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About 4,722 papers for “knapsack problem”
Ali Lakhia · 2004
We explain how the Knapsack problem and interactive rendering are related. We also discuss several additional concerns regarding interactive rendering and how these affect the solution to the original Knapsack problem. Lastly, we present two approximate algorithms and compare how they meet the needs of interactive rendering.
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Eliška Šemnická · Digital Repository (National Repository of Grey Literature) · 2008
In the study are described integer programming, particular problems, as assignment problem, cover problem and city transportation problem, and method of solving these kinds of problems. It is depictured Lang and Doig method. Then is described knapsack problem and its types. A reader can find a method for solving zero-to-one problems, especially Balas method for minimisation of a target function. There is introduced a financial problem of optimisation portfolio in the study which is formulated as a zero-to-one problem and solved by Balas method.
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Ling, Haotian · TIB Data Manager · 2024
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2001
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Thomas Koshy · 2017
This chapter explores a few divisibility properties of Fibonacci and Lucas numbers. It discuses a theorem which shows that the greatest common divisor (GCD) of two Fibonacci numbers is also a Fibonacci number. Its proof uses the Euclidean algorithm. In 1965, M. Wunderlich of the University of Colorado employed the theorem to provide a beautiful proof that there are infinitely many primes, a fact that is universally known. A quick look at Lucas numbers shows that every third Lucas number is even.
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2011
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Rare & Special e-Zone (The Hong Kong University of Science and Technology) · 1988
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Carsten Murawski, Peter Bossaerts, Karlo Doroc et al. · OSF Preprints (OSF Preprints) · 2021
In this paper we report on the experimental data collected on the knapsack decision task at: DOI 10.17605/OSF.IO/T2JV7
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Umesh Chandra Jaiswal, Ankit Singh, Omkar Maurya et al. · Communications in computer and information science · 2011
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Algorithms and combinatorics · 2007
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Nikola Piskačová · Digital Repository (National Repository of Grey Literature) · 2018
This work deals with the theory of integer programming. In the first part, there are defined the basic concepts and there are mentioned the two most used methods for solving integer problems. Namely, it is the Branch and Bound method and the Cutting Plane method. In the second chapter, there is described the Knapsack Problem and its various formulations. This problem is a special case of integer optimalization. Next, there is a practical part, where a real problem is solved. The problem is how to place the products in shelves in equipment in the most effectively way. In this chapter is described how to process input data, create a model and solve the problem. In the second part of the practical part, the basics of stochastic optimalization and solution of these problems by the Scenario method are presented. This method is used to solve the previously mentioned problem if the delivery days are random. The aim of this work is to show the applicability of formulations of Knapsack Problem and to compare the obtained results. 1
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Senem Beken · 2011
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Nils Kyed · Lecture notes in economics and mathematical systems · 1973
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Hans Kellerer, Ulrich Pferschy, David Pisinger · 2004
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Vít Černý · Digital Repository (National Repository of Grey Literature) · 2010
The knapsack problem is one of the classical operations research problems. It belongs to the category of integer linear programming problems and is most often formulated as a binary problem. This thesis describes different categories of the problem and also some methods for finding their solution. Although there are precise algorithms for finding reliable optimal solution, some of the knapsack problems are so large that it would be impossible to follow the exact algorithms. Therefore, more complex knapsack problems belong to the complexity class of NP-complete. Yet there are a variety of heuristics and methods developed, which can lead to a sufficiently good solution in a relatively short time and relatively simple way. This paper focuses particularly on one of the problems described, the multiple knapsack problem. It is showed on a practical example how the problem can be solved.
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Hans Kellerer, Ulrich Pferschy, David Pisinger · 2004
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Chia‐Shin Chung, Ming S. Hung, Walter O. Rom · RePEc: Research Papers in Economics
In this article we develop a class of general knapsack problems which are hard for branch and bound algorithms. The number of alternate optimal solutions for these problems grows exponentially with problem parameters. In addition the LP bound is shown to be ineffective. Computational tests indicate that these problems are truly difficult for even very small problems. Implications for the testing of algorithms using randomly generated problems is discussed.
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Fabiano do Prado Marques · Digital Library of Theses and Dissertations of the University of São Paulo (Universidade de São Paulo) · 2000
Nesse trabalho, estudamos um problema de otimização combinatorial conhecido por Problema da Mochila Compartimentada, que é uma extensão do clássico Problema da Mochila. O problema consiste em determinar as capacidades adequadas de vários compartimentos que podem vir a ser alocados em uma mochila e como esses compartimentos devem ser carregados, respeitando as restrições de capacidades dos compartimentos e da mochila. Busca-se maximizar o valor de utilidade total. O problema é muito pouco estudado na literatura, apesar de surgir naturalmente em aplicações práticas. Nesse estudo, propomos uma modelagem matemática não linear para o problema e verificamos algumas heurísticas para sua resolução.
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Diptesh Ghosh, Boris Goldengorin · 2001
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Fatiha Bendali, Jean Mailfert, Eloise Mole Kamga et al. · 2022 8th International Conference on Control, Decision and Information Technologies (CoDIT) · 2022
We make interact here 2 Knapsack players, which may be related to energy management or robot cooperation. We first discuss the setting of this problem and provide it with an ILP formulation. Next we deal with it through Dynamic Programming and deduce from this DP a Polynomial Time Approximation Scheme.
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