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A Heuristic Ant Algorithm for Solving QoS Multicast Routing ProblemPowerPoint Presentation

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 Problem

- Introduction
- Ant Colony Behaviors
- QoS Multicast Routing Model
- Ant Algorithm
- Result and Analysis
- Conclusions

Introduction Problem

- 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) Problem

- 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) Problem

- The key features of an ant algorithm include：
- Distributed computation,
- Positive feedback,
- And constructive greedy heuristic.

QMR Model Problem

- 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) Problem

- 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) Problem

- 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 Problem

- 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 Problem

- 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) Problem

- 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) Problem

- 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) Problem

- 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) Problem

- 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

- For k:=1 to m (?)

Ant Algorithm (5) Problem

- 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 been passed.

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

Result and Analysis (2) Problem

Scalability of ant algorithm – 16 nodes

Scalability of ant algorithm – 20 nodes

Conclusions Problem

- 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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