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Genetic Algorithm for Multicast in WDM Networks

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a channel can consist of multiple light-paths and wavelength ... Each node of the tree is a multicast-Incapable optical switch (MI node) . 6. Introduction ... – PowerPoint PPT presentation

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Title: Genetic Algorithm for Multicast in WDM Networks


1
Genetic Algorithm for Multicast in WDM Networks
  • Der-Rong Din

2
Outline
  • Introduction
  • Problem formulation
  • Genetic Algorithm

3
Introduction
  • There are two types of architectures of WDM
    optical networks single-hop systems and
    multi-hop systems 2.
  • Single-hop system
  • a communication channel should use the same
    wavelength throughout the route of the channel
  • Multi-hop system
  • a channel can consist of multiple light-paths and
    wavelength conversion is allowed at the joint
    nodes of two light-paths in the channel.
  • In this paper, single-hop systems is considered,
    since all-optical wavelength conversion is still
    an immature and expensive technology. (no
    wavelength conversion)

4
Introduction
  • Multicast is a point to multipoint communication,
    by which a source node sends messages to multiple
    destination nodes.
  • A light-tree, as a point to multipoint extension
    of a light-path, is a tree in the physical
    topology and occupies the same wavelength in all
    fiber links in the tree.

5
Introduction
  • Each node of the tree is a multicast-Incapable
    optical switch (MI node) .

6
Introduction
  • The problem is formalized as follows
  • given an multicast request in a WDM network
    system, compute a set of routing trees and assign
    wavelengths to them.
  • The objective is to minimize the (cost a of
    wavelength)
  • number of distinct wavelengths to be used under
    the following constraints on each routing tree
  • the total cost of the tree.

7
System Models
  • WDM network
  • Connected and undirected graph G(V, E, c)
  • V vertex-set, Vn
  • E edge-set, Em
  • Each edge e in E is associated with a weight
    function
  • c(e) communication cost

8
System Models
  • Cost of path P(u,v)
  • A multicast request in the system are given,
    denoted by r (s, D)
  • source s
  • destination Dd1, d2, ..., dD

9
System Models
  • This paper assumes an input optical signal can
    only be forward to an output signal at a switch.
  • Tk (s, Dk) be the routing tree for request r
    (s, D) in wavelength k, where kltK, T?
    k1,2,...,KTk
  • D? k1,2,...,K Dk T is the light-forest.
  • The light signal is forwarded to the output port
    leading to its child, which then transmit the
    signal to its child until all nodes in the Dk
    receive it.

10
Objective
  • The cost of the tree
  • where yj 1 if wavelength j is used yj0,
    otherwise
  • Special case
  • One objective of the multicast routing is to
    construct a routing tree (or forest) which has
    the minimal cost. The problem is regarded as the
    minimum Steiner tree problem, which was proved to
    be NP-hard.
  • Another objective is to minimize the number of
    wavelengths used in the system.
  • In a single-hop WDM system, two channels must use
    different wavelengths if their routes share a
    common link, which is the wavelength conflict
    rule.

11
Genetic Algorithm for WDM Multicast Problem
(WDMMP)
  • Important components of GA
  • Chromosome encoding
  • Fitness function
  • Penalty function
  • Crossover operation
  • Mutation operation.

12
r(s, 1,2,3,4,5,6
13
Example of GA
  • since out-degree(s)4, D6, thus may be 2
    wavelengths are need to multicast the request.

14
Genetic Algorithm
  • Basic idea modified the GA of C. P. Ravikumar
    and Rajneesh Bajpai (Source-based delay-bounded
    multicasting in multimedia networks, Computer
    Communication 21 1998 126-132) to WDM network
  • Tree-based encoding method

15
Initial Population
  • A randomize depth first search algorithm was
    employed for this purpose. The search begins at
    the source node s and at each node randomly
    select the next node to be visited. The algorithm
    terminates when all destination nodes have been
    visited.

16
Transform Steiner tree into light-forest
  • A WDM multicasting forest is constructed from a
    tree be Light-Forest Construct Algorithm.

17
Light-Forest Construct Algorithm
  • Given a tree on a wavelength-graph
  • Step 0 Find the shortest paths from source node
    s to all destination nodes d in D say (p1,p2,...,
    pD).
  • Step 1 Sort paths in increasing order according
    to the cost of each path O(D log D) time.
    Assume that p1,p2,...., pD be the new index.
  • Step 2 p1 is assigned to wavelength 1,w1,
    T1p1, T2 ...Tkø. O(n)

18
Light-Forest Construct Algorithm
  • Step 3 For i 2 to D do
  • Begin
  • j1
  • while j?w do
  • if pi is not conflict with Tj
  • then
  • assigned pi to Tj
  • TjTj ?pi
  • flagTRUE
  • else jj1
  • if flag is not TRUE
  • then
  • ww1
  • TwTw ? pi
  • End

Time complexity O(D2n)
19
Example
p1s?7 ?1 (10) p2s?7 ?14 ?2 (13) p3s?9 ?13 ?3
(15) p4s?10 ?4 (8) p5s?10 ?4 ?5 (12) p6s?9
?13 ?5 ?6 (26)
cost81041513262a
20
p1s?7 ?1 (10) p2s?7 ?14 ?2 (13) p3s?9 ?13 ?3
(15) p4s?10 ?4 (8) p5s?10 ?4 ?5 (12) p6s?9
?13 ?5 ?6 (26)
21
Conflict Test Algorithm for path and Tree
  • light-tree is represented by a directed tree root
    at s.
  • O(n) time add path into a directed tree, then
    test the out-degree of the visited vertex, if the
    out-degree gt1 then conflict occurred.

22
Penalty Function
  • The light-forest construct a feasible solution of
    the WDM network, thus, there is no need for the
    penalty function.

23
Fitness Function
Algorithm
  • Minimized
  • Transform to maximization form
  • where Cmax denotes the maximum value observer so
    far of the cost function in the population.

Fitness Cmax-Cost
24
Crossover Operator
  • Given two trees TM and TF, the crossover
    algorithm construct a child Steiner tree as
    following
  • Step 1. Identify the links that are common to
    both TM and TF, and retaining them in T0.
  • The above method of forming a child Steiner tree
    is based on the heuristic that since both the
    selected parent are likely to have highly values
    of fitness measure, the link that are common to
    them represent good trail and must be passed on
    to the child.

25
Crossover Operator
  • T0 may be a disconnected graph and edges may have
    to be added to transform it into a tree.
  • This is done by identifying the connected
    components in T0 and merging two of the connected
    components as a time until T0 takes the form of a
    tree.
  • Note that no cycles can be formed when two
    connected components of a graph are joined.
  • The link l which is added to join two connected
    components is selected by following methods

26
Edge selected methods
  • 1.Random selected from parent
  • 2.Random selected from all
  • 3.Heuristic construct from parent (cost based)
  • 4.Heuristic construct from all (cost based)

27
Example
TM
TF
28
T0 and the remaining set of edges
T0
29
1.Random selected from parent
  • The edges of child is randomly selected from
    edges of parent.

30
2.Random selected from all
  • The edges of child is randomly selected from
    edges of graph.

31
3.Heuristic construct from parent (cost based)
T0
T0
32
3.Heuristic construct from parent (cost based)
33
4.Heuristic construct from all (cost based)
11
15 ?
34
Mutation Operator
  • random single edge removing mutation
  • random single edge adding mutation
  • heuristic single edge remove mutation
  • heuristic single edge adding mutation
  • best single edge mutation

35
random single edge removing mutation
  • Randomly remove a edge from tree
  • Find a edge (or a path) in G-T to construct a new
    tree (random selected from edge set to construct
    a tree)

36
random single edge adding mutation
  • Randomly add a edge into tree
  • If exist an cycle then random remove an edge from
    cycle

37
heuristic single edge remove mutation
38
heuristic single edge adding mutation
  • Randomly add a edge into tree
  • If exist an cycle then find the edge whose
    removing has minimal cost.

39
best single edge mutation
  • Find the edge whose removing result minimal cost.
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