mihaela Pintea
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-08-13
"Advances in Bio-inspired Combinatorial Optimization Problems" illustrates several recent bio-inspired efficient algorithms for solving NP-hard problems. Theoretical bio-inspired concepts and models, in particular for agents, ants and virtual robots are described. Large-scale optimization problems, for example: the Generalized Traveling Salesman Problem and the Railway Traveling Salesman Problem, are solved and their results are discussed. Some of the main concepts and models described in this book are: inner rule to guide ant search - a recent model in ant optimization, heterogeneous sensitive ants; virtual sensitive robots; ant-based techniques for static and dynamic routing problems; stigmergic collaborative agents and learning sensitive agents. This monograph is useful for researchers, students and all people interested in the recent natural computing frameworks. The reader is presumed to have knowledge of combinatorial optimization, graph theory, algorithms and programming. The book should furthermore allow readers to acquire ideas, concepts and models to use and develop new software for solving complex real-life problems.
Linear Integer Programming
Author: Elias Munapo
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2021-12-06
This book presents the state-of-the-art methods in Linear Integer Programming, including some new algorithms and heuristic methods developed by the authors in recent years. Topics as Characteristic equation (CE), application of CE to bi-objective and multi-objective problems, Binary integer problems, Mixed-integer models, Knapsack models, Complexity reduction, Feasible-space reduction, Random search, Connected graph are also treated.