Nonlinear Assignment Problems
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Nonlinear Assignment Problems
Author: Panos M. Pardalos
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-09
Nonlinear Assignment Problems (NAPs) are natural extensions of the classic Linear Assignment Problem, and despite the efforts of many researchers over the past three decades, they still remain some of the hardest combinatorial optimization problems to solve exactly. The purpose of this book is to provide in a single volume, major algorithmic aspects and applications of NAPs as contributed by leading international experts. The chapters included in this book are concerned with major applications and the latest algorithmic solution approaches for NAPs. Approximation algorithms, polyhedral methods, semidefinite programming approaches and heuristic procedures for NAPs are included, while applications of this problem class in the areas of multiple-target tracking in the context of military surveillance systems, of experimental high energy physics, and of parallel processing are presented. Audience: Researchers and graduate students in the areas of combinatorial optimization, mathematical programming, operations research, physics, and computer science.
On Some Nonlinear Assignment Problems
Linear assignment problem (commonly referred to as just assignment problem) is a fundamental problem in combinatorial optimization. The goal is to assign n workers to do n jobs so that the linear sum of corresponding costs is minimized. The linear assignment problem is thoroughly studied and has a O(n^3) solution with Hungarian algorithm. Nevertheless, a wide range of applications involving assignments are naturally modeled with more complex objective functions (for example quadratic sum as in quadratic assignment problem), and are much more computationally challenging. In this thesis we discuss our results on the bilinear assignment problem, which generalizes the quadratic assignment problem, and is also motivated by several unique applications. The focus is on computational complexity, solvable special cases, approximations, linearizations as well as local search algorithms and other heuristic approaches for the problem. We also present our results on few applied projects, where modelling the underlying problem as a nonlinear assignment was instrumental.
Handbook of combinatorial optimization
Author: Dingzhu Du
language: en
Publisher: Springer Science & Business Media
Release Date: 1998-12-15
This is the second of a multi-volume set. The various volumes deal with several algorithmic approaches for discrete problems as well as with many combinatorial problems. The emphasis is on late-1990s developments. Each chapter is essentially expository in nature, but scholarly in its treatment.