Knapsack Problems
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Knapsack Problems
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Author : Hans Kellerer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Knapsack Problems written by Hans Kellerer 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 2013-03-19 with Mathematics categories.
Thirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared. On this occasion a former colleague exclaimed back in 1990: "How can you write 250 pages on the knapsack problem?" Indeed, the definition of the knapsack problem is easily understood even by a non-expert who will not suspect the presence of challenging research topics in this area at the first glance. However, in the last decade a large number of research publications contributed new results for the knapsack problem in all areas of interest such as exact algorithms, heuristics and approximation schemes. Moreover, the extension of the knapsack problem to higher dimensions both in the number of constraints and in the num ber of knapsacks, as well as the modification of the problem structure concerning the available item set and the objective function, leads to a number of interesting variations of practical relevance which were the subject of intensive research during the last few years. Hence, two years ago the idea arose to produce a new monograph covering not only the most recent developments of the standard knapsack problem, but also giving a comprehensive treatment of the whole knapsack family including the siblings such as the subset sum problem and the bounded and unbounded knapsack problem, and also more distant relatives such as multidimensional, multiple, multiple-choice and quadratic knapsack problems in dedicated chapters.
Knapsack Problems
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Author : Silvano Martello
language : en
Publisher:
Release Date : 1990-12-14
Knapsack Problems written by Silvano Martello and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-14 with Computers categories.
Here is a state of art examination on exact and approximate algorithms for a number of important NP-hard problems in the field of integer linear programming, which the authors refer to as ``knapsack.'' Includes not only the classical knapsack problems such as binary, bounded, unbounded or binary multiple, but also less familiar problems such as subset-sum and change-making. Well known problems that are not usually classified in the knapsack area, including generalized assignment and bin packing, are also covered. The text fully develops an algorithmic approach without losing mathematical rigor.
Knapsack Problems
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Author : Hans Kellerer
language : en
Publisher:
Release Date : 2014-01-15
Knapsack Problems written by Hans Kellerer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Knapsack Problems
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Author : Silvano Martello
language : en
Publisher:
Release Date : 1990
Knapsack Problems written by Silvano Martello 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.
Algorithms For Knapsack Problems
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Author : David Pisinger
language : en
Publisher:
Release Date : 1995
Algorithms For Knapsack Problems written by David Pisinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with algoritmer, EDB categories.
Abstract: "This thesis considers a family of combinatorial problems known under the name Knapsack Problems. As all the problems are NP-hard we are searching for exact solution techniques having reasonable solution times for nearly all instances encountered in practice, despite having exponential time bounds for a number of highly contrived problem instances. A similar behavior is known from the Simplex algorithm, which despite its exponential worst-case behavior has reasonable solution times for all realistic problems. A promising approach for solving Knapsack Problems is to develop algorithms where the worst-case complexity is bounded by some appropriate measure of the 'hardness' of a problem, e.g. the magnitude of the coefficients, the number of undominated items, or the number of variables where the integer solution differs from the continuous solution. Although such bounds in the worst case degenerate to exponential solution times, they allow us to segregate several groups of easily solvable instances. The approach has been applied to several problem types within the Knapsack family, and thorough computational experiments document the attractive properties of the algorithms developed. Most of the exact algorithms have linear solution times for easy instances, while hard instances generally may be solved in pseudo-polynomial time."
Strongly Correlated Knapsack Problems Are Trivial To Solve
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Author : David Pisinger
language : en
Publisher:
Release Date : 1996
Strongly Correlated Knapsack Problems Are Trivial To Solve written by David Pisinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Operations research categories.
Abstract: "We consider a variant of the 0-1 Knapsack Problem, where the profit of each item corresponds to its weight plus a fixed constant. These so-called Strongly Correlated Knapsack Problems have attained much interest due to their apparent hardness and wide applicability in several fixed-charge problems. A specialized algorithm for the problem is presented, where the main approach is to derive an additional constraint from an extended cover. By surrogate relaxataion [sic] with optimal multipliers, we obtain a Subset-sum Problem defined in the profits of the items. It is proved that an optimal solution to the Subset-sum Problem is also an optimal solution to the original problem provided that the largest possible number of items is chosen. Based on this observation, a 2-optimal heuristic is derived which solves the problem to optimality for several large-sized problems. In those cases where the heuristic fails, we solve the problem to optimality by restricting the problem to a fixed number of chosen items [beta]. For each value of [beta] the problem is solved through dynamic programming. Extensive computational experiments are provided showing that we are able to solve strongly correlated instances faster than uncorrelated instances usually are solved. Thus problems with 100 000 [sic] items may be solved in less than 0.05 seconds."
Some Complexity Issues In A Class Of Knapsack Problems
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Author : D. Krass
language : en
Publisher:
Release Date : 2010
Some Complexity Issues In A Class Of Knapsack Problems written by D. Krass and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
We propose a new class of knapsack problems by assiuning that the sizes of the items to be put into a knapsack are known to be elements 0f a given subset S of the positive integers Z'^. The set S is treated as a parameter. We show that the family of knapsack problems obtained by varying the parameter S in the power set of Z'^ contains polynomially solvable problems and NP-complete problems, even when we restrict S to the class of polynomially recognizable sets.
Algorithms For Some Hard Knapsack Problems
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Author : Araya Kulanoot
language : en
Publisher:
Release Date : 2000
Algorithms For Some Hard Knapsack Problems written by Araya Kulanoot and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
This thesis considers a number of hard Knapsack Problems with a single constraint. A number of specialized algorithms are developed. Our work focuses on some hard instances of the 0-1Knapsack Problem, the Bounded Knapsack Problem, the Unbounded Knapsack Problem and the Change-Making Problem.
Efficient Algorithms For Large Boundary Knapsack Problems
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Author : Leo Boris Landa
language : en
Publisher:
Release Date : 2005
Efficient Algorithms For Large Boundary Knapsack Problems written by Leo Boris Landa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Partitioning Algorithms For A Class Of Knapsack Problems Classic Reprint
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Author : John F. Pierce
language : en
Publisher: Forgotten Books
Release Date : 2018-02-14
Partitioning Algorithms For A Class Of Knapsack Problems Classic Reprint written by John F. Pierce and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-14 with Mathematics categories.
Excerpt from Partitioning Algorithms for a Class of Knapsack Problems In this paper algorithms are presented for evaluating the knapsack function for a class of two-dimensional knapsack problems such as arises, for example, in the solution of cutting stock problems in staged guillotine cutting operations. This class includes as a special case the classical one-dimensional knapsack problem. In each algorithm evaluation proceeds from the larger knapsack sizes to the smaller, exploiting for each size the optimality of all partitions or descendents of an optimal solution for a knapsack of that Size. All of the algorithms discussed are based on the methods of combinatorial programming and are reliable in the respect that if carried to completion they guarantee optimal evaluations for knapsacks. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.