Optimal components assignment problem subject to system reliability, total lead-time, and total cost
constraints is studied in this paper. The problem is formulated as fuzzy linear problem using fuzzy
membership functions. An approach based on genetic algorithm with fuzzy optimization to sole the
presented problem. The optimal solution found by the proposed approach is characterized by maximum
reliability, minimum total cost and minimum total lead-time. The proposed approach is tested on different
examples taken from the literature to illustrate its efficiency in comparison with other previous methods
A HYBRID CLUSTERING ALGORITHM FOR DATA MININGcscpconf
ย
Data clustering is a process of arranging similar data into groups. A clustering algorithm
partitions a data set into several groups such that the similarity within a group is better than
among groups. In this paper a hybrid clustering algorithm based on K-mean and K-harmonic
mean (KHM) is described. The proposed algorithm is tested on five different datasets. The research is focused on fast and accurate clustering. Its performance is compared with the traditional K-means & KHM algorithm. The result obtained from proposed hybrid algorithm is much better than the traditional K-mean & KHM algorithm
Min-based qualitative possibilistic networks are one of the effective tools for a compact representation of decision problems under uncertainty. The exact approaches for computing decision based on possibilistic networks are limited by the size of the possibility distributions.
Generally, these approaches are based on possibilistic propagation algorithms. An important step in the computation of the decision is the transformation of the DAG into a secondary structure, known as the junction trees. This transformation is known to be costly and represents a difficult problem. We propose in this paper a new approximate approach for the computation
of decision under uncertainty within possibilistic networks. The computing of the optimal optimistic decision no longer goes through the junction tree construction step. Instead, it is performed by calculating the degree of normalization in the moral graph resulting from the merging of the possibilistic network codifying knowledge of the agent and that codifying its preferences.
A PSO-Based Subtractive Data Clustering AlgorithmIJORCS
ย
There is a tremendous proliferation in the amount of information available on the largest shared information source, the World Wide Web. Fast and high-quality clustering algorithms play an important role in helping users to effectively navigate, summarize, and organize the information. Recent studies have shown that partitional clustering algorithms such as the k-means algorithm are the most popular algorithms for clustering large datasets. The major problem with partitional clustering algorithms is that they are sensitive to the selection of the initial partitions and are prone to premature converge to local optima. Subtractive clustering is a fast, one-pass algorithm for estimating the number of clusters and cluster centers for any given set of data. The cluster estimates can be used to initialize iterative optimization-based clustering methods and model identification methods. In this paper, we present a hybrid Particle Swarm Optimization, Subtractive + (PSO) clustering algorithm that performs fast clustering. For comparison purpose, we applied the Subtractive + (PSO) clustering algorithm, PSO, and the Subtractive clustering algorithms on three different datasets. The results illustrate that the Subtractive + (PSO) clustering algorithm can generate the most compact clustering results as compared to other algorithms.
USING LEARNING AUTOMATA AND GENETIC ALGORITHMS TO IMPROVE THE QUALITY OF SERV...IJCSEA Journal
ย
A hybrid learning automataโgenetic algorithm (HLGA) is proposed to solve QoS routing optimization problem of next generation networks. The algorithm complements the advantages of the learning Automato Algorithm(LA) and Genetic Algorithm(GA). It firstly uses the good global search capability of LA to generate initial population needed by GA, then it uses GA to improve the Quality of Service(QoS) and acquiring the optimization tree through new algorithms for crossover and mutation operators which are an NPโComplete problem. In the proposed algorithm, the connectivity matrix of edges is used for genotype representation. Some novel heuristics are also proposed for mutation, crossover, and creation of random individuals. We evaluate the performance and efficiency of the proposed HLGA-based algorithm in comparison with other existing heuristic and GA-based algorithms by the result of simulation. Simulation results demonstrate that this paper proposed algorithm not only has the fast calculating speed and high accuracy but also can improve the efficiency in Next Generation Networks QoS routing. The proposed algorithm has overcome all of the previous algorithms in the literature..
MIXED 0โ1 GOAL PROGRAMMING APPROACH TO INTERVAL-VALUED BILEVEL PROGRAMMING PR...cscpconf
ย
This paper presents how the mixed 0-1 programming in the framework of goal programming (GP) can be used to solve interval-valued fractional bilevel programming (IVFBLP) problems by employing genetic algorithm (GA) in a hierarchical decision making system. In the model formulation of the problem, a goal achievement function for minimizing the lower-bounds of the necessary regret intervals defined for the target intervals of achieving the goals and thereby arriving at a compromise decision is constructed by using both the aspects of โminsumโ and โminmaxโ approaches in GP. In the decision process, an GA scheme is employed for execution
of the problems at the two stages, target interval specification and optimal decision determination, for distribution of decision powers to the decision makers (DMs) in the order of hierarchy. A numerical example is provided to illustrate the potential use of the approach.
Improve the Performance of Clustering Using Combination of Multiple Clusterin...ijdmtaiir
ย
The ever-increasing availability of textual
documents has lead to a growing challenge for information
systems to effectively manage and retrieve the information
comprised in large collections of texts according to the userโs
information needs. There is no clustering method that can
adequately handle all sorts of cluster structures and properties
(e.g. shape, size, overlapping, and density). Combining
multiple clustering methods is an approach to overcome the
deficiency of single algorithms and further enhance their
performances. A disadvantage of the cluster ensemble is the
highly computational load of combing the clustering results
especially for large and high dimensional datasets. In this paper
we propose a multiclustering algorithm , it is a combination of
Cooperative Hard-Fuzzy Clustering model based on
intermediate cooperation between the hard k-means (KM) and
fuzzy c-means (FCM) to produce better intermediate clusters
and ant colony algorithm. This proposed method gives better
result than individual clusters.
A HYBRID CLUSTERING ALGORITHM FOR DATA MININGcscpconf
ย
Data clustering is a process of arranging similar data into groups. A clustering algorithm
partitions a data set into several groups such that the similarity within a group is better than
among groups. In this paper a hybrid clustering algorithm based on K-mean and K-harmonic
mean (KHM) is described. The proposed algorithm is tested on five different datasets. The research is focused on fast and accurate clustering. Its performance is compared with the traditional K-means & KHM algorithm. The result obtained from proposed hybrid algorithm is much better than the traditional K-mean & KHM algorithm
Min-based qualitative possibilistic networks are one of the effective tools for a compact representation of decision problems under uncertainty. The exact approaches for computing decision based on possibilistic networks are limited by the size of the possibility distributions.
Generally, these approaches are based on possibilistic propagation algorithms. An important step in the computation of the decision is the transformation of the DAG into a secondary structure, known as the junction trees. This transformation is known to be costly and represents a difficult problem. We propose in this paper a new approximate approach for the computation
of decision under uncertainty within possibilistic networks. The computing of the optimal optimistic decision no longer goes through the junction tree construction step. Instead, it is performed by calculating the degree of normalization in the moral graph resulting from the merging of the possibilistic network codifying knowledge of the agent and that codifying its preferences.
A PSO-Based Subtractive Data Clustering AlgorithmIJORCS
ย
There is a tremendous proliferation in the amount of information available on the largest shared information source, the World Wide Web. Fast and high-quality clustering algorithms play an important role in helping users to effectively navigate, summarize, and organize the information. Recent studies have shown that partitional clustering algorithms such as the k-means algorithm are the most popular algorithms for clustering large datasets. The major problem with partitional clustering algorithms is that they are sensitive to the selection of the initial partitions and are prone to premature converge to local optima. Subtractive clustering is a fast, one-pass algorithm for estimating the number of clusters and cluster centers for any given set of data. The cluster estimates can be used to initialize iterative optimization-based clustering methods and model identification methods. In this paper, we present a hybrid Particle Swarm Optimization, Subtractive + (PSO) clustering algorithm that performs fast clustering. For comparison purpose, we applied the Subtractive + (PSO) clustering algorithm, PSO, and the Subtractive clustering algorithms on three different datasets. The results illustrate that the Subtractive + (PSO) clustering algorithm can generate the most compact clustering results as compared to other algorithms.
USING LEARNING AUTOMATA AND GENETIC ALGORITHMS TO IMPROVE THE QUALITY OF SERV...IJCSEA Journal
ย
A hybrid learning automataโgenetic algorithm (HLGA) is proposed to solve QoS routing optimization problem of next generation networks. The algorithm complements the advantages of the learning Automato Algorithm(LA) and Genetic Algorithm(GA). It firstly uses the good global search capability of LA to generate initial population needed by GA, then it uses GA to improve the Quality of Service(QoS) and acquiring the optimization tree through new algorithms for crossover and mutation operators which are an NPโComplete problem. In the proposed algorithm, the connectivity matrix of edges is used for genotype representation. Some novel heuristics are also proposed for mutation, crossover, and creation of random individuals. We evaluate the performance and efficiency of the proposed HLGA-based algorithm in comparison with other existing heuristic and GA-based algorithms by the result of simulation. Simulation results demonstrate that this paper proposed algorithm not only has the fast calculating speed and high accuracy but also can improve the efficiency in Next Generation Networks QoS routing. The proposed algorithm has overcome all of the previous algorithms in the literature..
MIXED 0โ1 GOAL PROGRAMMING APPROACH TO INTERVAL-VALUED BILEVEL PROGRAMMING PR...cscpconf
ย
This paper presents how the mixed 0-1 programming in the framework of goal programming (GP) can be used to solve interval-valued fractional bilevel programming (IVFBLP) problems by employing genetic algorithm (GA) in a hierarchical decision making system. In the model formulation of the problem, a goal achievement function for minimizing the lower-bounds of the necessary regret intervals defined for the target intervals of achieving the goals and thereby arriving at a compromise decision is constructed by using both the aspects of โminsumโ and โminmaxโ approaches in GP. In the decision process, an GA scheme is employed for execution
of the problems at the two stages, target interval specification and optimal decision determination, for distribution of decision powers to the decision makers (DMs) in the order of hierarchy. A numerical example is provided to illustrate the potential use of the approach.
Improve the Performance of Clustering Using Combination of Multiple Clusterin...ijdmtaiir
ย
The ever-increasing availability of textual
documents has lead to a growing challenge for information
systems to effectively manage and retrieve the information
comprised in large collections of texts according to the userโs
information needs. There is no clustering method that can
adequately handle all sorts of cluster structures and properties
(e.g. shape, size, overlapping, and density). Combining
multiple clustering methods is an approach to overcome the
deficiency of single algorithms and further enhance their
performances. A disadvantage of the cluster ensemble is the
highly computational load of combing the clustering results
especially for large and high dimensional datasets. In this paper
we propose a multiclustering algorithm , it is a combination of
Cooperative Hard-Fuzzy Clustering model based on
intermediate cooperation between the hard k-means (KM) and
fuzzy c-means (FCM) to produce better intermediate clusters
and ant colony algorithm. This proposed method gives better
result than individual clusters.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Critical Paths Identification on Fuzzy Network Projectiosrjce
ย
In this paper, a new approach for identifying fuzzy critical path is presented, based on converting the
fuzzy network project into deterministic network project, by transforming the parameters set of the fuzzy
activities into the time probability density function PDF of each fuzzy time activity. A case study is considered as
a numerical tested problem to demonstrate our approach.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The International Journal of Engineering and Science (The IJES)theijes
ย
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
EXPERIMENTS ON HYPOTHESIS "FUZZY K-MEANS IS BETTER THAN K-MEANS FOR CLUSTERING"IJDKP
ย
Clustering is one of the data mining techniques that have been around to discover business intelligence by grouping objects into clusters using a similarity measure. Clustering is an unsupervised learning process that has many utilities in real time applications in the fields of marketing, biology, libraries, insurance, city-planning, earthquake studies and document clustering. Latent trends and relationships among data objects can be unearthed using clustering algorithms. Many clustering algorithms came into existence. However, the quality of clusters has to be given paramount importance. The quality objective is to achieve
highest similarity between objects of same cluster and lowest similarity between objects of different clusters. In this context, we studied two widely used clustering algorithms such as the K-Means and Fuzzy K-Means. K-Means is an exclusive clustering algorithm while the Fuzzy K-Means is an overlapping clustering algorithm. In this paper we prove the hypothesis โFuzzy K-Means is better than K-Means for Clusteringโ through both literature and empirical study. We built a prototype application to demonstrate the differences between the two clustering algorithms. The experiments are made on diabetes dataset
obtained from the UCI repository. The empirical results reveal that the performance of Fuzzy K-Means is better than that of K-means in terms of quality or accuracy of clusters. Thus, our empirical study proved the hypothesis โFuzzy K-Means is better than K-Means for Clusteringโ.
Memory Polynomial Based Adaptive Digital PredistorterIJERA Editor
ย
Digital predistortion (DPD) is a baseband signal processing technique that corrects for impairments in RF
power amplifiers (PAs). These impairments cause out-of-band emissions or spectral regrowth and in-band
distortion, which correlate with an increased bit error rate (BER). Wideband signals with a high peak-to-average
ratio, are more susceptible to these unwanted effects. So to reduce these impairments, this paper proposes the
modeling of the digital predistortion for the power amplifier using GSA algorithm.
Robust Watermarking through Dual Band IWT and Chinese Remainder TheoremjournalBEEI
ย
CRT was a widely used algorithm in the development of watermarking methods. The algorithm produced good image quality but it had low robustness against compression and filtering. This paper proposed a new watermarking scheme through dual band IWT to improve the robustness and preserving the image quality. The high frequency sub band was used to index the embedding location on the low frequency sub band. In robustness test, the CRT method resulted average NC value of 0.7129, 0.4846, and 0.6768 while the proposed method had higher NC value of 0.7902, 0.7473, and 0.8163 in corresponding Gaussian filter, JPEG, and JPEG2000 compression test. Meanwhile the both CRT and proposed method had similar average SSIM value of 0.9979 and 0.9960 respectively in term of image quality. The result showed that the proposed method was able to improve the robustness and maintaining the image quality.
A HYBRID K-HARMONIC MEANS WITH ABCCLUSTERING ALGORITHM USING AN OPTIMAL K VAL...IJCI JOURNAL
ย
Large quantities of data are emerging every year and an accurate clustering algorithm is needed to derive
information from these data. K-means clustering algorithm is popular and simple, but has many limitations
like its sensitivity to initialization, provides local optimum solutions. K-harmonic means clustering is an
improved variant of K-means which is insensitive to the initialization of centroids, but still in some cases it
ends up with local optimum solutions. Clustering using Artificial Bee Colony (ABC) algorithm always gives
global optimum solutions. In this paper a new hybrid clustering algorithm (KHM-ABC) is presented by
combining both K-harmonic means and ABC algorithm to perform accurate clustering. Experimental
results indicate that the performance of the proposed algorithm is superior to the available algorithms in
terms of the quality of clusters.
FAST ALGORITHMS FOR UNSUPERVISED LEARNING IN LARGE DATA SETScsandit
ย
The ability to mine and extract useful information automatically, from large datasets, is a
common concern for organizations (having large datasets), over the last few decades. Over the
internet, data is vastly increasing gradually and consequently the capacity to collect and store
very large data is significantly increasing.
Existing clustering algorithms are not always efficient and accurate in solving clustering
problems for large datasets.
However, the development of accurate and fast data classification algorithms for very large
scale datasets is still a challenge. In this paper, various algorithms and techniques especially,
approach using non-smooth optimization formulation of the clustering problem, are proposed
for solving the minimum sum-of-squares clustering problems in very large datasets. This
research also develops accurate and real time L2-DC algorithm based with the incremental
approach to solve the minimum
A New Method to Solving Generalized Fuzzy Transportation Problem-Harmonic Mea...AI Publications
ย
Transportation Problem is one of the models in the Linear Programming problem. The objective of this paper is to transport the item from the origin to the destination such that the transport cost should be minimized, and we should minimize the time of transportation. To achieve this, a new approach using harmonic mean method is proposed in this paper. In this proposed method transportation costs are represented by generalized trapezoidal fuzzy numbers. Further comparative studies of the new technique with other existing algorithms are established by means of sample problems.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Proposing a scheduling algorithm to balance the time and cost using a genetic...Editor IJCATR
ย
Grid computing is a hardware and software infrastructure and provides affordable, sustainable, and reliable access. Its aim is
to create a supercomputer using free resources. One of the challenges to the Grid computing is scheduling problem which is regarded
as a tough issue. Since scheduling problem is a non-deterministic issue in the Grid, deterministic algorithms cannot be used to improve
scheduling.
In this paper, a combination of genetic algorithms and binary gravitational attraction is used for scheduling problem solving, where the
reduction in the duty performance timing and cost-effective use of simultaneous resources are investigated. In this case, the user
determines the execution time parameter and cost-effective use of resources. In this algorithm, a new approach that has led to a
balanced load of resources is used in the selection of resources. Experimental results reveals that our proposed algorithm in terms of
cost-time and selection of the best resource has reached better results than other algorithm.
Fault-Tolerance Aware Multi Objective Scheduling Algorithm for Task Schedulin...csandit
ย
Computational Grid (CG) creates a large heterogeneous and distributed paradigm to manage and execute the applications which are computationally intensive. In grid scheduling tasks are assigned to the proper processors in the grid system to for its execution by considering the execution policy and the optimization objectives. In this paper, makespan and the faulttolerance of the computational nodes of the grid which are the two important parameters for the task execution, are considered and tried to optimize it. As the grid scheduling is considered to be NP-Hard, so a meta-heuristics evolutionary based techniques are often used to find a solution for this. We have proposed a NSGA II for this purpose. The performance estimation ofthe proposed Fault tolerance Aware NSGA II (FTNSGA II) has been done by writing program in Matlab. The simulation results evaluates the performance of the all proposed algorithm and the results of proposed model is compared with existing model Min-Min and Max-Min algorithm which proves effectiveness of the model.
Hybrid method for achieving Pareto front on economic emission dispatch IJECEIAES
ย
In this paper hybrid method, Modified Nondominated Sorted Genetic Algorithm (MNSGA-II) and Modified Population Variant Differential Evolution(MPVDE) have been placed in effect in achieving the best optimal solution of Multiobjective economic emission load dispatch optimization problem. In this technique latter, one is used to enforce the assigned percent of the population and the remaining with the former one. To overcome the premature convergence in an optimization problem diversity preserving operator is employed, from the tradeoff curve the best optimal solution is predicted using fuzzy set theory. This methodology validated on IEEE 30 bus test system with six generators, IEEE 118 bus test system with fourteen generators and with a forty generators test system. The solutions are dissimilitude with the existing metaheuristic methods like Strength Pareto Evolutionary Algorithm-II, Multiobjective differential evolution, Multiobjective Particle Swarm optimization, Fuzzy clustering particle swarm optimization, Nondominated sorting genetic algorithm-II.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Critical Paths Identification on Fuzzy Network Projectiosrjce
ย
In this paper, a new approach for identifying fuzzy critical path is presented, based on converting the
fuzzy network project into deterministic network project, by transforming the parameters set of the fuzzy
activities into the time probability density function PDF of each fuzzy time activity. A case study is considered as
a numerical tested problem to demonstrate our approach.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The International Journal of Engineering and Science (The IJES)theijes
ย
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
EXPERIMENTS ON HYPOTHESIS "FUZZY K-MEANS IS BETTER THAN K-MEANS FOR CLUSTERING"IJDKP
ย
Clustering is one of the data mining techniques that have been around to discover business intelligence by grouping objects into clusters using a similarity measure. Clustering is an unsupervised learning process that has many utilities in real time applications in the fields of marketing, biology, libraries, insurance, city-planning, earthquake studies and document clustering. Latent trends and relationships among data objects can be unearthed using clustering algorithms. Many clustering algorithms came into existence. However, the quality of clusters has to be given paramount importance. The quality objective is to achieve
highest similarity between objects of same cluster and lowest similarity between objects of different clusters. In this context, we studied two widely used clustering algorithms such as the K-Means and Fuzzy K-Means. K-Means is an exclusive clustering algorithm while the Fuzzy K-Means is an overlapping clustering algorithm. In this paper we prove the hypothesis โFuzzy K-Means is better than K-Means for Clusteringโ through both literature and empirical study. We built a prototype application to demonstrate the differences between the two clustering algorithms. The experiments are made on diabetes dataset
obtained from the UCI repository. The empirical results reveal that the performance of Fuzzy K-Means is better than that of K-means in terms of quality or accuracy of clusters. Thus, our empirical study proved the hypothesis โFuzzy K-Means is better than K-Means for Clusteringโ.
Memory Polynomial Based Adaptive Digital PredistorterIJERA Editor
ย
Digital predistortion (DPD) is a baseband signal processing technique that corrects for impairments in RF
power amplifiers (PAs). These impairments cause out-of-band emissions or spectral regrowth and in-band
distortion, which correlate with an increased bit error rate (BER). Wideband signals with a high peak-to-average
ratio, are more susceptible to these unwanted effects. So to reduce these impairments, this paper proposes the
modeling of the digital predistortion for the power amplifier using GSA algorithm.
Robust Watermarking through Dual Band IWT and Chinese Remainder TheoremjournalBEEI
ย
CRT was a widely used algorithm in the development of watermarking methods. The algorithm produced good image quality but it had low robustness against compression and filtering. This paper proposed a new watermarking scheme through dual band IWT to improve the robustness and preserving the image quality. The high frequency sub band was used to index the embedding location on the low frequency sub band. In robustness test, the CRT method resulted average NC value of 0.7129, 0.4846, and 0.6768 while the proposed method had higher NC value of 0.7902, 0.7473, and 0.8163 in corresponding Gaussian filter, JPEG, and JPEG2000 compression test. Meanwhile the both CRT and proposed method had similar average SSIM value of 0.9979 and 0.9960 respectively in term of image quality. The result showed that the proposed method was able to improve the robustness and maintaining the image quality.
A HYBRID K-HARMONIC MEANS WITH ABCCLUSTERING ALGORITHM USING AN OPTIMAL K VAL...IJCI JOURNAL
ย
Large quantities of data are emerging every year and an accurate clustering algorithm is needed to derive
information from these data. K-means clustering algorithm is popular and simple, but has many limitations
like its sensitivity to initialization, provides local optimum solutions. K-harmonic means clustering is an
improved variant of K-means which is insensitive to the initialization of centroids, but still in some cases it
ends up with local optimum solutions. Clustering using Artificial Bee Colony (ABC) algorithm always gives
global optimum solutions. In this paper a new hybrid clustering algorithm (KHM-ABC) is presented by
combining both K-harmonic means and ABC algorithm to perform accurate clustering. Experimental
results indicate that the performance of the proposed algorithm is superior to the available algorithms in
terms of the quality of clusters.
FAST ALGORITHMS FOR UNSUPERVISED LEARNING IN LARGE DATA SETScsandit
ย
The ability to mine and extract useful information automatically, from large datasets, is a
common concern for organizations (having large datasets), over the last few decades. Over the
internet, data is vastly increasing gradually and consequently the capacity to collect and store
very large data is significantly increasing.
Existing clustering algorithms are not always efficient and accurate in solving clustering
problems for large datasets.
However, the development of accurate and fast data classification algorithms for very large
scale datasets is still a challenge. In this paper, various algorithms and techniques especially,
approach using non-smooth optimization formulation of the clustering problem, are proposed
for solving the minimum sum-of-squares clustering problems in very large datasets. This
research also develops accurate and real time L2-DC algorithm based with the incremental
approach to solve the minimum
A New Method to Solving Generalized Fuzzy Transportation Problem-Harmonic Mea...AI Publications
ย
Transportation Problem is one of the models in the Linear Programming problem. The objective of this paper is to transport the item from the origin to the destination such that the transport cost should be minimized, and we should minimize the time of transportation. To achieve this, a new approach using harmonic mean method is proposed in this paper. In this proposed method transportation costs are represented by generalized trapezoidal fuzzy numbers. Further comparative studies of the new technique with other existing algorithms are established by means of sample problems.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Proposing a scheduling algorithm to balance the time and cost using a genetic...Editor IJCATR
ย
Grid computing is a hardware and software infrastructure and provides affordable, sustainable, and reliable access. Its aim is
to create a supercomputer using free resources. One of the challenges to the Grid computing is scheduling problem which is regarded
as a tough issue. Since scheduling problem is a non-deterministic issue in the Grid, deterministic algorithms cannot be used to improve
scheduling.
In this paper, a combination of genetic algorithms and binary gravitational attraction is used for scheduling problem solving, where the
reduction in the duty performance timing and cost-effective use of simultaneous resources are investigated. In this case, the user
determines the execution time parameter and cost-effective use of resources. In this algorithm, a new approach that has led to a
balanced load of resources is used in the selection of resources. Experimental results reveals that our proposed algorithm in terms of
cost-time and selection of the best resource has reached better results than other algorithm.
Fault-Tolerance Aware Multi Objective Scheduling Algorithm for Task Schedulin...csandit
ย
Computational Grid (CG) creates a large heterogeneous and distributed paradigm to manage and execute the applications which are computationally intensive. In grid scheduling tasks are assigned to the proper processors in the grid system to for its execution by considering the execution policy and the optimization objectives. In this paper, makespan and the faulttolerance of the computational nodes of the grid which are the two important parameters for the task execution, are considered and tried to optimize it. As the grid scheduling is considered to be NP-Hard, so a meta-heuristics evolutionary based techniques are often used to find a solution for this. We have proposed a NSGA II for this purpose. The performance estimation ofthe proposed Fault tolerance Aware NSGA II (FTNSGA II) has been done by writing program in Matlab. The simulation results evaluates the performance of the all proposed algorithm and the results of proposed model is compared with existing model Min-Min and Max-Min algorithm which proves effectiveness of the model.
Hybrid method for achieving Pareto front on economic emission dispatch IJECEIAES
ย
In this paper hybrid method, Modified Nondominated Sorted Genetic Algorithm (MNSGA-II) and Modified Population Variant Differential Evolution(MPVDE) have been placed in effect in achieving the best optimal solution of Multiobjective economic emission load dispatch optimization problem. In this technique latter, one is used to enforce the assigned percent of the population and the remaining with the former one. To overcome the premature convergence in an optimization problem diversity preserving operator is employed, from the tradeoff curve the best optimal solution is predicted using fuzzy set theory. This methodology validated on IEEE 30 bus test system with six generators, IEEE 118 bus test system with fourteen generators and with a forty generators test system. The solutions are dissimilitude with the existing metaheuristic methods like Strength Pareto Evolutionary Algorithm-II, Multiobjective differential evolution, Multiobjective Particle Swarm optimization, Fuzzy clustering particle swarm optimization, Nondominated sorting genetic algorithm-II.
This paper discusses the possible applications of particle swarm optimization (PSO) in the Power system. One of the problems in Power System is Economic Load dispatch (ED). The discussion is carried out in view of the saving money, computational speed โ up and expandability that can be achieved by using PSO method. The general approach of the method of this paper is that of Dynamic Programming Method coupled with PSO method. The feasibility of the proposed method is demonstrated, and it is compared with the lambda iterative method in terms of the solution quality and computation efficiency. The experimental results show that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.
AN IMPROVED METHOD FOR IDENTIFYING WELL-TEST INTERPRETATION MODEL BASED ON AG...IAEME Publication
ย
This paper presents an approach based on applying an aggregated predictor formed by multiple versions of a multilayer neural network with a back-propagation optimization algorithm for helping the engineer to get a list of the most appropriate well-test interpretation models for a given set of pressure/ production data. The proposed method consists of three stages: (1) data decorrelation through principal component analysis to reduce the covariance between the variables and the dimension of the input layer in the artificial neural network, (2) bootstrap replicates of the learning set where the data is repeatedly sampled with a random split of the data into train sets and using these as new learning sets, and (3) automatic reservoir model identification through aggregated predictor formed by a plurality vote when predicting a new class. This method is described in detail to ensure successful replication of results. The required training and test dataset were generated by using analytical solution models. In our case, there were used 600 samples: 300 for training, 100 for cross-validation, and 200 for testing. Different network structures were tested during this study to arrive at optimum network design. We notice that the single net methodology always brings about confusion in selecting the correct model even though the training results for the constructed networks are close to 1. We notice also that the principal component analysis is an effective strategy in reducing the number of input features, simplifying the network structure, and lowering the training time of the ANN. The results obtained show that the proposed model provides better performance when predicting new data with a coefficient of correlation approximately equal to 95% Compared to a previous approach 80%, the combination of the PCA and ANN is more stable and determine the more accurate results with lesser computational complexity than was feasible previously. Clearly, the aggregated predictor is more stable and shows less bad classes compared to the previous approach.
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SOLVING OPTIMAL COMPONENTS ASSIGNMENT PROBLEM FOR A MULTISTATE NETWORK USING FUZZY OPTIMIZATION
1. International Journal of Mobile Network Communications & Telematics ( IJMNCT), Vol.9, No.3, June 2019
DOI : 10.5121/ijmnct.2019.9301 1
SOLVING OPTIMAL COMPONENTS ASSIGNMENT
PROBLEM FOR A MULTISTATE NETWORK USING
FUZZY OPTIMIZATION
H. Hamdy1
, M. R. Hassan1
, M. Eid1
and M. Khalifa2
1
Computer Science Branch, Mathematics Department, Faculty of Science, Aswan
University, Egypt.
2
Mathematics Department, Faculty of Science, South Valley University,Qena, Egypt.
ABSTRACT
Optimal components assignment problem subject to system reliability, total lead-time, and total cost
constraints is studied in this paper. The problem is formulated as fuzzy linear problem using fuzzy
membership functions. An approach based on genetic algorithm with fuzzy optimization to sole the
presented problem. The optimal solution found by the proposed approach is characterized by maximum
reliability, minimum total cost and minimum total lead-time. The proposed approach is tested on different
examples taken from the literature to illustrate its efficiency in comparison with other previous methods.
KEYWORDS
Components Assignment Problem, Stochastic-Flow Networks, Network Reliability, Fuzzy Multi-Objective
Linear Programming, Genetic Algorithms.
1. INTRODUCTION
Network reliability of stochastic-flow network (SFN) is defined as the probability that a specified
amount of flow can be transmitted successfully from source to destination through SFN [1].
Components assignment problem (CAP) is one important problem in the field of system
reliability analysis, finding an optimal component assignment is significant to maximize the
system reliability and improve the system performance [2]. Many researchers studied CAP for a
SFN to maximize the network reliability under different constraints, [3], proposed an algorithm to
generate all minimal system states fulfilling the demand, time and budget constraints, then the
system reliability is evaluated in terms of such system states. The authors in [4] focused on
finding the optimal carrier selection based on network reliability criterion under a budget
constraint, an optimization algorithm integrating a genetic algorithm, minimal paths and the
recursive sum of disjoint products is proposed to solve such a problem. Multi-state CAP was
discussed in [5] to maximize the network reliability under an assignment budget constraint, in
which each component has an assignment cost, they suggested an optimization method based on
genetic algorithm. In [6] they studied the optimal network line assignment with maximal network
reliability and minimal total coast, they presented an approach based on Non-dominated Sorting
Genetic Algorithm II (NSGA-II) and Technique for Order Preference by Similarity to Ideal
Solution (TOPSIS) to solve multi-objective optimization for stochastic computer networks. In
order to solve multi-objective CAP, [7], proposed two-stage approach to solving the multi-
2. International Journal of Mobile Network Communications & Telematics ( IJMNCT), Vol.9, No.3, June 2019
2
objective CAP subject to reliability and assignment cost for SFN. In [8] he proposed an approach
to get the exact optimal double-resource assignment for the robust design problem in multistate
computer networks, a minimum capacity assignment for each link and node is searched to keep
the network working even both links and nodes are subject to failures.
In the case of CAP for stochastic-flow network under lead-time constraint,[9], discussed this and
he suggested Genetic Algorithm(GA) to search the optimal components for a minimum total lead-
time that maximizes the system reliability, such that the total lead-time cannot exceed a specified
amount. In addition, [10] studied multi-objective CAP subject to lead-time constraint they
proposed GA based on the NSGA-II to search the optimal components that maximize the
reliability. In the case of each component has both an assignment cost and lead -time constraints,
[11], the CAP for SFN was studied and solved by a proposed approach based on a random
weighted GA. The objective of proposed approach was to maximize the network reliability,
minimize total leadโtime and minimize cost.
The concept of decision making in the fuzzy environments is presented by [12]. In [13] illustrated
that without increasing the computational effort, Fuzzy Linear Programming( FLP) problems can
be solved. In addition, [14] presented general look at core ideas that make up the burgeoning
body of fuzzy mathematical programming emphasizing the methodological view, and so [15]
aggregated the concept of multi-objective programming application and using a membership
function of the linear expression to represent and integrate each fuzzy objective, he let the
solution is converted to another form of linear programming solution by using the way solve the
application problem of fuzzy theory. Where in[16] they presented an inexact approach and
recommended genetic algorithm to get a family of inexact solutions with acceptable membership
degree to solve objective and resource type of FLP problems. A type of model of fuzzy quadratic
programming problems is proposed in [17], according to different types of fuzzy resource
constraints and fuzzy objective in actual production problems, they described the fuzzy objective
and resource constraints with different type of membership functions. Furthermore, FLP problem
formulations and membership functions were discussed by many researchers, [18 โ 31] to apply
FLP to various problems and improve the obtained solutions.
Recently, FLP is used to solve various problems [32-37]. By using a fuzzy multi-objective GA,
[33] succeed in obtaining high quality solutions to solve the multi-objective decision problem.
While in [34] they applied a fuzzy multi-objective linear programming model to combine the
existed components with a new character by using an optimization method of the highest match.
In [35] a new ranking methods of Subinterval average and subinterval addition is presented in
order to solve FLP problem. A fuzzy linear programming model for a problem of food industry is
presented and solved by [36] .The FLP is applied to the tri generation system (power generation,
heat generation, and the generation of cooling effect), [37], to find the optimal design to the
proposed system.
The aim of this paper is to solve the CAP for an SFN under system reliability, total lead time and
total cost constraints. An approach based on fuzzy linear programming is presented to solve the
CAP.
The paper is organized as follows: Section 2 illustrates needed notations. Section 3 presents the
problem formulation. Next, section 4 illustrates the fuzzy linear formulation to the presented
problem. Section 5 explains the proposed multi-objective GA based on fuzzy linear
3. International Journal of Mobile Network Communications & Telematics ( IJMNCT), Vol.9, No.3, June 2019
3
programming. To demonstrate the usability of the proposed approach, several examples included
in Section 6. Section 7 presents comparison and discussion, the last section shows conclusion.
2. NOTATIONS
๐ No. of nodes.
๐ฃ {๐ ๐|1 โค ๐ โค ๐ฃ} : No. of arcs.
๐๐๐ Minimal paths.
๐๐ Number of minimal paths.
๐๐๐ Minimal path no. ๐; ๐ = 1, 2, โฆ , ๐๐.
๐ฃ๐ The number of available components.
๐ฃ๐ ๐ The components number ๐, ๐ = 1,2, โฆ , ๐ฃ๐.
๐(๐ฃ๐ ๐) Lead time of components๐ฃ๐ ๐.
๐(๐ฃ๐ ๐) Cost of components๐ฃ๐ ๐.
๐ฟ๐ The lead time of๐๐๐.
๐ ๐,๐ The system reliability to the demand d under time limit ๐, for simplicity using ๐ .
๐ Capacity vector defined as ๐ณ = (๐ฅ1, ๐ฅ2, โฆ . . , ๐ฅ ๐,).
๐ (๐1, ๐2, โฆ , ๐ ๐ฃ) The components assignment in which ๐ฃ๐ ๐ is assigned to the arc ๐ ๐ if
๐ ๐ = ๐.
๐๐( ๐) Total lead time.
๐ถ( ๐) Total cost.
๐ฎ Population size.
โ Maximum number of generations.
๐๐ Generation number.
๐ ๐ GA mutation rate.
๐๐ GA crossover rate.
๐๐
๐๐๐
Minimum acceptable feasible values of๐๐( ๐).
๐๐
0
Maximum acceptable feasible values of๐๐( ๐).
๐ ๐๐๐ Maximum acceptable feasible values of ๐ .
๐ 0 Minimum acceptable feasible values of ๐ .
๐ถ๐๐๐ Minimum acceptable feasible values of ๐ถ( ๐).
๐ถ0 Maximum acceptable feasible values of ๐ถ( ๐).
๐(R) Fuzzy objective membership functions of ๐ .
๐( ๐๐) Fuzzy objective membership functions of ๐๐( ๐).
๐( ๐ถ) Fuzzy objective membership functions of๐ถ( ๐).
ฮฑ The acceptable membership degree level.
3. PROBLEM FORMULATION
The mathematical programming formulation of the multi-objective optimization problem to
maximize system reliability of a flow network, minimize the total lead-time and cost illustrating
as follow:
Maximize ๐ ๐,๐( ๐) (1)
Minimize ๐๐( ๐) (2)
Minimize๐ถ( ๐) (3)
4. International Journal of Mobile Network Communications & Telematics ( IJMNCT), Vol.9, No.3, June 2019
4
Subject to:
๐ ๐ = ๐, ๐ โ {1,2, โฆ , ๐ฃ๐}for e = 1,2, โฆ , v. (4)
๐ ๐ โ ๐โfor ๐ โ โ (5)
๐ฟ๐ โค ๐, j = 1,2, โฆ , np (6)
Where:
๐ฟ๐ = โ ๐(๐ ๐
๐
๐=1 ) |
๐ ๐ โ ๐๐๐
(7)
๐๐( ๐) = โ ๐(๐ ๐
๐
๐=1 ) (8)
๐ถ( ๐) = โ ๐ถ(๐ ๐
๐
๐=1 ) (9)
And, constraints (4) and (5) emphasize that each link should be given one component and that
each component can be assigned to at most one link. All feasible component assignments are
generated using constraints (4) and (5). Constraint (6) assures that the lead-time of the path ๐๐๐
(๐ฟ๐) is less than the time limit (๐), [9].
4. FUZZY LINEAR FORMULATION
To transform the mathematical formulation defined in section 3 into fuzzy linear formulation we
will define that๐ ๐๐๐ ,๐๐
๐๐๐
and ๐ถ๐๐๐are the objective values with the consideration that
๐ โค ๐ ๐๐๐ ,๐๐( ๐) โฅ ๐๐
๐๐๐
, ๐ถ( ๐) โฅ ๐ถ๐๐๐.
๐( ๐ ) =
{
1 if ๐ > ๐ ๐๐๐
1 โ
๐ ๐๐๐ โ ๐
๐ซ0
๐๐ ๐ ๐๐๐ โ ๐ซ0 โค ๐ โค ๐ ๐๐๐
0 if ๐ < ๐ 0
(10)
๐( ๐๐) =
{
1 ๐๐ ๐๐( ๐) < ๐๐
๐๐๐
1 โ
๐๐( ๐) โ ๐๐
๐๐๐
๐ซ1
๐๐ ๐๐
๐๐๐
โค ๐๐( ๐) โค ๐๐
๐๐๐
+ ๐ซ1 (11)
0 ๐๐ ๐๐( ๐) > ๐๐
0
And,
๐( ๐ถ)
{
1 ๐๐ ๐ถ( ๐) < ๐ถ๐๐๐
1 โ
๐ถ( ๐) โ ๐ถ๐๐๐
๐ซ2
๐๐ ๐ถ๐๐๐ โค ๐ถ( ๐) โค ๐ถ๐๐๐ + ๐ซ2 (12)
0 ๐๐ ๐ถ( ๐) > ๐ถ0
Where:
๐ซ0Tolerance of๐( ๐๐), ๐ซ0 = ๐ ๐๐๐ โ ๐ 0.
๐ซ1Tolerance of๐( ๐ ), ๐ซ1 = ๐๐
0
โ ๐๐
๐๐๐
.
๐ซ2Tolerance of๐( ๐ถ), ๐ซ2 = ๐ถ0 โ ๐ถ๐๐๐.
5. International Journal of Mobile Network Communications & Telematics ( IJMNCT), Vol.9, No.3, June 2019
5
Hence, the membership function of the decision space ๐ฬ is ๐ ๐ ฬ ( ๐)is given by:
Max ๐ ๐ ฬ ( ๐) = Max{0, min{๐(R), ๐( ๐๐), ๐( ๐ถ)}} (13)
5. THE GENETIC ALGORITHM
5.1. Chromosome Representation
The chromosome ๐ contains ๐ฃfields, where ๐ฃis the number of arcs (components) for the network.
Each field in ๐โrepresents the components number assigned to an arc.
๐ = (๐1, ๐2,โฆ , ๐ ๐ฃ)
Where๐1, ๐2 ๐๐๐ ๐ ๐ฃare random component numbers between 1 and๐ฃ๐, this mean that the
component ๐1is assigned to arc๐1, the component ๐2 is assigned to arc ๐2,โฆand the component
๐ ๐ฃis assigned to arc ๐ ๐ฃ.
5.2. Initial Population
The initial population is generated according to the following steps:
Step1: randomly generate chromosome ๐ in the initial population in the form:
๐ = (๐1, ๐2, โฆ , ๐ ๐ฃ).
Step 2: calculate ๐ , ๐ถ( ๐) ๐๐๐ ๐๐( ๐).
Step 3: calculate the membership function of the decision space ๐ ๐ ฬ ( ๐) using equation 13.
Step4: if ๐ ๐ ฬ ( ๐) of the generated chromosome in step 1 is less than ๐ผ discard it and go to step1.
Step 5: repeat step 1to 3 to generate ๐ฎchromosomes.
5.3. The Fitness Function
We take the membership function of the fuzzy optimal solution, ๐ ๐ ฬ ( ๐)as the fitness function ๐น of
the genetic algorithm.
5.4. Genetic Selection
We will use the roulette wheel selection method to select the parent population to the next
generation from the current population as follow:
Step 1: calculate a cumulative probability for each chromosome ๐๐( ๐๐), ๐๐ = 1,2, โฆ , ๐ฎ by:
๐๐( ๐๐) =
๐ ๐ ฬ (๐)
โ ๐ ๐ ฬ (๐)+ ๐๐ฎ
๐๐=1
(14)
Where๐ is small positive integer, it used to guarantee a nonzero denominator.
Step 2: generate random real number ๐ in [0, 1].
Step 3: if r โค ๐๐(1) , select the first chromosome, otherwise select the ๐๐๐กโ chromosome
(2 โค ๐๐ โค ๐ฎ) ๐๐ ๐๐( ๐๐ โ 1) < ๐ โค ๐๐( ๐๐).
Step 4: Repeat steps 2 and 3, ๐ฎ times and obtain ๐ฎ chromosomes.
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6
5.5. Genetic Crossover Operation
In the proposed GA, uniform crossover is used to breed a child from two parents by randomly
taking a component from the corresponding component of the child as shown in fig.1.The
crossover operation is performed as follows:
Step 1: select two chromosome according to the selection strategy, section 5.4.
Step 2: randomly take a component from one of the two chromosomes to form a corresponding
components of the child.
Step3: repeat step 2 until the components of the child fill up perfectly.
Figure 1.Uniform crossover operator
5.6. Genetic Mutation Operation
A child undergoes mutation according to the mutation probability ๐ ๐ and the mutation
probability for each component๐ ๐ .
Step 1: generate a random number ๐1 โ [0,1].
Step 2: if๐1 < ๐ ๐, the chromosome is chosen to mutate and go to step 3, otherwise skip this
chromosome.
Step 3: for each component of the child do:
Step 3.1: Generate a random number ๐2 โ [0,1].
Step 3.2: if ๐2 < ๐ ๐ then mutate this component as follows:
Step 3.2.1: if๐๐ = ๐ฃ๐ ๐, then randomly choose one in {1,2, โฆ , ๐ฃ๐} โ {๐ฃ๐ ๐}.
Step 3.2.2:if previous step does not achieve skip this component.
Figure 2 shows an example of performing the mutation operation on a given chromosome.
Figure 2. Mutation operation
5.7. The Proposed Algorithm
This section presents the proposed GA for solving the multi-objective optimization problem to
maximize system reliability of a flow network, minimize the total lead-time and cost which
described in section 3, with its fuzzy linear optimization presented in section 4.the steps of this
algorithm are as follow:
Step 1: Set the parameters:๐ฎ, โ, ๐ ๐, ๐๐, ๐๐
๐๐๐
, ๐๐
0
, ๐ ๐๐๐, ๐ 0, ๐ถ๐๐๐, ๐ถ0 ๐๐๐ ฮฑ .
Step 2: Generate the initial population and calculate the membership function for each
chromosome in it according to equations 10, 11, 12 and 13.
Step 3: Calculate the fitness function ๐ ๐ ฬ ( ๐)and cumulative probability ๐๐( ๐๐) for each
chromosome ๐ in the current population using equation 13,14.
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7
Step 4:In the new generation set ๐ = 0.
Step 5: To obtain one child select two chromosomes from the current population according to๐๐,
apply crossover then mutate the new child according to ๐ ๐ parameter.
Step 6:Evaluate the current child ( ๐) by calculating ๐ ๐ ฬ ( ๐).
Step 7: If ๐ ๐ ฬ ( ๐) โฅ ๐ผ then increment ๐.Otherwise go to step 5.
Step 8: If ๐๐ < ๐ฎ then goto step 9.
Step 9: Save best solution with high ๐ ๐ ฬ ( ๐).
Step 10: Set ๐๐ = ๐๐ + 1.
Step 11: If ๐๐ = โexit, otherwise go to step 4.
6. EXPERIMENTAL RESULTS
In this section we illustrated the results of applying the proposed approach on three networks,
four nodes, six nodes and TANET (Taiwan Academic Network). The genetic parameters used in
the proposed GA are: ๐ฎ = 10, โ = 100, ๐๐ = 0.95, ๐ ๐ = 0.05, 0.3 โค ๐ผ โค 0.8.
6.1. Four Node Network Example
The network shown in Figure3 has four nodes and six arcs. The capacity, probability, lead-time
and cost of each component (๐ฃ๐) is shown in Table1. There are six minimal paths:
๐๐1 = {๐1, ๐2}, ๐๐2 = {๐1, ๐5, ๐8},mp3 = {a1, a2, a6}, mp4 = {a1, a2, a7a8}, mp5
= {๐3, ๐6} ๐๐๐ ๐๐6
= {๐3, ๐7, ๐8}.We studied different values for T under different values of ๐ผ when d=4 as
illustrated in table 2, 3, 4, 5.where ๐ ๐๐๐ = 200, ๐0 = 250, ๐ ๐๐๐ = 0.99, ๐ = 0.9, ๐ ๐๐๐, = 9, ๐0 =
12.
Figure3. Computer network with 4 nodes and 6 arcs
Table 1. Components capacities, probabilities, lead-time and cost.
๐๐ ๐
Capacity
๐(๐๐ ๐) ๐(๐๐ ๐)
0 1 2 3 4 5 6
1 0.01 0.00 0.01 0.00 0.01 0.00 0.97 2 10
2 0.05 0.05 0.05 0.15 0.20 0.50 0 3 60
3 0.07 0.08 0.00 0.85 0 0 0 2 10
4 0.70 0.00 0.00 0.00 0.00 0.30 0 2 20
5 0.01 0.00 0.00 0.05 0.00 0.00 0.94 1 50
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69 8 21 33
0.4 0.438 0.991574 61 2305
71 59 39 53 5 11 60 78 72 8 64 44 28 14
30 9 26 54 31 52 56 37 20 23 2 79 1 43 74
10 33 38 13
0.5 0.538 0.997141 59 2465
24 12 61 53 77 40 6 21 7 52 60 48 1 3 72
34 8 9 38 15 23 62 59 42 54 50 29 41 32
75 55 79 20
Table 24. Optimal results founded by proposed approach to the network in fig.6, when d=9, T=18.
d,t ๐ ๐๐๐ฌ๐ญ ๐๐ฌ ๐ ๐,๐ญ ๐๐ฅ(๐ฉ) ๐(๐ฉ) Assigned components
9,18
0.3 0.496 0.989470 57 2080
44 46 21 80 1 6 26 33 23 39 40 34 14 28
12 79 15 4 55 20 70 18 50 37 71 49 7 24
30 65 56 42 75
0.4 0.512 0.999175 63 2430
18 68 15 25 27 72 31 56 53 50 61 6 2 9 19
10 67 14 75 12 48 30 38 59 13 47 34 16 39
26 24 3 51
0.5 0.627 0.966636 61 2295
46 67 73 26 13 18 42 44 21 59 61 79 56 19
1 23 9 38 52 5 15 27 55 3 8 39 4 65 74 63
30 28 62
7. DISCUSSION AND COMPARISON
This section presents a comparison between the proposed algorithm and that one proposed by
Aissou et al.,[11] based on RWGA.Table 25 and 26 show the comparison results for two studied
networks, Six-node and TANNET with 30 links respectively. The results in Table 25show that
the proposed approach obtains the optimal solution better than that obtained by [11]. While in
Table 26the reliability values are less than that obtained by [11]. But, lead-time and cost values
are less than those obtained by [11]. These results lead to that the proposed algorithm finds the
optimal solution.
Table 25. Comparison results for the Six-node network example.
d,t
Aissouโs approach Proposed approach
๐ ๐,๐ก ๐๐(๐) C(p) ๐๐๐ ๐ก ๐๐ ๐ ๐,๐ก ๐๐(๐) C(p)
6,7 0.973036 15 510 0.987 0.988833 12 440
6,8 0.987345 14 520 0.999 0.989945 12 460
6,9 0.985979 19 540 0.997 0.989773 14 420
8,9 - 0.999 0.989896 14 420
Table 26. Comparison results for the TANETwith 30 linksexample.
d,t
Aissouโs approach Proposed approach
๐ ๐,๐ก ๐๐(๐) C(p) ๐๐๐ ๐ก ๐๐ ๐ ๐,๐ก ๐๐(๐) C(p)
4,16 0.9999745 66 1735 0.993 0.998347 43 1460
6,16 0.999986
61
1435 0.999 0.998934 42 1485
8,18 0.999172 1825 0.998 0.998810 43 1425
9,18 0.985317 1825 0.990 0.997983 44 1515
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8. CONCLUSIONS
An approach based on GA with fuzzy optimization is presented in this paper. The presented
approach was succeeded to solve the optimal CAP problem in which each components has three
attributes; probability, cost, and lead-time. Using fuzzy membership function as fitness, the
proposed approach succeeded to find the best optimal solution with maximum system reliability,
minimum total assignment cost, and minimum total lead-time in comparison with previous
algorithms.
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AUTHORS
Heba Hamdy Ahmed is a Demonstrator in Computer Science Branch, Department of Mathematics,
Faculty of Science, Aswan University, Aswan, Egypt.
Motamad Refaat Hassan is an Assistant Professor in Computer Science Branch, Department of
Mathematics, Faculty of Science, Aswan University, Aswan, Egypt.
Mohamed Eid Mohamedis a lecture in Computer Science Branch, Department of Mathematics, Faculty of
Science, Aswan University, Aswan, Egypt.
Mosa khalifa Ahmed is an Assistant Professor in Department of Mathematics, Faculty of Science, South
Valley University, Qena, Egypt.