The Linear Ordering Problem

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The Linear Ordering Problem

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Author : Rafael Martí
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-03

The Linear Ordering Problem written by Rafael Martí and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-03 with Computers categories.

Faced with the challenge of solving the hard optimization problems that abound in the real world, existing methods often encounter great difficulties. Important applications in business, engineering or economics cannot be tackled by the techniques that have formed the predominant focus of academic research throughout the past three decades. Exact and heuristic approaches are dramatically changing our ability to solve problems of practical significance and are extending the frontier of problems that can be handled effectively. This monograph details state-of-the-art optimization methods, both exact and heuristic, for the LOP. The authors employ the LOP to illustrate contemporary optimization technologies as well as how to design successful implementations of exact and heuristic procedures. Therefore, they do not limit the scope of this book to the LOP, but on the contrary, provide the reader with the background and practical strategies in optimization to tackle different combinatorial problems.

The Linear Ordering Problem

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Author : Gerhard Reinelt
language : en
Publisher:
Release Date : 1985

The Linear Ordering Problem written by Gerhard Reinelt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.

An Algorithm For The Exact Solution Of The Linear Ordering Problem

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Author : Allen R. Mushi
language : en
Publisher:
Release Date : 1994

An Algorithm For The Exact Solution Of The Linear Ordering Problem written by Allen R. Mushi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Algorithms categories.

Reliability Of Solutions In Linear Ordering Problem

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Author : Leszek Szczecinski
language : en
Publisher:
Release Date : 2023

Reliability Of Solutions In Linear Ordering Problem written by Leszek Szczecinski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.

The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, little was done to verify if the obtained solutions are valid and thus if they have a meaningful interpretation. To remedy this problem, we propose to characterize the reliability of the LOP solutions by adopting a probabilistic perspective where the results of pairwise comparisons are modeled as Bernoulli variables with a common parameter which we estimate from the observed data. Estimation by brute-force enumeration has a prohibitive complexity of O(M!) we thus reformulate the problem and introduce a concept of Slater's spectrum which generalizes Slater's index, and next, devising an efficient algorithm to find the spectrum, we lower the complexity to O(M22 M ) which is manageable for moderate-size LOPs. Furthermore, with a minor modification of the algorithm, we are able to find all solutions of the LOP. Numerical examples on synthetic and real-world data are shown and the Python-implemented algorithms are publicly available.

The Linear Ordering Problem

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Author : Rafael Martí
language : en
Publisher: Springer
Release Date : 2011-01-05

The Linear Ordering Problem written by Rafael Martí and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-05 with Computers categories.

Faced with the challenge of solving the hard optimization problems that abound in the real world, existing methods often encounter great difficulties. Important applications in business, engineering or economics cannot be tackled by the techniques that have formed the predominant focus of academic research throughout the past three decades. Exact and heuristic approaches are dramatically changing our ability to solve problems of practical significance and are extending the frontier of problems that can be handled effectively. This monograph details state-of-the-art optimization methods, both exact and heuristic, for the LOP. The authors employ the LOP to illustrate contemporary optimization technologies as well as how to design successful implementations of exact and heuristic procedures. Therefore, they do not limit the scope of this book to the LOP, but on the contrary, provide the reader with the background and practical strategies in optimization to tackle different combinatorial problems.

Modeling Hierarchy

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Author : John Milton Roberts
language : en
Publisher:
Release Date : 1990

Modeling Hierarchy written by John Milton Roberts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.

A Polynomial Algorithm For The Linear Ordering Problem With Weights In Product Form

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Author : Antoon Kolen
language : en
Publisher:
Release Date : 1986

A Polynomial Algorithm For The Linear Ordering Problem With Weights In Product Form written by Antoon Kolen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.

On The Relaxation Polytope Of The Linear Ordering Problem

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Author : Eberhard Girlich
language : en
Publisher:
Release Date : 1998

On The Relaxation Polytope Of The Linear Ordering Problem written by Eberhard Girlich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Optimal Linear Ordering

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Author : Donald Lee Adolphson
language : en
Publisher:
Release Date : 1973

Optimal Linear Ordering written by Donald Lee Adolphson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.

A Cutting Plane Algorithm For The Linear Ordering Problem

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Author : Martin Grötschel
language : de
Publisher:
Release Date : 1983

A Cutting Plane Algorithm For The Linear Ordering Problem written by Martin Grötschel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.