CHAPTER 4
ANALYSIS OF PHEROMONE
DECAY TECHNIQUES FOR ACO
BASED ROUTING
Routing packets on a network is a difficult task and its efficiency depends on the
routing algorithm used. It involves calculating the shortest and most efficient path
between sender and receiver in order to route a packet with minimum effort. Data
packets rely on many intermediate nodes to reach a destination. ACO algorithm
through route discovery finds multiple paths to destination. The data packet decides
the shortest path based on the highest pheromone intensity found in their respective
pheromone tables.
The major challenge in ACO is fine tuning of the pheromone trials. If not handled
efficiently then, even after the route failure in the network, the packets try to follow
the same path (since there are still some traces of pheromone concentration on that
path) and leads to packet drop. The pheromone intensity of each path in the network
should be decayed parallel with the pheromone deposition laid by the artificial ants,
otherwise there will be a probability of losing quality solutions or a possibility of
retaining stale paths due to slow decay rate.
ACO deals with artificial systems, which are inspired from food foraging behavior of
real ants, which can find optimal solutions despite changes in the environment. The
main idea is indirect communication between the ants by means of pheromone trails,
which helps them to find the shortest path between their nest and food. A major
problem with ACO algorithm is “stagnation” or premature convergence to local
optimum [66]. This occurs when all the ants try to follow the same path to reach the
destination (since there is more pheromone). This when applied to MANETs comes to
a convergence state (equilibrium) and attracts all the data packets to follow the same
path, which leads to congestion. The next packet without any awareness of the
37
congestion follows a non-optimal path and loses its packets due to frequent packet
drops.
To mitigate the problem of congestion in ACO algorithms, different methodologies
[16, 58] were adopted and are categorized as follows.

Privileged pheromone laying

Pheromone-heuristic control

Pheromone control
In privileged pheromone laying approach, a selected subset of ants are used to update
pheromone values on the best path. This reduces the probability of ants following the
stagnant paths that are non-optimal and congested due to overload.
In the Pheromone–heuristic control approach, ants not only try find the best path
based on pheromone concentration on that edge, but also the other factors like queue
length, delay and distance. These factors alter the selection of the best path and avoid
the stagnation.
The last approach for stagnation problem is controlling the pheromone concentration.
Pheromone control can be done in many ways.
1. Evaporation
2. Aging
3. Limiting Pheromone
4. Smoothing Pheromone
The above pheromone control approaches discourage non-optimal paths and reduce
the influence from past experience. In the Evaporation approach, all the edges with
certain pheromone concentration evaporate as the time increases. This is done by an
evaporation factor ‘p’. Evaporation not only removes the stale entries, it also balances
pheromone concentration in optimal paths. This helps other ants to survey new paths
(better).
Aging is another technique to reduce stale entries in the network. In the Aging
technique, older ants deposit lesser pheromone as compared to younger ants. Older
38
ants are those ants that have taken a longer time to reach the destination. Aging and
Evaporation techniques aim at finding the new best path when there is congestion. In
the Limiting pheromone technique, pheromone is limited for every edge by placing an
upper bound. A variant of the Limiting pheromone is pheromone smoothing. In this
approach the pheromone is increased along an edge as by Eqn (4.1).
 i , j t'   i , j t   .( max   i , j t) ………………………………… (4.1)
Where δ varies from 0 to 1.New
 i, j
is calculated based on pheromone max bound,
previous pheromone concentration and tunable factor δ.
It is also observed that a smaller amount of pheromone is deposited gradually until the
upper bound is reached. Evaporation is performed in a uniform manner on all edges.
This technique seems to be more effective in avoiding the generation of a dominant
path.
4.1
Network Design
The network is represented as G = (V, E), a connected graph with ‘V’ nodes and an
edge ‘E’ connecting two nodes. An edge is directional, starting at a vertex x  V and
ending at y  V. Thus, each edge is described by an ordered pair of vertices e={x,y} 
E. The neighbors of node ‘x’ can be defined as a set Sx containing all other nodes for
which ‘x’ is the starting point and other nodes act as ending points ;Sx = {y  V: {x,
y}  E; x  Sx; Sx  V . Every pair of links between two nodes can be thought as
bidirectional link if x  Sy and y  Sx.
The metric of optimization is delay. In order to apply trail update/decay in networks
routing, routing tables are replaced by tables of probability, which are also called as
pheromone tables, as shown in Table 4.1. These probabilities are used by ants to
explore a network and possibly find new and better routes.
The goal of MANET is to find the shortest path between a source node Vs and
destination Vd, where Vs and Vd belong to V. The path length is given by the number
39
of nodes along the path. Each node maintains a table keeping track of the amount of
pheromone on each neighbor edge/ link e (i,j) represented as φi,j.
The table may be visualized as a matrix
with rows representing neighbor nodes Ni
and columns representing destination nodes Di. Table entries depend on pheromone
updation, pheromone decay. Size of the table depends on the number of source and
destination nodes. This table captures different aspects of the network dynamics at
any given node.
Table 4.1 Pheromone table for node ‘V i ’
Neighbor
Node
Destination Nodes
1
2
3
…………
1
P11
P12
P13
…………. P1N
2
P21
P22
P23
…………. P2N
3
P31
P32
P33
…………. P3N
………….. ……
PL1
N
…..
PL2
D
………….
PL3
…………. PLN
The probability at node Vi can be computed based on the packet forwarding equation
as follows
pi,j =φi,j / (Σφi,j )
pi,j =
0
for j εNi
Otherwise
The integral solution for the above combination of equation decides the path to be
followed or the path in which packet has to be forwarded. pi,j is the probability that the
node i, will get selected by current node for packet forwarding . Once pi, j for all i’s
where i represents the neighbor of the current node are calculated, Maximum among
the pi,j are calculated and node corresponding to the Maximum pi,j is determined as the
node to which packet has to be forwarded.
40
The value of φi,j is incremented by ‘γ’ by the ant packet which moves along the path
Vi to Vj. That is φi,j = φi,j + γ. The concentration φi,j indicates the usage of the link.
Parallel to it the concentration of the pheromone should decrease with time, at every
constant interval ‘t’, the value of φi,j between the nodes Vi to Vj is decreased by Decay
Factor(DF). The rate of increase in pheromone (γ) is greater than the rate of decrease
in pheromone.
4.2
Structured chart for pheromone update
The structure chart shown in Figure 4.1 depicts the structure and calling relationships
in the implementation of a pheromone update. The pheromone update is responsible
for updating pheromone matrix according to the pheromone deposition by the data
packets. It also includes different pheromone decay techniques for ACO.
Pheromone update mechanism acts as a balancing act in the form of exploitation of
previous experiences and exploration of improved paths, whereas decay helps in
removing stale routes.
Pheromone
Update
Adjacent
Matrix
Adjacent
Matrix
Pheromone
Deposition
Pheromone Decay
Techniques
3
1
2
Polynomial
Decay
Exponential
Decay
Discrete
Decay
Fig 4.1 Structured chart for Pheromone Update.
41
4.2.1
Pheromone decay
Swarm Intelligent (SI) adopts pheromone decay in order to provide a negative
feedback mechanism to the system. This mechanism helps in removing old solutions.
However, past SI based routing algorithms have either adopted decay on regular basis
or decay upon packet arrival. In the proposed work an analysis is made to understand
the decay rates in adhoc wireless network.
The pheromone intensity of each path in the network is decayed or evaporated
continuously using different decay techniques. Pheromone evaporation is necessary in
order to avoid local maxima problem.
Three different decay techniques used in the research are Discrete Decay, Polynomial
Decay and Exponential Decay. Different techniques are selected as they behaved
pretty much same when they were used in networks which were static. However when
this concept is applied in MANETs there was significant changes in the performance
of the network. Constant values with which both Discrete and Polynomial
were
implemented was decided after many trials with different values as shown in Eqn
(4.2), Eqn (4.3) and Eqn (4.4).
Technique 1: Discrete decay
φi,j = φi,j (φi,j -0.1,0) ……………………… (4.2)
Technique 2: Polynomial decay
φi,j = φi,j *0.95 ……………………………… (4.3)
Technique 3: Exponential decay
φi,j = φi,j * e-τ;……………………………….. (4.4)
Discrete decay is the scalar value for a path between nodes denoting the pheromone
concentration where it is decremented by 0.1 from the original pheromone value as
shown in Eqn 4.2. Polynomial decay multiplies with 0.95 every time till it reaches
some threshold as shown in Eqn 4.3. Exponential decay multiplies with exponent
42
value with the power of – τ (Time difference between the current time and last
successful transaction (Rank of Freshness of the link).
Different parameters used for analysis are pheromone intensity and probability of
choosing path. With this methodology, it is found that the decay techniques become
application specific (i.e The rate of decay needed in the algorithm to cope up with the
QoS needed and to maintain the stable network with minimum packet losses depends
on various factors such as the traffic intensity, velocity of the nodes, direction of
nodes, the frequency at which the nodes are coming in/out of the neighborhood of
another node etc.,).
4.3
Efficient fine tuning pheromone technique to alleviate
stagnation problem
Evaporation is fine tuned based on the stability factor of the node in the vicinity of the
node that forwards the packet. During packet forwarding time, each node calculates
the ‘hello’ sent and ‘hello’ received by its neighboring nodes and calculates the
stability ratio shown in Eqn (4.5). The links are virtually classified into two categories
viz., stable links and unstable links. The extent of decrement is determined by time
difference between the current time and last successful transaction (Rank of Freshness
of the link) and also the stability factor, which is generic to any link. Its value is
decided after running through several models of analytics and routing scenarios.
∆ = (Hello Replied / Hello Sent) * 100 ………………………. (4.5)
An exploration on approximation of pheromone value in the exponential decay can be
controlled using additive value which helps in controlling the trail evaporation.
Various values for τ has been tested and came to the conclusion that the following
values forms the most fitted curve for the decay rate. Hence, they are taken as the
testing parameters under decay rate. ‘Δ’ is the stability factor which acts as
pheromone controlling agent for exponential decay as shown in Eqn (4.6).
φi,j = φi,j .( e-τ + ∆)………………………………………..…….. (4.6)
43
This technique helps the AWN to overcome stagnation problem, it also reduces the
control overhead and has efficient packet delivery ratio. ‘∆’ is tunable based on the
application and the node mobility i.e if ‘∆’ =0.1 instead of 0.001 the behavior of the
pheromone being decayed can be controlled based on whether the decay should be
fast or slow.
4.4
Results and discussion
The pre-processing is done using MATLAB. Pre-built functions are used wherever
possible. Using pre-built functions, as opposed to writing, debugging, and validating
our own functions, will save a great deal of programming time. Customized programs
are written in C/C++ to understand and fine tune the mathematical operations.
Three different decay techniques Polynomial, Discrete and Exponential are used to
measure change of probability and pheromone intensities for selecting an optimal
path. A major problem in ACO is stagnation which causes heavy traffic on the
optimal path. To avoid this, the saturation level for a pheromone (0.89) was found to
be more appropriate as compared to other values tested. If the pheromone level has
reached the saturation limit then the next optimal path is chosen to forward the
packets. The parameters, change of probability and pheromone intensities of the
selected new path are analyzed.
4.4.1
Discrete decay technique
Using the Discrete decay technique, the Probability of optimal path selection and the
pheromone intensity with saturation has been determined and plotted against the
period (simulation time) and results shown in Figure 4.2 (a) and Figure 4.2 (b). The
shortest path (Blue), the intermediate path (Green) and the longest path (Red) (Many
paths can be considered, however for research purpose and to analyze the behavior of
decay technique, first three optimal paths are considered for routing purposes )
calculated in terms of delay are also shown in the same figure.
44
Fig 4.2 (a) Pheromone intensity vs. period
(b) Probability of path selection vs period
Figure 4.2 (a) shows the pheromone intensity profiles as derived for discrete decay
pheromone intensity (Eqn.4.2) as a function of simulation time for the three different
optimal paths. The Figure 4.2 (b) shows the probability of selection of different
optimal paths namely short, intermediate and long paths for data packet flow.
It can be seen from Figure 4.2 (a) that in the shortest path, the pheromone intensity
first increases rapidly and then saturates with the intensity becoming constant with
time. Figure 4.2 (b) shows that the probability of short optimal path selection first
reaches a maximum value of 0.89 and starts decaying with time by a factor of (0.35)
when the pheromone intensity remains constant. When the shortest path is found,
most of the data packets follow that path. It is also seen from the figure that the
probability of the intermediate optimal path increases (0.2) during the saturation phase
of the pheromone intensity and the data packets also choose an intermediate path for
propagation. It is also found that during the saturation phase of pheromone intensity,
the probability of selection of longest optimal path increases by a small amount (0.15)
and some data packets also choose the longest optimal path for propagation. The
discrete decay of pheromone intensity (Due to slow pheromone decay) shows that for
45
both intermediate and longer optimum paths probability is significant and both the
paths are chosen for data packets propagation in the network.
4.4.2
Polynomial decay technique
Analysis is performed using the Polynomial decay technique as shown in Figure 4.3
(a) and Figure 4.3 (b).
Fig 4.3 (a) Pheromone intensity vs. period (b) Probability of path selection vs. period
It can be seen from the Figure 4.3 (a) that in the shortest path, the pheromone intensity
first increases rapidly and then saturates with the intensity becoming constant with
time. Figure 4.3 (b) shows that the probability of short optimal path selection (first
reaches a maximum value 0.85 and starts decaying with time by a factor of 0.25 when
the pheromone intensity remains constant. When the shortest path is found, most of
the data packets follow that path. It is also seen from the figure that, the probability of
the intermediate optimal path increases by a factor of 0.2 during the saturation phase
of the pheromone intensity and the data packets also choose intermediate path for
propagation. It is also found that during the saturation phase of pheromone intensity,
the probability of selection of longest optimal path increases by a very small amount
0.02 and some data packets also choose the longest optimal path for propagation.
46
The Polynomial decay of pheromone intensity shows (Due to slow pheromone decay)
that for intermediate optimum paths probability is significant and the path is chosen
for data packets propagation in the network. This technique can be adopted (as
compared to Discrete decay) where the mobility of nodes is very less. However in
network like MANET (where mobility is found) due to large number of pheromone
traces in intermediate paths might lead to congestion and packet drops.
4.4.3
Exponential decay technique
Similar analysis is performed using the Exponential decay and results shown in Figure
4.4 (a) and Figure 4.4 (b). It can be seen from the Figure 4.4 (a) that in the shortest
path, the pheromone intensity first increases rapidly and then saturates with the
intensity becoming constant with time. Whereas the Figure 4.4 (b) shows that the
probability of short optimal path selection first reaches a maximum value 0.85 and
starts decaying with time by a factor of 0.15 when the pheromone intensity remains
constant.
When the shortest path is found, most of the data packets follow that path. It is also
seen from the figure that the probability of the intermediate optimal path increases by
a factor of 0.1 during the saturation phase of the pheromone intensity and the data
packets also choose an intermediate path for propagation. It is also found that during
the saturation phase of pheromone intensity, the probability of selection of the longest
optimal path remains constant and indicates that there is no data packet flow in the
longest optimal path. The exponential decay of pheromone intensity shows that
intermediate path probability is significant and only an intermediate path is chosen for
data packets propagation in the network.
47
Fig 4.4 (a) Pheromone intensity vs period (b) Probability of path selection vs period
The probability of selection of optimum paths for the three decay techniques is
summarized in Table 4.2. It may be noted from the Figure 4.2, Figure 4.3, Figure4.4
and Table 4.2 that the probability of selection of the longest optimal path for discrete
pheromone decay is ~0.15, for polynomial decay reduces to ~0.02 and becomes
almost zero for exponential decay of pheromone intensity.
This leads to the
elimination of data packet flow in the longest optimal path for the exponential
pheromone decay.
Table 4.2 Probability of path selection for different decay techniques
Technique /
Path Selection
Discrete
Decay
Polynomial
Decay
Exponential
Decay
Best Path
0.35
0.2
0.15
Intermediate path
0.25
0.2
0.02
Longest Path
0.15
0.1
~0
In exponential decay it is found that most of the data packet flow follows the shortest
optimal path and intermediate path, thus prohibiting the longest path for the data
packet flow. From these findings it may be suggested that the exponential decay
48
model for the pheromone intensity is more efficient compared to the discrete or
polynomial decay models for AWN networks. Out of the many decay functions
analyzed, the exponential decay techniques in ACO are more applicable for dynamic
networks like AWNs. The limitation of this technique is that pheromone evaporates
(uniformly) very quickly after some time leaving no traces for the data transmission.
Hence, fresh route discovery is established to know the destination address. This
causes more control overhead and makes bandwidth inefficient. To deal with this
problem, controlled exponential evaporation is adopted which fine tunes evaporation
based on the stability of the node.
It is clearly evident from Figure 4.5 that for the Exponential Pheromone Decay, the
data packet flow is maximum along the shortest path. Whereas for both Polynomial
and Discrete pheromone decay, all the three paths - short, intermediate and longest
paths are selected for the data packet flow. From the data presented in Figure 4.5, it
can be concluded that the Discrete decay and Polynomial decay are not preferable for
congestive networks.
Fig 4.5 Analysis of different decay techniques
4.4.4
Efficient fine tuning pheromone technique
The analysis has been continued further by using different values of the stability
factor ‘∆’ (here we are talking about more stable nodes who can help in transmitting
49
packet to destination ) to establish the probability of selecting the best path in the
network for the exponential decay of pheromone by fine tuning the pheromone
concentration to alleviate stagnation problem. The stability ratio ‘∆’ has been varied
from 0.001 to 0.1 to determine the optimum value of ‘∆’ that can be used for
confining the data pocket flow to the shortest (Blue) and the intermediate optimum
paths. The table shows the variation of the probability of selecting the best path for
different values of ‘∆’.
Table 4.3 Probability of path selection for different stability factor
SlNo
∆
1
0.001
0.15
0.03
0.001
2
0.002
0.16
0.15
0.001
3
0.003
0.18
0.16
0.001
4
0.004
0.16
0.15
0.002
5
0.005
0.18
0.13
0.002
6
0.006
0.17
0.11
0.001
7
0.007
0.17
0.14
0.005
8
0.008
0.18
0.14
0.01
9
0.009
0.09
0.08
0.18
10
0.01
0.1
0.09
0.12
11
0.1
0.03
0.14
0.13
Best Path Intermediate Path Longest Path
It is clearly evident from the Table 4.3 that for the lower range of values of ‘∆’
between 0.001- 0.008 the probability of selecting the longest optimum path (Red)
remains very low < 1% comparable to exponential pheromone decay. This indicates
that for ‘∆’ values < 0.008 the flow of data packets is confined to the shortest and the
50
intermediate optimum paths and there is no data packet flow in the longest optimum
path.
For values of ‘∆’> 0.09 the probability of selection of the optimal path for shortest
path and the intermediate path decreases dramatically and it is found that the packet
flow on the longest path starts increasing rapidly. This indicates that the probability of
selection of optimal path for the exponential decay is limited by the values of ‘∆’.
The flow in different paths can be controlled by changing the values of ‘∆’ between
0.001 - 0.008 for which the packet flow remains confined to the shortest and the
intermediate paths. Once the ‘∆’ value increases above 0.009 the data packet flow in
the longest path increases rapidly and the packet flow in three different paths comes
closer to the discrete Pheromone concentration decay model.
Further to highlight the observations made in the analysis, the pheromone intensity
and the probability of selection of the three optimal paths namely shortest (Blue),
intermediate (Green) and longest (Red) paths are plotted for the two different values
of ‘∆’= 0.08 and 0.09 and shown in Figure 4.6(a) , Figure 4.6 (b) and Figure 4.7 (a),
Figure 4.7 (b).
It is clearly seen in Figure 4.6 (b) for values of ‘∆’=0.08 the probability of selection of
the longest optimal paths is <1%, where as for the ‘∆’=0.09 as seen in the Figure 4.7
(b) the probability of selection of the longest optimal path increases to 18%. This
indicates that for ‘∆’ > 0.09, the Exponential decay model for the pheromone
concentration is not adequate to control the data packet flow in the AWN networks.
51
Change of Probability
0.8
800
0.7
700
0.6
600
0.5
probability
Pheromone Intensity
Growth of pheromone intensity
900
500
400
0.4
0.3
300
0.2
200
0.1
100
0
0
10
20
30
period
40
50
0
60
0
10
20
30
period
40
50
60
Fig 4.6 (a) Pheromone intensity vs period (b) Probability of path selection vs period
Growth of pheromone intensity
Change of Probability
1000
0.7
900
0.6
800
0.5
600
probability
Pheromone Intensity
700
500
400
300
0.4
0.3
0.2
200
0.1
100
0
0
10
20
30
period
40
50
60
0
0
10
20
30
period
40
50
60
Fig 4.7 (a) Pheromone intensity vs period (b) Probability of path selection vs period
In the present work, a detailed analysis of ACO based pheromone decay techniques
such as Discrete, Exponential and Polynomial has been carried out. Pheromone
intensity and probability of choosing path for packet transmission are used as
52
parameters for the analysis. It is found that the Discrete decay is not preferable for a
congestive network as it leaves a large amount of pheromone traces. The polynomial
decay technique chooses a better path and avoids the longest path (which leads to
delay at the time of packet delivery).
The Exponential decay has been found to exhibit better performance compared to
Discrete and Polynomial decay techniques, However it loses the pheromone traces
very fast. The efficient fine tuning of the exponential decay model can be achieved by
using stability factor ‘∆’. Introduction of the stability factor ‘∆’ improves AWN
performance in terms of packet delivery and routing overhead. This is due to
controlled evaporation of exponential decay (which otherwise lead to losing of best
path due to fast evaporation).In the case of Exponential Pheromone Decay the
pheromone traces evaporate faster leading to finding new paths to the destination.
The Exponential Pheromone Decay process can be controlled by fine tuning the decay
rates by introducing the node stability factor ‘∆’. The probability of the selection of
different paths of the data packet flow for different node stability factor ‘∆’ have been
computed.
4.4.5
Decay Rate (τ) Used in pheromone decay technique Versus PDR
Fig 4.8 PDR versus Combined view of decay rates
53
Different Decay rate values for τ associated with the stability factor, collectively
deciding the extent of pheromone decay are tested using network simulator software
developed as part of this work. These values are tested under various possible realtime scenarios usually faced in Mobile Ad hoc Networks such as mobility pattern of
nodes, velocity, and packet delay, etc. The ACO without pheromone decay technique
will experience congestion whereas the ACO with pheromone decay technique will
avoid the congestion due to efficient decay (controlled manner) of pheromone on all
the links. Figure 4.8 shows the obtained results for different values of decay rate and
it shows that the value 0.001 is best suited in most of the scenarios. Also from the
figure it is observed that the decay rate is acceptable for the range of values 0.001–
0.003 in most of the situations. The values of 0.01 and 0.1 are applicable in very rare
scenarios of MANETs. The decay rates decide the extent of decrement and also
periodicity is the factor which accounts to final PDR of the particular scenario.
54