Search results for: knapsack
10 A New Knapsack Public-Key Cryptosystem Based on Permutation Combination Algorithm
Authors: Min-Shiang Hwang, Cheng-Chi Lee, Shiang-Feng Tzeng
Abstract:
A new secure knapsack cryptosystem based on the Merkle-Hellman public key cryptosystem will be proposed in this paper. Although it is common sense that when the density is low, the knapsack cryptosystem turns vulnerable to the low-density attack. The density d of a secure knapsack cryptosystem must be larger than 0.9408 to avoid low-density attack. In this paper, we investigate a new Permutation Combination Algorithm. By exploiting this algorithm, we shall propose a novel knapsack public-key cryptosystem. Our proposed scheme can enjoy a high density to avoid the low-density attack. The density d can also exceed 0.9408 to avoid the low-density attack.Keywords: Public key, Knapsack problem, Knapsack cryptosystem, low-density attack.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19439 The Knapsack Sharing Problem: A Tree Search Exact Algorithm
Authors: Mhand Hifi, Hedi Mhalla
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In this paper, we study the knapsack sharing problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of a tree search for optimally solving the problem. The used method combines two complementary phases: a reduction interval search phase and a branch and bound procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for decomposing the problem into a series of knapsack problems. Second, the tree search procedure is applied in order to attain a set of optimal capacities characterizing the knapsack problems. Finally, the performance of the proposed optimal algorithm is evaluated on a set of instances of the literature and its runtime is compared to the best exact algorithm of the literature.
Keywords: Branch and bound, combinatorial optimization, knap¬sack, knapsack sharing, heuristics, interval reduction.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15498 An Enhanced Cryptanalytic Attack on Knapsack Cipher using Genetic Algorithm
Authors: Poonam Garg, Aditya Shastri, D.C. Agarwal
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With the exponential growth of networked system and application such as eCommerce, the demand for effective internet security is increasing. Cryptology is the science and study of systems for secret communication. It consists of two complementary fields of study: cryptography and cryptanalysis. The application of genetic algorithms in the cryptanalysis of knapsack ciphers is suggested by Spillman [7]. In order to improve the efficiency of genetic algorithm attack on knapsack cipher, the previously published attack was enhanced and re-implemented with variation of initial assumptions and results are compared with Spillman results. The experimental result of research indicates that the efficiency of genetic algorithm attack on knapsack cipher can be improved with variation of initial assumption.Keywords: Genetic Algorithm, Knapsack cipher, Key search.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16797 The Multi-scenario Knapsack Problem: An Adaptive Search Algorithm
Authors: Mhand Hifi, Hedi Mhalla, Mustapha Michaphy
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In this paper, we study the multi-scenario knapsack problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of an adaptive algorithm for solving heuristically the problem. The used method combines two complementary phases: a size reduction phase and a dynamic 2- opt procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for reducing the size problem. Second, the adaptive search procedure is applied in order to attain a feasible solution Finally, the performances of two versions of the proposed algorithm are evaluated on a set of randomly generated instances.
Keywords: combinatorial optimization, max-min optimization, knapsack, heuristics, problem reduction
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16106 Centre Of Mass Selection Operator Based Meta-Heuristic For Unbounded Knapsack Problem
Authors: D.Venkatesan, K.Kannan, S. Raja Balachandar
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In this paper a new Genetic Algorithm based on a heuristic operator and Centre of Mass selection operator (CMGA) is designed for the unbounded knapsack problem(UKP), which is NP-Hard combinatorial optimization problem. The proposed genetic algorithm is based on a heuristic operator, which utilizes problem specific knowledge. This center of mass operator when combined with other Genetic Operators forms a competitive algorithm to the existing ones. Computational results show that the proposed algorithm is capable of obtaining high quality solutions for problems of standard randomly generated knapsack instances. Comparative study of CMGA with simple GA in terms of results for unbounded knapsack instances of size up to 200 show the superiority of CMGA. Thus CMGA is an efficient tool of solving UKP and this algorithm is competitive with other Genetic Algorithms also.
Keywords: Genetic Algorithm, Unbounded Knapsack Problem, Combinatorial Optimization, Meta-Heuristic, Center of Mass
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16885 A Comparison of Exact and Heuristic Approaches to Capital Budgeting
Authors: Jindřiška Šedová, Miloš Šeda
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This paper summarizes and compares approaches to solving the knapsack problem and its known application in capital budgeting. The first approach uses deterministic methods and can be applied to small-size tasks with a single constraint. We can also apply commercial software systems such as the GAMS modelling system. However, because of NP-completeness of the problem, more complex problem instances must be solved by means of heuristic techniques to achieve an approximation of the exact solution in a reasonable amount of time. We show the problem representation and parameter settings for a genetic algorithm framework.Keywords: Capital budgeting, knapsack problem, GAMS, heuristic method, genetic algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17284 A New Heuristic Approach for Large Size Zero-One Multi Knapsack Problem Using Intercept Matrix
Authors: K. Krishna Veni, S. Raja Balachandar
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This paper presents a heuristic to solve large size 0-1 Multi constrained Knapsack problem (01MKP) which is NP-hard. Many researchers are used heuristic operator to identify the redundant constraints of Linear Programming Problem before applying the regular procedure to solve it. We use the intercept matrix to identify the zero valued variables of 01MKP which is known as redundant variables. In this heuristic, first the dominance property of the intercept matrix of constraints is exploited to reduce the search space to find the optimal or near optimal solutions of 01MKP, second, we improve the solution by using the pseudo-utility ratio based on surrogate constraint of 01MKP. This heuristic is tested for benchmark problems of sizes upto 2500, taken from literature and the results are compared with optimum solutions. Space and computational complexity of solving 01MKP using this approach are also presented. The encouraging results especially for relatively large size test problems indicate that this heuristic can successfully be used for finding good solutions for highly constrained NP-hard problems.
Keywords: 0-1 Multi constrained Knapsack problem, heuristic, computational complexity, NP-Hard problems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18433 Decision Support System for Suppliers
Authors: Babak Tashakori Bafghi, Laleh Tashakori, Reza Allahyari Soeini, Mohammad Mokhtari
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Supplier selection is a multi criteria decision-making process that comprises tangible and intangible factors. The majority of previous supplier selection techniques do not consider strategic perspective. Besides, uncertainty is one of the most important obstacles in supplier selection. For the first, time in this paper, the idea of the algorithm " Knapsack " is used to select suppliers Moreover, an attempt has to be made to take the advantage of a simple numerical method for solving model .This is an innovation to resolve any ambiguity in choosing suppliers. This model has been tried in the suppliers selected in a competitive environment and according to all desired standards of quality and quantity to show the efficiency of the model, an industry sample has been uses.
Keywords: Knapsack, linear programming, supplier select, supply chain management.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15952 Application of 0-1 Fuzzy Programming in Optimum Project Selection
Authors: S. Sadi-Nezhad, K. Khalili Damghani, N. Pilevari
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In this article, a mathematical programming model for choosing an optimum portfolio of investments is developed. The investments are considered as investment projects. The uncertainties of the real world are associated through fuzzy concepts for coefficients of the proposed model (i. e. initial investment costs, profits, resource requirement, and total available budget). Model has been coded by using LINGO 11.0 solver. The results of a full analysis of optimistic and pessimistic derivative models are promising for selecting an optimum portfolio of projects in presence of uncertainty.Keywords: Fuzzy Programming, Fuzzy Knapsack, FuzzyCapital Budgeting, Fuzzy Project Selection
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17171 Exploring Counting Methods for the Vertices of Certain Polyhedra with Uncertainties
Authors: Sammani Danwawu Abdullahi
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Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.Keywords: Approximation, counting with uncertainties, mathematical programming, optimization, vertex enumeration.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1348