Ants first evolved around 120 million years ago, took form in over 11,400 different species, and are considered one of the most successful insects due to their highly organised colonies, sometimes consisting of millions of ants.
One particular notability of ants is their ability to create "ant streets". Long, bi-directional lanes of single file pathways in which they navigate landscapes in order to reach a destination in optimal time. These ever-changing networks are made possible by the use of pheromones which guide them using a shortest path mechanism. This technique allows an adaptive routing system which is updated should a more optimal path be found or an obstruction placed across an existing pathway.
Computer scientists began researching the behaviour of ants in the early 1990's to discover new routing algorithms. The result of these studies is Ant Colony Optimisation (ACO), and in the case of well implemented ACO techniques, optimal performance is comparative to existing top-performing routing algorithms.
This article details how ACO can be used to dynamically route traffic efficiently. An efficient routing algorithm will minimise the number of nodes that a call will need to connect to in order to be completed thus; minimising network load and increasing reliability. An implementation of ANTNet based on Marco Dorigo and Thomas Stützle has been designed, and through this a number of visually aided tests were produced to compare the genetic algorithm to a non-generic algorithm. The report will finally conclude with a summary of how the algorithm performs and how it could be further optimised.
Electronic communication networks can be categorised as either circuit-switched or packet-switched. Circuit-switched networks rely on a dedicated connection from source to destination, which is made once at start-up and remains constant until the tear-down of the connection. An example of a circuit switched network would be the British Telecoms telephone network. Packet-switched networks work quite differently, however, and all data to be transmitted is divided into segments and sent as data-packets. Data-packets can arrive out of order in a packet-switched network, with a variety of paths taken through different nodes in order to get to their destination. The internet and office local area networks are both good examples of packet-switched networks.
A number of techniques can be employed to optimise the flow of traffic around a network. Such techniques include flow and congestion control, where nodes send packet acknowledgements from destination nodes to either ramp-up or decrease packet transmission speed. The area of interest in this report concentrates on the idea of network routing and routing tables. These tables hold information used by a routing algorithm to make a local forwarding decision for the packet on the next node it will visit in order to reach its final destination.
One of the issues with network routing (especially in very large networks such as the internet) is adaptability. Not only can traffic be unpredictably high, but the structure of a network can change as old nodes are removed and new nodes added. This perhaps makes it almost impossible to find a combination of constant parameters to route a network optimally.
Packet-switched networks dynamically guide packets to their destination via routing tables stored in a link state and are selected via a link state algorithm.
A link state algorithm works by giving every node in the network a connectivity graph of the network. This graph depicts which nodes are directly connected. Values are stored for connected nodes in a map which represents the shortest path to other nodes. One such link state algorithm used in network routing is Dijkstra's algorithm. When a path between two nodes is found, its weight is updated in the table. Should a shorter path be found, the new optimal weight will be updated to the table, replacing the old value.
The algorithm allows traffic to be routed around the network whilst connecting to the least number of nodes as possible. The system works, but doesn't take into account influx of traffic and load balancing.
By replacing Dijkstra's algorithm with a generic algorithm, paths taken by calls could be scored by how short of a path they took; that way, if they were queued on a busy network, they would perform badly. Consequently, other paths would score relative and be chosen. This would work in real time, and allow the routing system to adapt as packets are transmitted. ANTNet uses virtual pheromone tables much like when an ant follows a path, dropping pheromone to re-enforce it. The quicker the ants move down a path, the more throughput of ants, thus a greater concentration of pheromones. In the same way, pheromone tables in ANTNet allow fast routes to score a higher chance of being selected, whilst the less optimal route scores a low chance of being selected.
The idea behind ANTNet is when a call is placed, an Ant will traverse across the network using a link-state deterministic algorithm. Every node holds a pheromone table for all other nodes of the network. Each pheromone table holds a list of table entries containing all the connected nodes of the current node.
To begin with, each possible path has an even likelihood of being chosen. An ant is placed on a network of 4 nodes, with the source node 1 and destination node 2. A chance mechanism is invoked and a path is chosen.
Figure 3.1 - The network graph
Table 3.1 - Pheromone table for node 1
In this case, node 2 has been selected [Figure 3.2] and the ant arrives at its source destination.
The ant then moves and updates the pheromone tables for the visited nodes with a higher (and more mathematically biased) value. This would be calculated for Figure 3.2 and Table 3.2 in the following way:
- Node 2 was the final destination
- It took 1 hop to get to its destination
- Divide 1 (hop) by 100: 100%
- Add 100 to the probability value of node 2 (currently 33.3333): 133.3333
- Add the values of the other nodes to 133.3333 (133.3333 + 33.3333 + 33.3333): 200 (approximately)
- Calculate the ratio: ratio = 100/200 0.5
- Set the probability of the node to its current value multiplied by the ratio
- Node 2: 133.3333 * ratio (0.5) = 66.6666%
- Node 3: 33.3333 * ratio (0.5) = 16.6666%
- Node 4: 33.3333 * ratio (0.5) = 16.6666%
- Node 2 (66.6666%) + Node 3 (16.6666%) + Node 4 (16.6666%) = 99.9999%
The system isn't 100% accurate as the total will never add up to exactly 100%, but it will be close enough to allow accuracy within the level required.
The following diagram depicts how the path and pheromone table after the update has taken place.
For the purpose of this program, a bi-directional, un-weighted topological network consisting of 30 nodes has been created, and closely resembles the British Synchronous Digital Hierarchy (SDH) network. After a basic number of parameters have been set, the simulation is run. Firstly, all pheromone tables are defaulted to equal weights, and then calls are generated and placed on the network. Initially, the routes chosen are random. If a call cannot connect to a node, it is forced to wait, and the wait counter is enumerated to reflect the quantum (in timer ticks). Once a node has reached its destination node, it will work its way backwards, altering the local node's pheromone table as it traverses. The shorter the route taken, the greater increase in probability given to its table entry in the pheromone table. This happens repeatedly until the weight of the fastest node is shifted such that slower routes have a very low probability of being chosen.
Note: in order to compile and run the program, you will need to download dotnetcharting from dotnetcharting.com
- ANTNet On/Off - Switches the algorithm on and off
- Simulation speed - 1 tick p/s - 1,000 tick p/s (or as near speed as the system can run)
- Total calls to make - Number of completed calls before simulation termination
- Maximum concurrent calls - Number of calls allowed at the same time
- Node capacity - The number of calls a node can route at once
- Call duration - The length (in ticks) of a call
- Reduce I/O - Bypasses the network visualisation to increase simulation speed
- Return on connection - Returns the node immediately to source after connection
- Real-time network load visualisation - View node ID, capacity, and routing state (blue = OFF)
- Graphing facility with labeling and simulation overlay
- Render pheromone tables to HTML
MainForm - The GUI for the application
DrawPanel - The real-time network visualisation custom control
Global - Contains static variables that are accesses by the application
Node - Represents a node and holds an array of
PheromoneTable objects for routing
Call - Represents a call on the network and holds a source and destination node
Simulation - Represents a completed simulation and is used for creating graphs
PheromoneTable - A routing table for a
The network contains 30
Nodes, and each
Node contains an array of
PheromoneTable objects, one for every other
Node in the network (29). Every
PheromoneTable contains an array of
TableEntrys, one for each
Node connected to the current
The following diagram represents the relationships between classes in the program:
Updating the pheromone table:
public int ProbablePath(ArrayList VisitedNodes)
Random r = new Random(Global.Seed);
double count = 0;
double Lastcount = -1;
ArrayList tempTEVector=new ArrayList();
Node n = Global.Nodes[tableEntry[i].NodeID];
val = r.NextDouble()*val;
count += ((TableEntry)tempTEVector[i]).Probablilty;
if(val>Lastcount && val < count)
Returning the next node via the pheromone table:
public void UpdateProbabilities(double newVal, int EntryTableNodeID)
t = tableEntry[j];
total += t.Probablilty;
total += newVal;
t = tableEntry[j];
t.Probablilty += newVal;
double ratio = 100/total;
tableEntry[j].Probablilty *= ratio;
public PheromoneTable(Node n, int conns)
this.NodeID = n.ID;
this.tableEntry = new TableEntry[conns.Length];
tableEntry[i] = new TableEntry(conns[i]);
tableEntry[i].Probablilty = (100 / (double)conns.Length);
The following tests will illustrate how the ANTNet algorithm affects the routing of traffic. These tests will show the effectiveness of the algorithm against the system running without ANTNet. Since it is possible to switch nodes on and off, a number of test comparisons will be done to show how ANTNet can improve the routing of a network when paths are no longer valid and new routes have to be chosen.
These tests have been run with the following parameters:
- ANTNet On
- Simulation speed -1,000 tick p/s
- Total calls to make - 5000
- Maximum concurrent calls - 60
- Node capacity - 35
- Call duration - 170 (the length (in ticks) of a call)
- Reduce I/O - bypasses the network visualisation to increase simulation speed
- Return on connection - returns the node immediately to source after connection
ANTNet vs. non-ANTNet
The first test contains two simulations:
- Simulation 1 (Orange) - ANTNet algorithm OFF
- Simulation 2 (Blue) - ANTNet ON
From this simulation, it is clear that even by the first 500 calls completed, ANTNet has reduced the average number of hops by approximately 1.5 nodes. This is made more apparent by the end of the simulation where the best paths are made more biased as a choice, and are re-enforced as the optimal route, resulting in ANTnet improving network performance by almost 3.5 hops.
Figure 5.1 - Non-adaptive algorithm (Orange) vs. ANTNet algorithm (Blue)
To view the algorithm from a different perspective, the following graph depicts the system running with the ANTNet algorithm off and then activated on the 2,000th call. This can be identified by a label, and follows with a decline of average hops by almost 2.
Figure 5.2 - ANTNet activated after the 2000th call
Before an ant returns back to its source node, an optimisation technique of loop elimination can be invoked. The problem with loops is that they can receive several times the amount of pheromones than they should, leading to the problem of self re-enforcing loops.
Figure 5.3 - Loop removal (Blue) vs. non-loop removal (Orange)
Figure 5.3 shows two simulations:
- Simulation 1 (Orange) - Loop elimination OFF
- Simulation 2 (Blue) - Loop elimination ON
From this test, loop elimination has reduced the average number of hops by 1 node with a much more stable adaptation. This would mean that when alternative paths must be chosen, the loop elimination algorithm responds much faster than the regular implementation.
Note: Both lines show the actual number of nodes traversed, and not the number after loop removal.
It is important to simulate how the network adapts when nodes are removed from the network. Static routing tables may hold the shortest path, but they don't necessarily take into account network traffic and nodes that are offline. Three simulations have been run on the program to display how the system adapts compared to a non-adaptive algorithm.
Figure 5.4 - Adaptive vs. non-adaptive algorithm
Simulation 1 (Orange)
This is a normal run of the simulator to create optimised pheromone tables for the next two simulations.
Simulation 2 (Blue)
Adaptive algorithm switched OFF.
Nodes 14, 15, and 17 are switched off as these are the main northern access hubs into London, so traffic needs to be diverted to the west of England. Since the network is non-adaptive, the pheromone tables are biased towards nodes that have been taken offline and subsequently being continuously redirected and taking longer journeys every time. This increase is displayed in Figure 6.4 by the blue line.
Simulation 3 (Green)
Adaptive algorithm switched ON.
Nodes 14, 15, and 17 are still switched off, but since the network is now set to adaptive, the pheromone tables are readjusted and the system learns alternative routes. This can be seen in Figure 6.4 by the green line.
If anyone has any questions, bugs, or suggestions, then please make a comment.
- Appleby, S., Steward, S. (1994). Mobile software agents for control in telecommunication networks. In BT Technology Journal, Vol. 12, No.2.
- ANTNet: A Mobile Agents Approach to Adaptive Routing. Gianni Di Caro and Marco Dorigo.
- Ant-based load balancing in telecommunication networks. Ruud Schoonderwoerd1,2, Owen Holland3, Janet Bruten1, and Leon Rothkrantz.
- Data Networks. Bertsekas, D., Gallager, R. (1992).