Search results for: Unbounded Knapsack Problem

Authors: D.Venkatesan, K.Kannan, S. Raja Balachandar

Abstract:

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

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Authors: Mhand Hifi, Hedi Mhalla

Abstract:

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.

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Authors: Mhand Hifi, Hedi Mhalla, Mustapha Michaphy

Abstract:

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

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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.

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Authors: Jindřiška Šedová, Miloš Šeda

Abstract:

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.

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Authors: Poonam Garg, Aditya Shastri, D.C. Agarwal

Abstract:

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.

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Authors: K. Krishna Veni, S. Raja Balachandar

Abstract:

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.

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Authors: Yunquan Ke, Chunfang Miao

Abstract:

In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.

Keywords: Inertial neural networks, unbounded delay, fixed-point theorem, Lyapunov function, periodic solutions, exponential stability.

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Authors: Babak Tashakori Bafghi, Laleh Tashakori, Reza Allahyari Soeini, Mohammad Mokhtari

Abstract:

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.

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Authors: Safae El Alaoui, Mohamed Ouzahra

Abstract:

In this work, we investigate the exponential stability of a linear system described by x˙ (t) = Ax(t) − ρBx(t). Here, A generates a semigroup S(t) on a Hilbert space, the operator B is supposed to be of Desch-Schappacher type, which makes the investigation more interesting in many applications. The case of Miyadera-Voigt perturbations is also considered. Sufficient conditions are formulated in terms of admissibility and observability inequalities and the approach is based on some energy estimates. Finally, the obtained results are applied to prove the uniform exponential stabilization of bilinear partial differential equations.

Keywords: Exponential stabilization, unbounded operator, Desch-Schappacher, Miyadera-Voigt operator.

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Authors: Min Kyung An

Abstract:

In this paper, we study the data collection problem in Wireless Sensor Networks (WSNs) adopting the two interference models: The graph model and the more realistic physical interference model known as Signal-to-Interference-Noise-Ratio (SINR). The main issue of the problem is to compute schedules with the minimum number of timeslots, that is, to compute the minimum latency schedules, such that data from every node can be collected without any collision or interference to a sink node. While existing works studied the problem with unit-sized and unbounded-sized message models, we investigate the problem with the bounded-sized message model, and introduce a constant factor approximation algorithm. To the best known of our knowledge, our result is the first result of the data collection problem with bounded-sized model in both interference models.

Keywords: Data collection, collision-free, interference-free, physical interference model, SINR, approximation, bounded-sized message model, wireless sensor networks, WSN.

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Authors: Rana Khalid Naeem, Waseem Ahmed Khan, Muhammad Akhtar, Asif Mansoor

Abstract:

The Navier Stokes Equations (NSE) for an incompressible fluid of variable viscosity in the presence of an unknown external force in Von-Mises system x,\ are transformed, and some new exact solutions for a class of flows characterized by equation y f x a\b for an arbitrary state equation are determined, where f x is a function, \ the stream function, a z 0 and b are the arbitrary constants. In three, out of four cases, the function f x is arbitrary, and the solutions are the solutions of the flow equations for all the flows characterized by the equationy f x a\b. Streamline patterns for some forms of f x in unbounded and bounded regions are given.

Keywords: Bounded and unbounded region, Exact solution, Navier Stokes equations, Streamline pattern, Variable viscosity, Von- Mises system

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Authors: Noura Boudiaf, Allaoua Chaoui

Abstract:

To analyze the behavior of Petri nets, the accessibility graph and Model Checking are widely used. However, if the analyzed Petri net is unbounded then the accessibility graph becomes infinite and Model Checking can not be used even for small Petri nets. ECATNets [2] are a category of algebraic Petri nets. The main feature of ECATNets is their sound and complete semantics based on rewriting logic [8] and its language Maude [9]. ECATNets analysis may be done by using techniques of accessibility analysis and Model Checking defined in Maude. But, these two techniques supported by Maude do not work also with infinite-states systems. As a category of Petri nets, ECATNets can be unbounded and so infinite systems. In order to know if we can apply accessibility analysis and Model Checking of Maude to an ECATNet, we propose in this paper an algorithm allowing the detection if the ECATNet is bounded or not. Moreover, we propose a rewriting logic based tool implementing this algorithm. We show that the development of this tool using the Maude system is facilitated thanks to the reflectivity of the rewriting logic. Indeed, the self-interpretation of this logic allows us both the modelling of an ECATNet and acting on it.

Keywords: ECATNets, Rewriting Logic, Maude, Finite-stateSystems, Infinite-state Systems, Boundness Property Checking.

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Authors: S. Sadi-Nezhad, K. Khalili Damghani, N. Pilevari

Abstract:

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

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Authors: Minghui Wang, Shanrui Hu

Abstract:

An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.

Keywords: doubly center matrix, electric network theory, iterative methods, least-square problem.

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Authors: Awadhesh Kumar Singh

Abstract:

Jayanti-s algorithm is one of the best known abortable mutual exclusion algorithms. This work is an attempt to overcome an already known limitation of the algorithm while preserving its all important properties and elegance. The limitation is that the token number used to assign process identification number to new incoming processes is unbounded. We have used a suitably adapted alternative data structure, in order to completely eliminate the use of token number, in the algorithm.

Keywords: Abortable, deterministic, local spin, mutual exclusion.

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Authors: Bilal Barakeh

Abstract:

In this paper we discuss the effect of unbounded particle interaction operator on particle growth and we study how this can address the choice of appropriate time steps of the numerical simulation. We provide also rigorous mathematical proofs showing that large particles become dominating with increasing time while small particles contribute negligibly. Second, we discuss the efficiency of the algorithm by performing numerical simulations tests and by comparing the simulated solutions with some known analytic solutions to the Smoluchowski equation.

Keywords: Stochastic processes, coagulation of particles, numerical scheme.

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Authors: Darwin Gouwanda, S. G. Ponnambalam

Abstract:

Set covering problem is a classical problem in computer science and complexity theory. It has many applications, such as airline crew scheduling problem, facilities location problem, vehicle routing, assignment problem, etc. In this paper, three different techniques are applied to solve set covering problem. Firstly, a mathematical model of set covering problem is introduced and solved by using optimization solver, LINGO. Secondly, the Genetic Algorithm Toolbox available in MATLAB is used to solve set covering problem. And lastly, an ant colony optimization method is programmed in MATLAB programming language. Results obtained from these methods are presented in tables. In order to assess the performance of the techniques used in this project, the benchmark problems available in open literature are used.

Keywords: Set covering problem, genetic algorithm, ant colony optimization, LINGO.

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Authors: Sammani Danwawu Abdullahi

Abstract:

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.

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Authors: Chao Wang, Ting-Zhu Huang Chen Jia

Abstract:

In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.

Keywords: Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Error estimation, P-matrix, M-matrix.

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Authors: Sukhveer Singh, Sandeep Singh

Abstract:

A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: Transportation problem, efficient solution, ranking function, fuzzy transportation problem.

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Authors: Kenza Aida Amara, Bachir Djebbar

Abstract:

We treat the two-dimensional bin packing problem which involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. This combinatorial problem is NP-hard. We propose a pretreatment for the oriented version of the problem that allows the valorization of the lost areas in the bins and the reduction of the size problem. A heuristic method based on the strategy first-fit adapted to this problem is presented. We present an approach of resolution by bee colony optimization. Computational results express a comparison of the number of bins used with and without pretreatment.

Keywords: Bee colony optimization, bin packing, heuristic algorithm, pretreatment.

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Authors: Tsuyoshi Okita, Tatsuya Niwa

Abstract:

For a given specific problem an efficient algorithm has been the matter of study. However, an alternative approach orthogonal to this approach comes out, which is called a reduction. In general for a given specific problem this reduction approach studies how to convert an original problem into subproblems. This paper proposes a formal modeling language to support this reduction approach. We show three examples from the wide area of learning problems. The benefit is a fast prototyping of algorithms for a given new problem.

Keywords: Formal language, statistical inference problem, reduction.

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Authors: M. Ahmad, M. Gourgand, C. Caux

Abstract:

The Resource-Constrained Project Scheduling Problem (RCPSP) is concerned with single-item or small batch production where limited resources have to be allocated to dependent activities over time. Over the past few decades, a lot of work has been made with the use of optimal solution procedures for this basic problem type and its extensions. Brucker and Knust[1] discuss, how timetabling problems can be modeled as a RCPSP. Authors discuss high school timetabling and university course timetabling problem as an example. We have formulated two mathematical formulations of course timetabling problem in a new way which are the prototype of single-mode RCPSP. Our focus is to show, how course timetabling problem can be transformed into RCPSP. We solve this transformation model with genetic algorithm.

Keywords: Course Timetabling, Integer programming, Combinatorial optimizations

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Authors: Nicolas Zufferey

Abstract:

The vehicle routing problem (VRP) is a famous combinatorial optimization problem. Because of its well-known difficulty, metaheuristics are the most appropriate methods to tackle large and realistic instances. The goal of this paper is to highlight the key ideas for designing VRP metaheuristics according to the following criteria: efficiency, speed, robustness, and ability to take advantage of the problem structure. Such elements can obviously be used to build solution methods for other combinatorial optimization problems, at least in the deterministic field.

Keywords: Vehicle routing problem, Metaheuristics, Combinatorial optimization.

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Authors: Mohammed Salem Alzahrani

Abstract:

In this paper the optimality of the solution of an existing real word assignment problem known as the seat assignment problem using Seat Assignment Method (SAM) is discussed. SAM is the newly driven method from three existing methods, Hungarian Method, Northwest Corner Method and Least Cost Method in a special way that produces the easiness & fairness among all methods that solve the seat assignment problem.

Keywords: Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM), A Real Word Assignment Problem.

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Authors: Zohreh O. Akbari

Abstract:

In this paper a deterministic polynomial-time algorithm is presented for the Clique problem. The case is considered as the problem of omitting the minimum number of vertices from the input graph so that none of the zeroes on the graph-s adjacency matrix (except the main diagonal entries) would remain on the adjacency matrix of the resulting subgraph. The existence of a deterministic polynomial-time algorithm for the Clique problem, as an NP-complete problem will prove the equality of P and NP complexity classes.

Keywords: Clique problem, Deterministic Polynomial-time Algorithm, Equality of P and NP Complexity Classes.

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Authors: Ben Mohamed Ahemed Mohamed, Yassine Adnan

Abstract:

The problem of bin-packing in two dimensions (2BP) consists in placing a given set of rectangular items in a minimum number of rectangular and identical containers, called bins. This article treats the case of objects with a free orientation of 90Ôùª. We propose an approach of resolution combining optimization by colony of ants (ACO) and the heuristic method IMA to resolve this NP-Hard problem.

Keywords: Ant colony algorithm, bin-packing problem, heuristics methods.

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Authors: Maricar G. Misola, Bryan B. Navarro

Abstract:

Facility Layout Problem (FLP) is one of the essential problems of several types of manufacturing and service sector. It is an optimization problem on which the main objective is to obtain the efficient locations, arrangement and order of the facilities. In the literature, there are numerous facility layout problem research presented and have used meta-heuristic approaches to achieve optimal facility layout design. This paper presented genetic algorithm to solve facility layout problem; to minimize total cost function. The performance of the proposed approach was verified and compared using problems in the literature.

Keywords: Facility Layout Problem, Genetic Algorithm, Material Handling Cost, Meta-heuristic Approach.

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Authors: Aldy Gunawan, Kien Ming Ng, Kim Leng Poh

Abstract:

This paper presents a hybrid algorithm for solving a timetabling problem, which is commonly encountered in many universities. The problem combines both teacher assignment and course scheduling problems simultaneously, and is presented as a mathematical programming model. However, this problem becomes intractable and it is unlikely that a proven optimal solution can be obtained by an integer programming approach, especially for large problem instances. A hybrid algorithm that combines an integer programming approach, a greedy heuristic and a modified simulated annealing algorithm collaboratively is proposed to solve the problem. Several randomly generated data sets of sizes comparable to that of an institution in Indonesia are solved using the proposed algorithm. Computational results indicate that the algorithm can overcome difficulties of large problem sizes encountered in previous related works.

Keywords: Timetabling problem, mathematical programming model, hybrid algorithm, simulated annealing.

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