Amin Samadi Ghoushchi; Caren Abrinia; Mohammad Kazem Besharati Givi
Abstract
Slab method of analysis has been used for solving metal forming problems for a long time. However it has been restricted to plane strain and axisymmetric problems due to limitations in its formulations. In this paper a new formulation has been proposed so that it could be applied to three dimensional ...
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Slab method of analysis has been used for solving metal forming problems for a long time. However it has been restricted to plane strain and axisymmetric problems due to limitations in its formulations. In this paper a new formulation has been proposed so that it could be applied to three dimensional problems in metal forming. A parametric slab has been considered in this analysis and the force balance on the slab was carried to obtain equilibrium equations in terms of these parameters. The parameters in fact are related to the geometry of the final extruded shape, the die and the material flow regime assumed in the formulation. In this way most of the limitations encountered in previous formulations were surpassed. The effect of reduction of area, frictional conditions and other process parameters on the extrusion pressure was investigated. The theoretical results obtained in this paper were compared with the results of finite element method and a good agreement was observed between them.
Farshad Kowsari; Seyyed Morteza Azimi
Abstract
In this paper the optimal control of boundary heat flux in a 2-D solid body with an arbitrary shape is performed in order to achieve the desired temperature distribution at a given time interval. The boundary of the body is subdivided into a number of components. On each component a time-dependent heat ...
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In this paper the optimal control of boundary heat flux in a 2-D solid body with an arbitrary shape is performed in order to achieve the desired temperature distribution at a given time interval. The boundary of the body is subdivided into a number of components. On each component a time-dependent heat flux is applied which is independent of the others. Since the thermophysical properties are temperature-dependent, the problem is treated as a nonlinear inverse heat conduction problem. Conjugate gradient method (CGM) along with adjoint problem is utilized in order to solve the inverse problem. Optimization process is employed for the heat flux imposed on each of the boundary component individually which was previously shown to be more efficient than optimizing the entire heat flux array simultaneously. Three versions of CGM; that is, the Fletcher-Reeves (FR), Polak-Ribiere (PR) and Powell-Beale are utilized for comparison. As a test case, heating of an Aluminum bar with a square cross section and temperature-dependent thermo-physical properties is considered. Results show that for large time-steps the Powell-Beale version with normalized search direction, and for small time-steps the Polak-Ribiere version are the most efficient method with the least error in the estimated temperature field. Moreover, for large time step size results show that addition of regularization term to the Error Function reduces the amplitude of oscillations in the estimated heat flux.
Seyyed Masoud Marandi; Mehdi Tajdari; Khosro Rahmani
Abstract
Foreign object damage (FOD) occurs when hard, millimeter-sized objects such as gravel or sand and even the pieces of the engine components are ingested into aircraft jet engines. Particles impacting blades produce small indentation craters which can become sites for fatigue crack initiation, severely ...
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Foreign object damage (FOD) occurs when hard, millimeter-sized objects such as gravel or sand and even the pieces of the engine components are ingested into aircraft jet engines. Particles impacting blades produce small indentation craters which can become sites for fatigue crack initiation, severely limiting the lifetime of the blade. In this study, the impact on the edge of a thin plate is investigated by using the finite element method. Then residual stresses are compared between the quasi-static indentation and fully dynamic impact for three critical locations where the residual hoop stresses are tensile. At the end, experimental stress analysis is performed for investigating the stress concentration factor at the crater base and comparing with data from the finite element method. The comparison shows that the finite element method result agrees well with experimental data at the crater base.
Abdorrasoul Mayyahi; Aghil Yousefikoma; Ali Rangin Kaman; Hesam Maleki
Abstract
An autonomous underwater vehicle (AUV) with less noise and vortices as well as efficient power consumption, is pursued in this research by inspiration of shark swimming. Design, hydrodynamic analysis, modeling, fabrication, navigation, and control of this novel AUV is the main goal of this research. ...
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An autonomous underwater vehicle (AUV) with less noise and vortices as well as efficient power consumption, is pursued in this research by inspiration of shark swimming. Design, hydrodynamic analysis, modeling, fabrication, navigation, and control of this novel AUV is the main goal of this research. Detailed explanation of the test and experiment with a brief overview on fabrication are provided. The transfer function of the system has been extracted from the experimental data. The transfer function is then employed for dynamic analysis and control system development. Zigler-Nickols method is used to predetermine the PID control coefficients. Consequently, small modifications have been done by trial and error. Trajectory control in a 10 cm off the wall and in a 20 cm band in a large swimming pool has been examined by a 3 DOF AUV.
Ali Naserian; Masoud Tahani
Abstract
The Levy-type analytical solution is employed for the problem of bending of cross-ply and antisymmetric angle-ply piezoelectric hybrid laminated plates with at least two simply supported opposite edges. The governing equations of equilibrium are derived in the framework of the first-order shear deformation ...
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The Levy-type analytical solution is employed for the problem of bending of cross-ply and antisymmetric angle-ply piezoelectric hybrid laminated plates with at least two simply supported opposite edges. The governing equations of equilibrium are derived in the framework of the first-order shear deformation plate theory. The equations are classified according to the crystallography type of piezoelectric layers and a comprehensive discussion on limitations of the method for the analysis of this kind of structures is performs. Finally, the governing equations of equilibrium are solved analytically with the aid of the state-space approach. We concluded that during the analysis of piezoelectric hybrid laminated plates with Levy-type method, simultaneous applying of all electrical forces and moments is not possible (depending on type of lay-up, crystallography of piezoelectric layers, and expansion of electrical potential, some of electrical forces and moments may not be considered). In order to study the accuracy and convergence rate of the proposed method, several numerical examples are examined. The numerical results are compared with those obtained by the Navier method and those presented in the other published articles. It is found that the present results have very good agreements with those obtained by other methods.
Vahid Norouzifard; Aghil Yousefikoma
Abstract
The built up layer thickness in secondary deformation zone is one of the important parameters in metal cutting process. The built up layer (BUL) is formed in second deformation zone near the tool-chip interface in the back of the chip. This parameter influences the tool life and machined surface quality. ...
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The built up layer thickness in secondary deformation zone is one of the important parameters in metal cutting process. The built up layer (BUL) is formed in second deformation zone near the tool-chip interface in the back of the chip. This parameter influences the tool life and machined surface quality. This BUL should not be confused with the built up edge (BUE). The deformation of the BUL in the secondary shear zone is a stable and continues process; leading to an uniform thickness of the BUL along the chip's back but the deformation of the BUE is an unstable process in front of the tool edge. Numerical simulation is a suitable method for determination of temperature, stress and strain distribution in metal cutting since it dose not suffer the analytical methods limitations and experimental methods cost. In this paper a new method is presented to calculate the built up layer thickness in secondary deformation zone using finite element simulation of orthogonal metal cutting process. There are two main concepts about chip separation mechanisms from work piece, i. e. crack propagation and pour deformation without crack. In the present work chip formation process is assumed as a pour plastic deformation, considering second chip separation mechanism. There is no separation criterion in the simulations based on pour deformation, but Adaptive remeshing is performed during simulation to avoid the difficulties associated with deformation-induced element distortion. An updated Lagrangian finite element model of two-dimensional orthogonal cutting process is developed. This model is meshed using 4-node plain strain elements. Thermo-mechanical coupled analysis, with adaptive remeshing is performed by LS-DYNA finite element code. Johnson-Cook material model is used for determination of the work piece material flow stress and the cutting tool is assumed as a rigid body. An updated coulomb friction law is used to describe friction condition in tool-chip interface. The temperature and equivalent strain distribution diagrams in cutting zone are shown at various cutting speeds. The built up layer thickness in various cutting speed are also calculated by equivalent strain gradient in second deformation zone. The numerical calculated tool average temperatures and the built up layer thicknesses in various cutting speeds are compared with the experimental data given in literature and good agreement is observed between them.
Bertrand Teguia Tabuguia
Abstract
Linear and homogeneous recurrence equations having polynomial coefficients are said to be holonomic. These equations are useful for proving and discovering combinatorial and hypergeometric identities. Given a field $\mathbb{K}$ of characteristic zero, $a_n$ is a hypergeometric term with respect to $\mathbb{K}$, ...
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Linear and homogeneous recurrence equations having polynomial coefficients are said to be holonomic. These equations are useful for proving and discovering combinatorial and hypergeometric identities. Given a field $\mathbb{K}$ of characteristic zero, $a_n$ is a hypergeometric term with respect to $\mathbb{K}$, if the ratio $a_{n+1}/a_n$ is a rational function over $\mathbb{K}$. Two algorithms by Marko Petkov\v{s}ek (1993) and Mark van Hoeij (1999) were proposed to compute hypergeometric term solutions of holonomic recurrence equations. The latter algorithm is more efficient and was implemented by its author in the Computer Algebra System (CAS) Maple through the command \texttt{LREtools[hypergeomsols]}. We describe
a variant of van Hoeij's algorithm that performs with the same efficiency without considering certain recommendations of the original version. We implemented our algorithm in the CASes Maxima and Maple. It also appears for some particular cases that our code finds results where \texttt{LREtools[hypergeomsols]} fails.
Our implementation is part of the \texttt{FPS} software which can be downloaded at \url{http://www.mathematik.uni-kassel.de/~bteguia/FPS_webpage/FPS.htm}. The command is \texttt{HypervanHoeij} for Maxima 5.44 and \texttt{rectohyperterm} for Maple 2021.
Abstract
Linear and homogeneous recurrence equations having polynomial coefficients are said to be holonomic. These equations are useful for proving and discovering combinatorial and hypergeometric identities. Given a field $\mathbb{K}$ of characteristic zero, $a_n$ is a hypergeometric term with respect to $\mathbb{K}$, ...
Read More
Linear and homogeneous recurrence equations having polynomial coefficients are said to be holonomic. These equations are useful for proving and discovering combinatorial and hypergeometric identities. Given a field $\mathbb{K}$ of characteristic zero, $a_n$ is a hypergeometric term with respect to $\mathbb{K}$, if the ratio $a_{n+1}/a_n$ is a rational function over $\mathbb{K}$. Two algorithms by Marko Petkov\v{s}ek (1993) and Mark van Hoeij (1999) were proposed to compute hypergeometric term solutions of holonomic recurrence equations. The latter algorithm is more efficient and was implemented by its author in the Computer Algebra System (CAS) Maple through the command \texttt{LREtools[hypergeomsols]}.
We describe a variant of van Hoeij's algorithm that performs with the same efficiency without considering certain recommendations of the original version. We implemented our algorithm in the CASes Maxima and Maple. It also appears for some particular cases that our code finds results where \texttt{LREtools[hypergeomsols]} fails.
Abstract
A popular research topic in Graph Convolutional Networks (GCNs) is to speedup the training time of the network. The main bottleneck in training GCN is the exponentially growing of computations. In Cluster-GCN based on this fact that each node and its neighbors are usually grouped ...
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A popular research topic in Graph Convolutional Networks (GCNs) is to speedup the training time of the network. The main bottleneck in training GCN is the exponentially growing of computations. In Cluster-GCN based on this fact that each node and its neighbors are usually grouped in the same cluster, considers the clustering structure of the graph, and expand each node's neighborhood within each cluster when training GCN.The main assumption of Cluster-GCN is the weak relation between clusters; which is not correct at all graphs. Here we extend their approach by overlapped clustering, instead of crisp clustering which is used in Cluster-GCN. This is achieved by allowing the marginal nodes to contribute to training in more than one cluster. The evaluation of the proposed method is investigated through the experiments on several benchmark datasets.The experimental results show that the proposed method is more efficient than Cluster-GCN, in average.
Abstract
\noindent Let $G = (V, E)$ be a $(p,q)$ graph.\\Define \begin{equation*}\rho =\begin{cases}\frac{p}{2} ,& \text{if $p$ is even}\\\frac{p-1}{2} ,& \text{if $p$ is odd}\\\end{cases}\end{equation*}\\ and $L = \{\pm1 ,\pm2, \pm3 , \cdots ,\pm\rho\}$ called the set of labels.\\\noindent ...
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\noindent Let $G = (V, E)$ be a $(p,q)$ graph.\\Define \begin{equation*}\rho =\begin{cases}\frac{p}{2} ,& \text{if $p$ is even}\\\frac{p-1}{2} ,& \text{if $p$ is odd}\\\end{cases}\end{equation*}\\ and $L = \{\pm1 ,\pm2, \pm3 , \cdots ,\pm\rho\}$ called the set of labels.\\\noindent Consider a mapping $f : V \longrightarrow L$ by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when $p$ is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge $uv$ of $G$ there exists a labeling $\left|f(u) - f(v)\right|$ such that $\left|\Delta_{f_1} - \Delta_{f_1^c}\right| \leq 1$, where $\Delta_{f_1}$ and $\Delta_{f_1^c}$ respectively denote the number of edges labeled with $1$ and number of edges not labeled with $1$. A graph $G$ for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate pair difference cordial labeling behavior of planar grid and mangolian tent graphs.
Abstract
In this paper, a type of fuzzy system is firstly investigated whereby the feasible region is defined by the fuzzy relational equalities and the geometric mean as fuzzy composition. Some related basic and theoretical properties are derived and the feasible region is completely determined. Moreover, a ...
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In this paper, a type of fuzzy system is firstly investigated whereby the feasible region is defined by the fuzzy relational equalities and the geometric mean as fuzzy composition. Some related basic and theoretical properties are derived and the feasible region is completely determined. Moreover, a comparison is made between this region and FRE defined by product t-norm. Finally, an example is described to illustrate the differences of these two FRE systems.
Abstract
We introduce a new invariant vulnerability parameter named “J-Tightness” or “J(G)” for graphs. As a stability measure, its properties along with comparisons to other parameters of a graph are proposed. We show how it is calculated for complete graphs and cycles. We show that J-Tightness ...
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We introduce a new invariant vulnerability parameter named “J-Tightness” or “J(G)” for graphs. As a stability measure, its properties along with comparisons to other parameters of a graph are proposed. We show how it is calculated for complete graphs and cycles. We show that J-Tightness better fits the properties of vulnerability measures and can be used with more confidence to assess the vulnerability of any classes of graphs.
Abstract
In this paper, a linear programming problem is investigated in which the feasible region is formed as a special type of fuzzy relational equalities (FRE). In this type of FRE, fuzzy composition is considered as the weighted power mean operator (WPM). Some theoretical properties of the feasible region ...
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In this paper, a linear programming problem is investigated in which the feasible region is formed as a special type of fuzzy relational equalities (FRE). In this type of FRE, fuzzy composition is considered as the weighted power mean operator (WPM). Some theoretical properties of the feasible region are derived and some necessary and sufficient conditions are also presented to determine the feasibility of the problem. Moreover, two procedures are proposed for simplifying the problem. Based on some structural properties of the problem, an algorithm is presented to find the optimal solutions and finally, an example is described to illustrate the algorithm.
Abstract
The statistical methods based on cumulative distribution function is a start point for many parametric or nonparametric statistical inferences. However, there are many practical problems that require dealing with observations/parameters that represent inherently imprecise. However, Hesamian ...
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The statistical methods based on cumulative distribution function is a start point for many parametric or nonparametric statistical inferences. However, there are many practical problems that require dealing with observations/parameters that represent inherently imprecise. However, Hesamian and Taheri (2013) was extended a concept of fuzzy cumulative distribution function. Applying a common notion of fuzzy random variables, they extended a vague concept of fuzzy cumulative distribution function. However, the main properties of the proposed method has not yet been considered in fuzzy environment. This paper aims to extend the classical properties of the fuzzy cumulative distribution function in fuzzy environment.
Abstract
In this paper, a linear programming problem is investigated in which the feasible region is formed as the intersection of fuzzy relational equalities and the harmonic mean operator is considered as fuzzy composition. Theoretical properties of the feasible region are derived. It is proved that the feasible ...
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In this paper, a linear programming problem is investigated in which the feasible region is formed as the intersection of fuzzy relational equalities and the harmonic mean operator is considered as fuzzy composition. Theoretical properties of the feasible region are derived. It is proved that the feasible solution set is comprised of one maximum solution and a finite number of minimal solutions. Furthermore, some necessary and sufficient conditions are additionally presented to determine the feasibility of the problem. Moreover, an algorithm is presented to find the optimal solutions of the problem and finally, an example is described to illustrate the algorithm.
Abstract
Let $S$ be a set of points in the plane that are in convex position. Let~$\cal O$ be a set of simple polygonal obstacles whose vertices are in $S$. The visibility graph $Vis(S,{\cal O})$ is the graph which is obtained from the complete graph of $S$ by removing all edges intersecting some obstacle ...
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Let $S$ be a set of points in the plane that are in convex position. Let~$\cal O$ be a set of simple polygonal obstacles whose vertices are in $S$. The visibility graph $Vis(S,{\cal O})$ is the graph which is obtained from the complete graph of $S$ by removing all edges intersecting some obstacle of $\cal O$. In this paper, we show that there is a plane $5.19$-spanner of the visibility graph $Vis(S,{\cal O})$ of degree at most 6. Moreover, we show that there is a plane $1.88$-spanner of the visibility graph $Vis(S,{\cal O})$. These improve the stretch factor and the maximum degree of the previous results by A. van Renssen and G. Wong ({\em Theoretical Computer Science, 2021}) in the context of points in convex position.
Abstract
Confirming the integrity of transmitted sensitive digital content is a significant issue due to the evolution in communication technologies and the accessibility of image processing tools. Watermarking has been a successful method of authentication and integrity verification recently. However, several ...
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Confirming the integrity of transmitted sensitive digital content is a significant issue due to the evolution in communication technologies and the accessibility of image processing tools. Watermarking has been a successful method of authentication and integrity verification recently. However, several significant problems remain such as confronting some serious attacks and recovery after higher tampering rates. We propose a hybrid method to enable an image to be recovered successfully after a range of attacks. A blind watermarking approach is adopted which includes fragile authentication but robust recovery references. This is performed by embedding verification code as part of the watermarked data along with key features of the original image into a location that is resistant to the attack. To combat different kinds of attacks, the areas of the image have been investigated to find which area is more likely to be affected in each type of specific attack.
Abstract
In this paper, a linear programming problem is investigated in which the feasible region is formed as a special type of fuzzy relational equalities (FRE). In this type of FRE, fuzzy composition is considered as the convex combination operator. It is proved that the feasible region of the problem can ...
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In this paper, a linear programming problem is investigated in which the feasible region is formed as a special type of fuzzy relational equalities (FRE). In this type of FRE, fuzzy composition is considered as the convex combination operator. It is proved that the feasible region of the problem can be written by one maximum solution and a finite number of minimal solutions. Some theoretical properties of the feasible region are derived and some necessary and sufficient conditions are also presented to determine the feasibility of the problem. Based on some structural properties of the problem, an algorithm is presented to find the optimal solutions and finally, an example is described to illustrate the algorithm.
Abstract
Cloud computing is a high-performance computing environment that can remotely provide services to customers using a pay-per-use model. The principal challenge in cloud computing is task scheduling, in which tasks must be effectively allocated to resources. The mapping of cloud resources to customer ...
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Cloud computing is a high-performance computing environment that can remotely provide services to customers using a pay-per-use model. The principal challenge in cloud computing is task scheduling, in which tasks must be effectively allocated to resources. The mapping of cloud resources to customer requests (tasks) is a popular Nondeterministic Polynomial-time (NP)-Complete problem. Although the task scheduling problem is a multi-objective optimization problem, most task scheduling algorithms cannot provide an effective trade-off between makespan, resource utilization, and energy consumption. Therefore, this study introduces a Priority-based task scheduling algorithm using Harris Hawks Optimizer (HHO) which is entitled as PHHO. The proposed algorithm first prioritizes tasks using a hierarchical process based on length and memory. Then, the HHO algorithm is used for optimally assigning tasks to resources. The PHHO algorithm aims to decrease makespan and energy consumption while increasing resource utilization and throughput. To evaluate the effectiveness of the PHHO algorithm, it is compared with other well-known meta-heuristic algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Whale Optimization Algorithm (WOA), Salp Swarm Algorithm (SSA), and Moth-Flame Optimization (MFO). The experimental results show the effectiveness of the PHHO algorithm compared to other algorithms in terms of makespan, resource utilization, throughput, and energy consumption.
Abstract
\noindent Selecting suitable journals for publishing manuscripts for publication is one of the most essential processes before publishing any manuscript. Finding the relevant journal is a key factor which proves one's work valuable to the entire society. The final output and the performance of one's ...
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\noindent Selecting suitable journals for publishing manuscripts for publication is one of the most essential processes before publishing any manuscript. Finding the relevant journal is a key factor which proves one's work valuable to the entire society. The final output and the performance of one's research is ultimately validated only if the paper is published in a right journal. One of the greatest mistakes that the authors make is submitting their manuscript in an unsuitable journal. The author should also consider all the six parameters such as Scope, Cite Score, Impact factor, Acceptance Rate, Time to first decision and Time to publication. Some authors only consider the acceptance rate and the time to first decision and publication as their main criteria. The author should consider all these parameters while publishing the paper. An algorithm named DEAR is used in the work which can consider all these parameters to find the right journal among the various alternatives. This DEAR method serves as a user-friendly method in selecting the best journal.
Abstract
An edge coloring of a digraph $D$ is called a $P_3$-rainbow edge coloring if the edges of any directed path of $D$ with length 2 are colored with different colors. It is proved that for a $P_3$-rainbow edge coloring of a digraph $D$, at least $\left\lceil{log_2{\chi(D)}} ...
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An edge coloring of a digraph $D$ is called a $P_3$-rainbow edge coloring if the edges of any directed path of $D$ with length 2 are colored with different colors. It is proved that for a $P_3$-rainbow edge coloring of a digraph $D$, at least $\left\lceil{log_2{\chi(D)}} \right\rceil$ colors are necessary and $ 2\left\lceil{log_2{\chi(D)}}\right\rceil\}$ colors are enough. One can determine in linear time if a digraph has a $P_3$-rainbow edge coloring with 1 or 2 colors. In this paper, it is proved that determining that a digraph has a $P_3$-rainbow edge coloring with 3 colors is an NP-complete problem even for planar digraphs. Moreover, it is shown that $\left\lceil{log_2{\chi(D)}}\right\rceil$ colors is necessary and sufficient for a $P_3$-rainbow edge coloringof a transitive orientation digraph $D$.
Abstract
On a graph with a negative cost cycle, the shortest path is undefined, but the number of edges of the shortest negative cost cycle could be computed. It is called Negative Cost Girth (NCG). The NCG problem is applied in many optimization issues such as scheduling and model verification. The existing ...
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On a graph with a negative cost cycle, the shortest path is undefined, but the number of edges of the shortest negative cost cycle could be computed. It is called Negative Cost Girth (NCG). The NCG problem is applied in many optimization issues such as scheduling and model verification. The existing polynomial algorithms suffer from high computation and memory consumption. In this paper, a powerful Map-Reduce framework implemented to find the NCG of a graph. The proposed algorithm runs in $O(\log_{}{k})$ parallel time over $O(n^3)$ on each Hadoop nodes, where $n, k$ are the size of the graph and the value of NCG, respectively. The Hadoop implementation of the algorithm shows that the total execution time is reduced by 50\% compared with polynomial algorithms, especially in large networks concerning increasing the numbers of Hadoop nodes. The result proves the efficiency of the approach for solving the NCG problem to process big data in a parallel and distributed way.
Saeid Alikhani; Davood Bakhshesh; Nasrin Jafari; Maryam Safazadeh
Abstract
Let $G=(V, E)$ be a simple graph. A dominating set of $G$ is a subset $D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$.
The cardinality of the smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. For $k \geq 1$, a $k$-fair ...
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Let $G=(V, E)$ be a simple graph. A dominating set of $G$ is a subset $D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$.
The cardinality of the smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. For $k \geq 1$, a $k$-fair dominating set ($kFD$-set) in $G$, is a dominating set $S$ such that $|N(v) \cap D|=k$ for every vertex $ v \in V\setminus D$. A fair dominating set in $G$ is a $kFD$-set for some integer $k\geq 1$. Let ${\cal D}_f(G,i)$ be the family of the
fair dominating sets of a graph $G$ with cardinality $i$ and let
$d_f(G,i)=|{\cal D}_f(G,i)|$.
The fair domination polynomial of $G$ is $D_f(G,x)=\sum_{ i=1}^{|V(G)|} d_f(G,i) x^{i}$. In this paper, after computation of the fair domination number of power of cycle, we count the number of the fair dominating sets of certain graphs such as cubic graphs of order~$10$, power of paths, and power of cycles. As a consequence, all cubic graphs of order $10$ and especially the Petersen graph are determined uniquely by their fair domination polynomial.
Amin Ghodousian; Mahdi Mollakazemiha; Noushin Karimian
Abstract
This paper proposes a novel population-based meta-heuristic optimization algorithm, called Perfectionism SearchAlgorithm (PSA), which is based on the psychological aspects of perfectionism. The PSA algorithm takes inspiration from one of the most popular model of perfectionism, which was proposed by ...
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This paper proposes a novel population-based meta-heuristic optimization algorithm, called Perfectionism SearchAlgorithm (PSA), which is based on the psychological aspects of perfectionism. The PSA algorithm takes inspiration from one of the most popular model of perfectionism, which was proposed by Hewitt and Flett. During each iteration of the PSA algorithm, new solutions are generated by mimicking different types and aspects of perfectionistic behavior. In order to have a complete perspective on the performance of PSA, the proposed algorithm is tested with various nonlinear optimization problems, through selection of 35 benchmark functions from the literature. The generated solutions for these problems, were also compared with 11 well-known meta-heuristics which had been applied to many complex andpractical engineering optimization problems. The obtained results confirm the high performance of the proposedalgorithm in comparison to the other well-known algorithms.
A. Ghodousian; Sara Falahatkar
Abstract
In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated whereby the feasible region is formed as the intersection of two inequality fuzzy systems and \textquotedblleft Fuzzy Max-Min\textquotedblright \ averaging operator is considered as ...
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In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated whereby the feasible region is formed as the intersection of two inequality fuzzy systems and \textquotedblleft Fuzzy Max-Min\textquotedblright \ averaging operator is considered as fuzzy composition. It is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. An algorithm is presented to solve the problem and an example is described to illustrate the algorithm.
