Optimal resource assignment to maximize multistate network reliability for a computer network Yi-Kuei Lin, Cheng-Ta Yeh Advisor : Professor Frank Y. S. Lin Presented by: Tuan-Chun Chen Presentation date: May 8, 2012

Agenda Introduction Problem formulation Development of MSNRA-GA Experimental results Conclusions and further research

Agenda Introduction Introduction Problem formulation Development of MSNRA-GA Experimental results Conclusions and further research

Introduction How to evaluate and enhance network reliability is an important issue for organizations, especially to maximize network reliability. search for the optimal resource assignment (RA) The multistate network (MSN) reliability is the probability that the maximal flow of the MSN is no less than the demand

Introduction The existed optimization problems of MSN reliability are categorized into two types: (1) Achieving the optimal MSN reliability subject to different constraints. (2) Minimizing the resources needed for providing a required reliability level.

Introduction Many researches involve the issues of network structure, flow assignment, and commodity allocation. This paper focuses on “searching for the optimal resource assignment with maximal MSN reliability”.(MSNRA problem) Resources denote transmission lines of a computer network. The MSNRA problem is solved at the design phase.

Introduction Implicit enumeration method can be applied intuitively to solve the MSNRA problem, but it is very time-consuming. This Study develops an optimization method named MSNRA-GA (genetic algorithm) based on the simple GA (SGA) architecture. Chromosome  resource assignment. Fitness value of a chromosome  MSN reliability. Evaluated in terms of MPs.

Introduction Higher MSN reliabilities have higher possibility to be preserved and to propagate their offspring. Thus, MSNRA-GA can avoid searching for the worse solutions and the optimal solution can be found in a reasonable time.

Agenda Introduction Problem formulation Problem formulation Development of MSNRA-GA Experimental results Conclusions and further research

Problem formulation Multistate network (N,E)(N,E)a network that has a single source s and a single sink t. NSet of nodes E{i|1,2,...,q}, set of q edges mp 1, mp 2..., mp z All MPs of the network Γ {j|1,2,...,m}, set of m resources, in which each resource j has multiple capacities, 0=h j (1)<h j (2)<...<h j (M j ) hj(l)hj(l)lth capacity of resource j for l=1,2,..., M j h j (Mj)the maximal capacity of resource j X(x 11,x 12,...,x 1m,...,x q1,...,x qm ), resource assignment in which resource j is assigned to edge i if x ij =1 and otherwise x ij =0

Problem formulation Assumptions: 1. No resource is assigned to any node. 2. Flow in (N,E) must satisfy the flow-conservation law. 3. Each resource can be assigned to at most one edge and each edge must contain exact one resource. 4. The capacities of resources are statistically independent.

Problem formulation MSNRA problem formulation U(u 1,u 2...,u q ), a state vector, any U satisfying constraint(1) is under the resource assignment X uiui current capacity of edge i for all i E (1)

Problem formulation (2) SR d (X)the probability that d units of transmission data can be successively delivered from s to t under X.

Problem formulation (3) (4) Assumption3: Each resource can be assigned to at most one edge and each edge must contain exact one resource.

Problem formulation MSN reliability evaluation Any minimal state vector in the set is said to be a lower boundary point for d or d-MP. Suppose U 1,U 2,...,U b are b d-MPs. (5)

Problem formulation Flow vectors and state vectors (6) (7) F(f 1,f 2,...,f z ), a flow vector fvfv the flow through mp v, v=1,2,....,z flow vectors:

Problem formulation (8) (9) state vectors:

Problem formulation (11) (10) Generate all d-MPs

Problem formulation Check whether a d-MP candidate is a d-MP or not

Agenda Introduction Problem formulation Development of MSNRA-GA Development of MSNRA-GA Experimental results Conclusions and further research

Development of MSNRA-GA Determination of the GA’s parameters Popsizepopulation size, the number of chromosomes in the population PcPc crossover rate PmPm mutation rate< 0.1

Development of MSNRA-GA Representation of a chromosome

Development of MSNRA-GA Evolution process I. Selection operator Directs the MSNRA-GA to search toward a better region in the solution space. Determined from the fitness value of the chromosome (MSN reliability). Higher fitness value has a higher probability of being selected.

Development of MSNRA-GA The roulette wheel selection is implemented twice so that two chromosomes are selected to be the parents.

Development of MSNRA-GA II. Crossover operator Offspring are produced by the parents. The good genes is preserved in the next generation. Step 1: Randomly choose crossover point(CP)

Development of MSNRA-GA Step 2: Exchange

Development of MSNRA-GA Step 3: Modify

Development of MSNRA-GA III. Mutation operator The study develops a hybrid mutation method that combines simple mutation with uniform mutation. First, MuP is stochastically generated. Secondly, the gene at this point is mutated

Development of MSNRA-GA Condition 1: The mutated gene is the same as that of another in the child.

Development of MSNRA-GA Condition 2: The mutated gene is not the same as the others in the child. IV. Terminal condition When the number of iterations is 1000.

Agenda Introduction Problem formulation Development of MSNRA-GA Experimental results Experimental results Conclusions and further research

Experimental results Experiments are grouped into three parts: (1) MSNRA-GA is compared with the implicit enumeration method to show its efficiency (2) Implemented on six random networks and four commonly used networks. (3) A real computer network, Taiwan Academic Network (TANET).

Experimental results (1) Comparison with the implicit enumeration method in terms of the optimal reliability and CPU time. MSNRA-GA’s parameters: Using a simple network Popsize30 PcPc 0.9 PmPm 0.1 g time 200

Experimental results

(2) Experiment in ten networks 6 random networks:

Experimental results (2) Experiment in ten networks 4 commonly used networks:

Experimental results (2) Experiment in ten networks Parameters: Popsize30 PcPc 0.9 PmPm 0.1 g time 1500 d90Mb Num. of resources100

Experimental results

Discussions: I. Number of edges, Avg. CPU time (non-linearly), Avg. maximal MSN reliability II. Number of MPs, Avg. CPU time Avg. maximal MSN reliability

Experimental results (3) The experiments in TANET Parameters: Discuss 18 pairs of Popsize and g time. PcPc 0.9 PmPm 0.1 d90Mb

Experimental results MSN reliability is not reduced nor increase significantly as the Popsize changes.

Agenda Introduction Problem formulation Development of MSNRA-GA Experimental results Conclusions and further research Conclusions and further research

Conclusions and further research The paper presents a novel optimization problem for computer networks to search for the optimal resource assignment with maximal MSN reliability. Also develop an optimization method named MSNRA-GA, based on the SGA, to solve this MSNRA problem. Experimental results reveal that the MSNRA-GA has better computational efficiency than the implicit enumeration method and practice for large networks.

Conclusions and further research This paper focuses on the terminal-pair connectivity. The MSN reliability for multiple origins to multiple destinations is also an important issue worthy studying in the future. This problem can be developed into a multi-objective resource assignment problem, including maximizing the MSN reliability and minimizing resource assignment cost, or can consider the time constraint and multi-commodity transmission.

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