Geology Reference
In-Depth Information
According to Eq. (13), the heuristic desirability
of going from node
i
to node
j
is inversely propor-
tional to the distance between
i
and
j
. By definition,
the probability of choosing a city outside N
k
i
is
zero. By this probabilistic rule, the probability of
choosing a particular connection
i
,
j
increases with
the value of the associated pheromone trail
τ
i
,
j
and
of the heuristic information value
η
i
,
j
.
The selection of the superscript parameters
α
and
β
is very important: if
α
=0, the closest cities
are more likely to be selected which corresponds
to a classic stochastic greedy algorithm (with
multiple starting points since ants are initially
randomly distributed over the nodes). If
β
=0, only
pheromone amplification is at work, that is, only
pheromone is used without any heuristic bias (this
generally leads to rather poor results (Dorigo &
Stützle, 2004).
al., 1992). In general, connections that are used
by many ants and which are parts of short tours,
receive more pheromone and are therefore more
likely to be chosen by ants in future iterations of
the algorithm.
CASE STUDY
The real world case study considered is the city of
Patras in Greece, which is used in order to define
both the problem of the inspection assignment and
the inspection prioritization. The city of Patras
is decomposed into 112 structural blocks having
different areas and built-up percentages, while
two different sets of inspection groups (crews of
inspectors) are considered. A non-uniform distri-
bution of damages is examined with respect to the
damage level encountered on the structures due
to a strong earthquake. Four areas with different
structural damage levels are considered: (i) Level
0 - no damages, (ii) Level 1 - slight damages,
(iii) Level 2 - moderate damages and (iv) Level
3 - extensive damages. The subdivision of the city
of Patras into 112 structural blocks and the mean
damage level for each region are shown in Figure
5. Damages are assumed to follow the Gaussian
distribution with mean value 0, 1, 2 and 3 for the
four zones of Figure 5. The final distribution of
damages over the structural blocks can be seen in
Figure 6, where a big circle denotes severe damage.
In order to account for the influence of the
distribution of the damages in the city's regions,
the formulation of the optimal assignment problem
given in Eq. (4) is modified as follows
Pheromone Update Rule
After all the
m
ants have constructed their routes,
the amount of pheromone for each connection
between
i
and
j
nodes, is updated for the next
iteration
t
+1 as follows
m
A
(
)
⋅
∑
k
τ
(
t
+ = −
1
)
1
ρ τ
( )
t
+
∆
τ
( ),
t
∀
( , )
i j
∈
i j
,
i j
,
i j
,
k
=
1
(14)
where
ρ
is the rate of pheromone evaporation, a
constant parameter of the method, A is the set of
arcs (edges or connections) that fully connects
the set of nodes and Δ
τ
k
i
,
j
(
t
) is the amount of
pheromone ant
k
deposits on the connections it
has visited through its tour T
k
, typically given by
( )
i
N
n
IG
SB
∑
1
[
]
1
min
d SB C D k DF k
k
(
,
)
⋅
( )
⋅
( )
(16)
k
if connection ( ,
i j
)
belongs to
T
i
k
k
∆
τ
i j
=
L
(
T
)
i
=
1
k
=
,
0
otherwise
(15)
where
DF
(
k
) is the damage factor corresponding to
each damage level, as shown in Table 10. Figures
7(a) and 7(b) depict the solutions obtained for the
The coefficient
ρ
must be set to a value <1 to
avoid unlimited accumulation of trail (Colorni et
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