| Summary: | 博士 === 國立交通大學 === 資訊工程系 === 89 === In the reliability analysis of a distributed system, k-node set reliability is defined as the probabilities that all nodes in K are connected, where K denotes a subset of set of processing elements. A k-node set reliability computation can be very hard with exponential in many cases. Differing design goals, varying system assumptions, and constraints yield a disparity of optimal k-node set reliability. This dissertation focuses on the optimization of a k-node set reliability with capacity constraint, reliability-oriented task assignment, a k-node set reliability with order constraint and the minimal spanning trees of a distributed system. A k-node set reliability optimization with a capacity constraint problem is to select a k-node set of nodes in a distributed system such that the k-node set reliability is maximal and possesses sufficient node capacity. It is evident that this is an NP-hard problem. An exact method and a k-tree reduction method have been used to examine k-node set reliability optimization with capacity constraint. Such investigations either spent an exponential time or rarely obtained an optimal solution. There are many investigations has examined the task assignment problem. The k-DTA models the assignment of k copies of both distributed programs and their data-files to maximize the distributed system reliability under some resource constraints. This is also an NP-hard problem. The difficulty of conventional algorithms for constructing minimal spanning trees of a distributed system arises from a communication and synchronization problem.
Although the exhaustive method can obtain an optimal solution, it cannot reduce the computational time. Occasionally, an efficiency algorithm with an exact or nearly exact solution is attractive.
The field of practical genetic algorithm (GA) opened in 1973 with the J. H. Holland’s paper. GA can be applied to search large, complex problem spaces. The main steps for GA are reproduction, selection, crossover, and mutation. The process of selection, crossover, and mutation is repeated until the termination condition is satisfied.
In 1994, Leonard M. Adleman used biological experiments with DNA strands to solve computation problem. The potential benefits of using this particular molecule are enormous due to the massive inherent parallelism of performing concurrent operations on trillions of strands.
In this work, to reduce the computational time and the absolute error from the exact solution, some algorithms based on heuristic, and genetic algorithm are proposed for k-node set reliability with capacity constraint, reliability-oriented task assignment, a k-terminal reliability with order constraint. In addition, a DNA algorithm for solution of minimal spanning tree of a DS is also considered.
Computational results demonstrate that the number of reliability computation is constant. In addition, the proposed methods can obtain an exact solution in most case. When the proposed methods fail to provide an exact solution, the deviation from the exact solution is only slight. We conclude that these proposed algorithms may effectively reduce the computational time and the deviation from an exact solution.
CHINESE ABSTRACT ………………………………………… i
ENGLISH ABSTRACT ………………………………………… iii
ACKNOWLEDGEMENT ………………………………………v
LIST OF TABLES ………………………………………………xiv
LIST OF FIGURES …………………………………………….xvi
CHAPTER 1 INTRODUCTION ………………………………… 1
1.1 INTRODUCTION …………………………………………………. 1
1.2 NOTATIONS AND ACRONYMS ………………………………….. 5
1.3 DEFINITIONS ……………………………………………………11
1.4 PROBLEM STATEMENTS ………………………………………14
1.4.1 K-terminal reliability with order constraint problem ………14
1.4.2 K-node set reliability with capacity constraint problem ……15
1.4.3 Task assignment reliability …………..……………………16
1.4.4 Minimal spanning tree ………..……………………………17
1.5 SIMULATION ENVIRONMENT ……………………………18
CHAPTER 2 COMPUTATION OF DISTRIBUTED SYSTEM
RELIABILITY ………………………………….19
2.1 K-TERMINAL RELIABILITY WITH ORDER CONSTRAINT …19
2.2 K-node set RELIABILITY WITH CAPACITY CONSTRAINT .22
2.2.1 The description of an EM ………….………………………22
2.2.2 The description of an k-tree reduction method (KM) …27
2.3 DISTRIBUTED PROGRAM RELIABILITY ..….………………29
2.4 MINIMAL SPANNING TREE ………………………..…………33
CHAPTER 3 HEURISTIC METHODS ……………………….35
3.1 THE WEIGHT OF A NODE, A LINK AND A VIRTUAL LINK ..35
3.1.1 Compute the weight of each node ………………………….35
3.1.2 Compute the weight of each link ..…………………………37
3.1.3 Compute the weigh of a virtual link .………………………39
3.2 K-TERMINAL RELIABILITY WITH ORDER CONSTRAINT ..40
3.2.1 The concept of KTRPM1 algorithm ……………………….41
3.2.2 The KTRPM1 algorithm …………………………………43
3.2.3 Illustrative examples ………………………………………45
3.2.4 Comparison and discussion ……………………………….48
3.2.5 Conclusions ……………………………………………….54
3.3 k-NODE SET RELIABILITY ……………………………………55
3.3.1 KNRPM1 …………………………………………………..55
3.3.1.1 The KNRPM1 algorithm …….……………………..56
3.3.1.2 An illustrative example ….………………………….59
3.3.1.3 Simulation ………………………………………….60
3.3.1.4 Results and discussion ………………………………61
3.3.2 KNRPM2 …………………………………………………..65
3.3.2.1 The KNRPM2 algorithm …….……………………..66
3.3.2.2 An illustrative example ….…………………………69
3.3.2.3 Simulation …………………………………………72
3.3.2.4 Results and discussion ………………………………72
3.3.3 KNRPM3 …………………………………………………76
3.3.3.1 The KNRPM3 algorithm …….…………………….76
3.3.3.2 An illustrative example ….…………………………80
3.3.3.2 An illustrative example ….…………………………83
3.3.3.4 Results and discussion ………………………………83
3.3.4 KNRPM4 ………………………………………………….89
3.3.4.1 The KNRPM4 algorithm …….…………………….90
3.3.4.2 An illustrative example ….………………………….99
3.3.4.3 Simulation …………………………………………..102
3.3.4.4 Results and discussion ………………………………103
3.3.5 Conclusions …………………………………………………112
3.4 TASK ASSIGNMENT RELIABILITY ………………………113
3.4.1 Construct lists and task assignment ………………………113
3.4.1.1 Construct list APL(fi), AFL(pi) and AR-list …………113
3.4.1.2 Allocate each program and data file according to AR-
list and Q1 …………………………………………116
3.4.2 DTAPM1 …………………………….…………………….119
3.4.2.1 The DTAPM1 algorithm ……………………………119
3.4.2.2 An illustrate example ……………………………….121
3.4.3 DTAPM2 …………………………….…………………123
3.4.3.1 The DTAPM2 algorithm ……………………………123
3.4.3.2 An illustrate example ……………………………….126
3.4.4 DTAPM3 …………………………….……………………128
3.4.4.1 The DTAPM3 algorithm ……………………………128
3.4.4.2 An illustrate example ………………………………128
3.4.5 Results and discussion …………………………………….132
3.4.6 Conclusion …………………………………………………136
CHAPTER 4 GENETIC ALGORITHM METHODS ……..…137
4.1 GA BACKGROUND …………………………………………137
4.2 K-NODE SET RELIABILITY─GAKNR ……….………………139
4.2.1 Chromosomal-coding scheme ……………………………..139
4.2.2 Initialization approach …………………………………….139
4.2.3 The objective function …………………………………….140
4.2.4 Genetic reproduction and selection ……………………….141
4.2.5 Genetic crossover operators ……………………………….141
4.2.6 Genetic mutation operator …………………………………142
4.2.7 Replacement strategy and termination rules ……………….142
4.2.8 Genetic algorithm parameter ..……………………………..143
4.2.9 The GAKNR algorithm ……..…………………………….143
4.2.10 An illustrate example ……………………………………147
4.2.11 Results and discussion …….…………………………….149
4.3 TASK ASSIGNMET RELIABILITY …………….……….……….151
4.3.1 Chromosomal-coding scheme ……………………………152
4.3.2 Valid chromosome …………….………………………….153
4.3.3 Initialization approach ……………………………………154
4.3.4 Mask string generation ……………………………………155
4.3.5 Fast valid chromosome generation for population initialization 155
4.3.6 The weight of a 2-terminal for all pairs .…………………..159
4.3.7 Computing the 2-terminal access weight for all pairs ……..160
4.3.8 Computing the access weight of a program and chromosome 160
4.3.9 Computing the fitness value of chromosome using objective
function ……………………………………………………162
4.3.10 Genetic reproduction and selection …………………..….163
4.3.11 Genetic crossover operator ………………………….…..163
4.3.12 Genetic mutation operator ………………………………..165
4.3.13 Replacement strategy and termination rules ….…………..166
4.3.14 The GADTA algorithm ………………………………….167
4.3.15 An illustrate example …………………………………….172
4.3.16 Results and discussion ………………………….……….175
4.4 DISCUSSION ……………………………………………………..178
CHAPTER 5 DNA COMPUTATION ………………………….179
5.1 DNA BACKGROUND AND ITS OPERATIONS ……………179
5.1.1 DNA structure …………………………………….180
5.1.2 DNA operations ……………………………………………181
5.1.2.1 Synthesis ……………………………………………181
5.1.2.2 Melting and annealing ………………………………181
5.1.2.3 Ligation ……………………………………………182
5.1.2.4 Polymerase extension …………………………….182
5.1.2.5 Separate by subsequence …………………………182
5.1.2.6 Cut …………………………………………………183
5.1.2.7 Separate by length ………………………………….183
5.1.2.8 Destroy ………………………………………………183
5.1.2.9 Amplify ……………………………………………..184
5.2 DNA ALGORITHM FOR MINIMAL SPANNING TREE OF A
DISTRIBUTED SYSTEM ………………………………………184
5.2.1 Arithmetic operations with DNA ………………………….184
5.2.2 Development of DNAMST ……………………………….186
5.2.2.1 Encoding scheme …………………………………….186
5.2.2.2 The DNAMST algorithm ……………………………188
5.3 DISCUSSION ……………………………………………………..193
5.4 CONCLUSION ……………………………………………………196
CHAPTER 6 FURTHER RESEARCHES AND CONCLUSIONS ….197
6.1 FURTHER RESEARCHES ………………………………………197
6.2 CONCLUSIONS ………………………………………………….199
BIBLIOGRAPHY ……………………………………..………..202
VITA …………………………………………………………….209
PUBLICATION LISTS …………………………………………211
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