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  Conclusions

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

QMR Model  The network is considered as a connected, undirected and weighted graph.  N ： 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)  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)  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  To find a multicast tree T(s,M), which satisfies ： Delay constraint ： Delay(PT(s,t)) ≦ D t, Bandwidth constraint ： Bandwidth(PT(s,t)) ≧ B, Delay jitter constraint ： Delay_jitter(PT(s,t)) ≦ DJ t, Packet loss rate constraint ： Packet_loss(PT(s,t)) ≦ PL t, And Cost(T(s,M)) is minimized.

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)  1) Initialize network nodes t:=0; NC:=0; τ ij =c; △ τ ij =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)  3) Setup tabu table. s:=1; For k:=1 to m Put the values of source node into tabu k (s); /* Tabu is used to save the nodes that were reached before t. tabu k (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)  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)  5) Compute △ τ k ij and △ τ ij. For k:=1 to m (?) For every edge(i,j) For k:=1 to m Set Set △ τ ij := △ τ ij + △ τ k ij

Ant Algorithm (5)  6) Compute τ ij (t+n) for every edge (i,j). τ ij (t+n)=ρ*τ ij (t)+ △ τ ij t:=t+n; NC:=NC+1; Set △ τ ij :=0 for every edge (i,j).  7) Check stop condition. If (NC<NC max ) and (not develop state) then empty all tabu; goto step 2. else output the minimum cost path until all nodes have been passed.

Example Source Node Destination Node B=70,D=46, DJ=8, PL=0.001

Result and Analysis (1) Performance of Ant AlgorithmPerformance of Genetic Algorithm

Result and Analysis (2) Scalability of ant algorithm – 16 nodesScalability of ant algorithm – 20 nodes

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.