A heuristic ant algorithm for solving qos multicast routing problem
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A Heuristic Ant Algorithm for Solving QoS Multicast Routing Problem. Chao-Hsien Chu; JunHua Gu; Xiang Dan Hou; Qijun Gu Congress on Evolutionary Computation Proceedings of the 2002. Outline. Introduction Ant Colony Behaviors QoS Multicast Routing Model Ant Algorithm Result and Analysis

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A Heuristic Ant Algorithm for Solving QoS Multicast Routing Problem

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A heuristic ant algorithm for solving qos multicast routing problem

A Heuristic Ant Algorithm for Solving QoS Multicast Routing Problem

Chao-Hsien Chu; JunHua Gu; Xiang Dan Hou; Qijun Gu

Congress on Evolutionary Computation

Proceedings of the 2002


Outline

Outline

  • Introduction

  • Ant Colony Behaviors

  • QoS Multicast Routing Model

  • Ant Algorithm

  • Result and Analysis

  • Conclusions


Introduction

Introduction

  • QoS Multicasting Routing(QMR) Problem:

    • Concerns the search of optimal routing trees while meeting all QoS requirements;

    • Is NP-complete;

    • Can be solved by:

      • Dijkstra algorithm to find the shortest path,

      • Steiner tree routing algorithm to seek minimum networking cost,

      • Finding multicast tree that paths cost is minimized.


Ant colony behaviors 1

Ant Colony Behaviors (1)

  • When an obstacle appears on the moving path of an ant population, ants can find a new optimal path quickly. Because:

    • An ant can excrete a material, called pheromone, along the path on which it moves.

    • Ants can sense this material and detect its intensity.

    • They can then use pheromone intensity as a guide to move and tend to move toward the direction of higher intensity, thus the ants can find the food by this kind of information exchange.


Ant colony behaviors 2

Ant Colony Behaviors (2)

  • The key features of an ant algorithm include:

    • Distributed computation,

    • Positive feedback,

    • And constructive greedy heuristic.


Qmr model

QMR Model

  • The network is considered as a connected, undirected and weighted graph.

  • N<V,E>:

    • V denotes the set of network nodes,

    • E denotes the set of bi-directional links,

    • sєV is the source node in multicast,

    • is the set of destination node in multicast.


Qos measures 1

QoS Measures (1)

  • For any link eєE:

    • Delay function, delay(e):E→R,

    • Delay jitter function, delay_jitter(e):E→R,

    • Cost function, cost(e):E→R,

    • Bandwidth function, bandwidth(e):E→R.

  • For each node nєV:

    • Delay function, delay(n):V→R,

    • Delay jitter function, delay_jitter(e):V→R,

    • Cost function, cost(e):V→R,

    • Packet lost rate function, packet_loss(e):V→R.


Qos measures 2

QoS Measures (2)

  • Relationships exist in the multicast tree T(s,M):

    • Delay(PT(s,t))=

    • Cost(T(s,M))=

    • Bandwidth(PT(s,t))=min{bandwidth(e),eєPT(s,t)}

    • Delay_jitter(PT(s,t))=

    • Packet_loss(PT(s,t))=

    • Where PT(s,t) is the routing path from s to t.


Qmr s objective

QMR’s Objective

  • To find a multicast tree T(s,M), which satisfies:

    • Delay constraint:Delay(PT(s,t))≦Dt,

    • Bandwidth constraint:Bandwidth(PT(s,t))≧B,

    • Delay jitter constraint:Delay_jitter(PT(s,t))≦DJt,

    • Packet loss rate constraint:Packet_loss(PT(s,t))≦PLt,

    • And Cost(T(s,M)) is minimized.


Ant algorithm

Ant Algorithm

  • Init(); // step 1

  • CheckConstraint(PL,B); // step 2

  • SetupUp(tabu); // step 3

  • ChooseNextNode(tabu); // step 4

  • ComputeIntensity(); // step 5

  • UpdateIntensity(); // step 6

  • CheckStop(); // step 7


Ant algorithm 1

Ant Algorithm (1)

  • 1) Initialize network nodes

    • t:=0; NC:=0; τij=c; △τij =0;

  • 2) Check PL/B (packet loss rate/Bandwidth) of all nodes, deletes those edges that do not satisfy the PL/bandwidth constraint.


Ant algorithm 2

Ant Algorithm (2)

  • 3) Setup tabu table.

    • s:=1;

    • For k:=1 to m

      Put the values of source node into tabuk(s);

      /* Tabu is used to save the nodes that were reached before t. tabuk(s) denotes the s-th node visited by the k-th ant in the current route and s is the index of tabu table. */


Ant algorithm 3

Ant Algorithm (3)

  • 4) Repeat this step until tabu is full.

    • s:=s+1;

    • For k:=1 to m

      Choose a node j according to the probability:

    • Compute the delay and delay jitter to reach node j. If the result exceeds the constraints, choose a new node; otherwise move the k-th ant to node j.


Ant algorithm 4

Ant Algorithm (4)

  • 5) Compute △τkij and △τij .

    • For k:=1 to m (?)

      For every edge(i,j)

      For k:=1 to m

      Set

      Set △τij:=△τij+△τkij


Ant algorithm 5

Ant Algorithm (5)

  • 6) Compute τij(t+n) for every edge (i,j).

    • τij(t+n)=ρ*τij(t)+△τij

    • t:=t+n; NC:=NC+1;

    • Set △τij:=0 for every edge (i,j).

  • 7) Check stop condition.

    • If (NC<NCmax) and (not develop state) then

      empty all tabu; goto step 2.

      else

      output the minimum cost path until all nodes have beenpassed.


Example

Example

B=70,D=46, DJ=8, PL=0.001

Source Node

Destination

Node


Result and analysis 1

Result and Analysis (1)

Performance of Ant Algorithm

Performance of Genetic Algorithm


Result and analysis 2

Result and Analysis (2)

Scalability of ant algorithm – 16 nodes

Scalability of ant algorithm – 20 nodes


Conclusions

Conclusions

  • The ant algorithm has the characteristics:

    • The cost curve is stable,

    • Optimum or suboptimum can be found quickly,

    • Delay jitter curve can turn to stability quickly,

    • Good scalability.

  • Applying ant algorithm to solve QMR is a new attempt and needs more extensive tests.


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