Khaled Bashir Shaban
Department of Computer Science and Engineering, College of Engineering, Qatar University, Doha, Qatar
Abdunnaser Younes, Nathan Good, Mohammed Iqbal and Richard Lourenco
Department of Systems Design Engineering, Faculty of Engineering, University of Waterloo, Canada
Keywords: Hybridized Genetic Algorithm, Cost Estimation, Bridge Maintenance Systems.
Abstract: A hybridized genetic algorithm is proposed to determine a repair schedule for a network of bridges. The
schedule aims for the lowest overall cost while maintaining each bridge at satisfactory quality conditions.
Appreciation, deterioration, and cost models are employed to model real-life behaviour. To reduce the
computational time, pre-processing algorithms are used to determine an initial genome that is closer to the
optimal solution rather than a randomly generated genome. A post-processing algorithm that locates a local
optimal solution from the output of the genetic algorithm is employed for further reduction of computational
costs. Experimental work was carried out to demonstrate the effectiveness of the proposed approach in
determining the bridge repair schedule. The addition of a pre-processing algorithm improves the results if
the simulation period is constrained. If the simulation is run sufficiently long all pre-processing algorithms
converge to the same optimal solution. If a pre-processing algorithm is not implemented, however, the
simulation period increases significantly. The cost and deterioration tests also indicate that certain pre-
processing algorithms are better suited for larger bridge networks. The local search performed on the
genetic algorithm output is always seen as a positive add-on to further improve results.
There is an increasing need for immediate and long-
term infrastructure renewal of provincial and
municipal highways and roads, buildings, water
supply systems, wastewater treatment facilities,
sanitary and storm sewers, and bridges and
overpasses. The gross value of these assets
amounted to $286.2 billion in 2007. The need of the
renewal is caused in part by the large scale boom in
infrastructure that occurred 30 to 60 years ago. The
average life of these structure ranges from 28.2 years
for highways and roads to 43.3 years for bridges and
overpasses (CBC News, 2008). As such,
governments have the arduous task of budgeting for
a backlog of repairs and reconstructing of existing
infrastructure. To limit the current budgets,
alternative systems are presented to seek the optimal
cost per cycle solutions to support the repair or
reconstruction of the aging infrastructure.
Once built, bridges receive little maintenance,
unlike other infrastructures, such as roads and water
infrastructure, which are maintained or repaired
periodically. Changing weather conditions and the
steady rise in traffic levels have caused existing
bridges to depreciate at a much higher rate.
According to a 2006 Statistics Canada study, bridges
are at 49% of their useful life (Charles Mandel,
2007). Saeed Mirza in (Charles Mandel, 2007) states
that the current situation is disastrous and estimates
that $100 billion should be invested to upgrade
existing bridges and other infrastructure. A 2007
report issued by the Residential and Civil
Construction Alliance of Ontario warns that 40% of
Ontario’s bridges will require significant repair over
the next few years (Bruce Campion-Smith, 2007).
The catastrophic collapse of the I-35 Bridge in
Minneapolis, Minnesota on August 2, 2007 has
increased public awareness of the importance of
maintaining bridges. Clearly there is an increasing
need to invest in bridge infrastructure.
Shaban K., Younes A., Good N., Iqbal M. and Lourenco R. (2010).
In Proceedings of the 12th International Conference on Enterprise Information Systems - Artificial Intelligence and Decision Support Systems, pages
DOI: 10.5220/0002974304280433
Traditionally, in bridge maintenance systems
(BMSs), experts use their judgment and experience
to determine which bridges to repair and the extent
of repair each year. However, as the number of
bridges increases, this task evolved into a complex
optimization problem that is well beyond the
abilities of even the most experienced experts. In
fact, this problem is a nondeterministic polynomial
(NP) problem, which is computationally intractable
for traditional methods. Genetic Algorithms (GAs)
have been shown to be effective in solving NP-hard
problems, and thus are good candidates for solving
this problem.
The bridge inventory contains a list of all the
bridges in the network. Each bridge component has a
condition rating. The deterioration and improvement
models quantify how much the bridge components
degrades or improves its condition each year,
depending upon whether a repair takes place or not.
The cost model determines how much a repair will
cost. This model depends on the current condition
rating of the bridge. All models occur over a
predetermined time period. The evolutionary
algorithms try to optimize (minimize) the total cost
spent over the time period. The total cost is
optimized by determining which bridges to repair
and which components on the bridge to repair.
The GA derives a solution based on a fitness
function and constraints. Parameters such as
mutation rate, the number of generations and
crossover rate are also to be tuned. The fitness
function is to minimize the overall repair cost for the
bridge network over the desired time period. The
overall repair cost is calculated by summing the
costs for each year. The other option was to make
the fitness function based on the quality of the
bridges. However, due to safety considerations, the
bridge quality was deemed better suited as a hard
constraint. Several constraints were added to the
implemented system including:
1. Repairs Constraint:
A bridge can only be repaired maximum of two
times over a 5 year period, or 5 times over a 20 year
period. This constraint reflects real life constraints.
Bridges that are repaired constantly incur higher
costs (both construction costs and user costs).
2. Condition Constraint:
The condition of a bridge cannot fall below 30. Fur-
thermore, a bridge cannot be repaired if its condition
exceeds 90. These conditions maintain a satisfactory
bridge quality level and eliminate the possibility of
repairing well-conditioned bridges.
3. Cost Constraint:
A predefined yearly budget is be defined. The yearly
budget is related to the number of bridges within the
system. This constraint reflects real life budget
In order to reduce the time to develop an
acceptable solution, some pre-processing of the data
must take place. The initial data set that the GA uses
to optimize the fitness function should be
conditioned to be within the ball park of the final
solution. For example, we know that in any given
year, because of budgetary limits, only several
bridges are repaired. Therefore, the GA chromosome
(i.e. bridges to repair) will initially be setup to repair
only a small percentage of the bridges per year. In
order to determine these initial values, we will use
fuzzy sets, among other approaches (to be
investigated). The fuzzy set outputs will be no
repair, light repair, medium repair and extensive
repair. They will correspond to the condition of the
bridge – the input fuzzy sets.
A post-processing algorithm can be used to
locate a local optimal solution. Genetic algorithms
are capable of determining the optimal solution.
However, even with the inclusion of pre-processing,
determining the optimal solution may take a
substantial amount of time. The post-processing
algorithm can determine a better solution by slightly
altering the bridge repair schedule (represented as
the genome). For example, if a heavy repair is made
in year X for a bridge, the post-processing algorithm
can determine if a local optimal solution is found by
downgrading the repair severity to a medium or light
repair, or altering the time or repair to year X+1 or
year X1. The post-processing algorithm can also be
used to check the output from the genetic algorithm.
An emphasis is made to limit the computations
required for the post-processing algorithm.
2.1 Pre-processing
The motivation behind pre-processing the genome is
to reduce the computational time required to produce
the optimal solution. Four pre-processing algorithms
were implemented.
The first algorithm randomly generates genome.
For any bridge/year combination, it has a 5% chance
of assigning a level 1 repair, a 3% chance of
assigning a level two repair, a 2% chance of
assigning a level three repair, and a 90% chance of
assigning no repair at all.
The second algorithm repairs 10% of the bridges
every year. If the bridge’s quality is below 35 it
assigns a level 3 repair. If the quality is between 35
and 50, it assigns a level 2 repair. If the quality is
above 50, it assigns a level 1 repair. After assigning
the repairs for each year, it recalculates the bridge
qualities for the subsequent years.
The third algorithm will repair any number of
bridges. If the bridge’s quality falls below 40, it will
be repaired. Given a five year study if this occurs in
the first year, a level 3 repair will be assigned. If the
quality falls below 40 in the second or third year, a
level 2 repair will be assigned. If it falls below 40 in
the fourth or fifth year, a level 1 repair will be
The fourth algorithm repairs a set number of
bridges each year. Given a five year study, three
bridges are repaired each year. It applies a level 2
repair to the worst bridge and level 1 repairs to the
other two bridges. It will not repair a bridge unless it
is below a quality of 50 and will not repair the same
bridge twice.
2.2 Post-processing
It was noticed during the testing that even with a
relatively small study size, the genetic algorithm
took a very long time to converge to the optimal
solution (6-7 hours). In order to combat this, a post-
processing algorithm was implemented. In these
cases, the post-processing algorithm can be run on
any results the GA produced before it was stopped to
improve upon those results.
The post-processing algorithm looks at each
repair that is being made, and examines the effect of
lowering it one level (e.g. level 3 repair to level 2, or
level 1 to no repair). If lowering the repair level does
not cause any bridge to fall below the quality
threshold of 30, it will be lowered. Otherwise it will
be kept at the same level. This is a local search that
is used to refine the genetic algorithm results.
2.3 Appreciation Model
After a repair, the quality of the bridge will increase.
The amount of increase is dependent on the severity
of the repair. There are three levels of repair in the
proposed system: light repair, medium repair, and
heavy repair. Light repair is used to recondition the
bridge elements; this includes but is not limited to
resurfacing the deck. Medium repair is used to
replace elements within the bridge. Elements can
include joints within the bridge structure. Heavy
repair is used to replace most of the bridge.
Given the limited information on the
deterioration of the bridges, all three types of repair
will produce a static improvement in the bridge
quality. For example, if a light repair is used on
bridge A, the quality of bridge A will increase by ten
points. A medium repair will result in an increase of
30 points. Heavy repair results in an increase of 50
points. All three types of repair are independent of
the age and existing condition of the bridge. The
maximum bridge quality after any repair is 90.
The formula used to calculate the condition of a
bridge after a repair is made is shown below and
Table 1 lists the i
and I constants for each repair
C bridge condition
P previous bridge condition
i condition improvement percentage
I bridge improvement
CP( i I
Table 1: Appreciation Model Constants.
Repair Level i
Light 15% 10
Medium 20% 30
Heavy 30% 50
2.4 Deterioration Model
The deterioration of the bridge is the process of
decline from its original condition under normal
operating circumstances (Abed-Al-Rahim, I. and
Johnston, W., 1995). This process excludes rare
phenomena such as natural disasters and includes
physical and chemical changes (Hatem Elbehairy,
2007) (Yang, Ming-Wing, 2007). Examples of each
include general wear to components of the bridge
like the deck and the bridge’s joints, and rusting on
bridge members.
Common factors which affect the rate at which a
bridge will deteriorate include the bridge’s age, the
average traffic levels, exposed environment
conditions, the design of the bridge, and the quality
of the material used to construct the bridge. The only
available information for this study is the bridge’s
age, its current depreciation, and it’s expected
remaining lifespan. As such, the depreciation model
will only reflect these parameters.
For this study a mechanistic deterioration model
(Hatem Elbehairy, 2007) will be employed. A
mechanistic model employs a known nonlinear
relationship in the form of Equation 2. The
mechanistic deterioration model is simple to
ICEIS 2010 - 12th International Conference on Enterprise Information Systems
implement and computationally inexpensive. The
values of A and B can be assigned or determined
using fuzzy inference. The mechanistic model
reflects changing deterioration per year, where the
deterioration rate decreases as the bridge gets older.
Ct Ae
Since the deterioration of the bridge is the
process of decline from its original condition under
normal operating circumstances, a simple decaying
exponential was used to approximate the
deterioration. In the formula used to calculate
deterioration shown in equation (2), the deterioration
is related to deterioration rate provided in the
original data. The inclusion of the deterioration rate
reflects the different rate of decay for each bridge.
The multiplier is a constant for each bridge. The
multiplier was modified until it conformed to a
deterioration rate found in various literature sources
on the subject.
The deterioration and appreciation models were
combined to produce a single model which updates
the condition of the bridges on a yearly basis.
C bridge condition
P previous bridge condition
d deterioration rate
m multiplier
2.5 Cost Model
The cost model is used to determine the costs
associated with repairing a bridge within the
network of bridges. Generally there are two cost
models associated with a BMS: the user cost model
and the repair cost model. The cost model used in
our approach will only look at repair costs. User
costs are extra costs which are paid by the bridge
user (i.e. financial cost of time spent in traffic). User
costs are omitted from our approach because they
are generally subjective.
Table 2: Repair Unit Costs.
The repair costs can be expressed either as a unit
cost or a percentage of the initial cost of the bridge.
Unit costs are associated with the costs of repairing
individual items of the bridge (Saito, M., and Sinha,
K., 1990). An example of user costs is shown in
Table 2. Our approach will determine the cost of
repair as a percentage of the initial cost. This
approach is less computational. Furthermore the
limited information provided for each bridge makes
the unit cost approach impossible to implement.
The formula to calculate the cost of a repair is
based on the initial construction cost of the bridge,
which was provided. The formula for the repair cost
is shown below and Table 3 lists the multiplier
constants for each repair level.
RC repair cost
C construction cost (specified for each bridge)
M repair type multiplier
Table 3: Cost Model Constants.
Repair Level M
Light 0.1
Medium 0.4
Heavy 0.6
Testing is focused on finding the best pre-processing
algorithm. The first step was to establish a set of
testing conditions which would allow us to properly
compare the different algorithms. We then changed
the testing conditions to observe the effect on the
optimal solutions.
To keep our testing consistent, we needed to fix
the number of bridges (study sample size) and the
number of years (study period). Although we had
data for 161 bridges, and could extrapolate the
bridge quality for any number of years using the
deterioration and appreciation models, we elected to
use a sample of 20 bridges over a 5 year period. The
crossover and mutation rate used for the genetic
algorithm was set at 0.5 and 0.1 respectively.
As mentioned, the main testing parameter will be
the pre-processing type. In addition to testing the
effectiveness of each pre-processing type, additional
tests will be conducted to determine the effects of
changing the deterioration rate and costs.
3.1 Pre-processing Algorithms
Although we created four pre-processing algorithms,
the first one, which was random, either failed to find
valid solutions or took a very long time to do so in
our testing. As a result, we concluded that this was
not a suitable method for pre-processing (as
expected) and focussed our attention on the
remaining three algorithms.
In order to compare the effectiveness of the three
remaining pre-processing algorithms, tests were run
that involved setting all the variables in the system
constant while only changing the pre-processing the
algorithm. Table 4 shows the systems settings for the
initial comparison.
Table 4: Initial Pre-Processing Comparison Settings.
Looking at the above table we see that the tests
were run for 8500 trials, which is a relatively short
period of time but sufficient enough to show a
system trend. Table 5 shows the results obtained
from running the tests with each pre-processing
algorithm over 5 runs.
Table 5: Initial Pre-Processing Results.
We can see that pre-processing algorithm 2 starts
in a state with the lowest total cost, among the three,
and finishes with the lowest total cost. Similarly, the
first pre-processing algorithm has the highest staring
and end total cost. This indicates that, with all
variables set, the quality of the starting state dictates
how good the end state will be, in a given amount of
Table 6: Optimized Pre-Processing Constants.
Of course, over a long enough time period all
solutions will converge to a global optimum, but our
concern is to determine which method will do this
the quickest or which method will produce the best
result in a given time frame.
To confirm that all methods will converge to an
optimum the tests were run for much longer. The
new systems constants are shown in Table 6.
The stop condition was changed from 8500 trials
to 30 minutes. The population size was reduced to
50 to reduce the consumption of computer memory.
The bridge repairs per year and yearly budget
constraints were reduced to find a solution with
fewer repairs. The random pre-processing algorithm
was also included. The test results are summarized
in Table 7.
Table 7: Optimized Pre-Processing Results.
The total cost converges to around $200,000 for
all of the pre-processing algorithms. This clearly
shows that there is a global optimum that is
eventually reached.
3.2 Other Parameter Testing
Changes to the cost and the deterioration models
were made to evaluate the effects on the optimal
solution determined in section 2.2. The random pre-
processing method was omitted from both tests.
The first test was to determine the effect of
changing the cost model. The repair type multiplier
for light repairs was changed to 0.2. Table 8 displays
the system constants used for the test. The test
results are shown in Table 9.
Table 8: Test Constants for Cost Model Testing.
The second test was to determine the effect of
changing the deterioration model. The deterioration
multiplier was changed from 10 to 5. Table 10
displays the system constants used for the test. The
test results are shown in Table 11.
ICEIS 2010 - 12th International Conference on Enterprise Information Systems
Table 9: Test Results for Cost Model Test.
Table 10: Test Constants for Deterioration Model Testing.
Table 11: Test Results for Deterioration Model Test.
As expected, the optimized total costs increased
for both tests. A more profound discovery is that the
pre-processing 2 algorithm outperformed the other
two algorithms for the deterioration model test. By
increasing the multiplier, the deterioration per year
increased significantly. As a result more bridges
required repair. Pre-processing algorithm 2 is better
equipped at handling larger bridge repair demands
since it is capable of repairing a constant number of
bridges per year. Pre-processing algorithms 3 and 4
will only repair the lowest quality bridges. If there is
a large number of bridges that fit this criterion in a
single year the algorithm may have difficulties
addressing all the bridges.
3.3 Post Processing Results
To demonstrate the effectiveness of the post-
processing algorithm, it was applied to the three
simulations for the network of 20 bridges over a five
year study term. The cost improved from $224,000
to $7,800.
Experimental tests showed that when a pre-
processing algorithm was applied prior to the genetic
algorithm, the genetic algorithm was able to obtain a
better solution in a fixed period of time than when
no pre-processing took place. More specifically, pre-
processing algorithms 3 and 4 generally resulted in
the best performance. However, when the
deterioration model was modified to increase the
rate of bridge deterioration, pre-processing
algorithm 2 was the top performer. This shows that
pre-processing algorithm two is the most flexible of
those tested. This is important, as different
municipalities or government may have very
different models for appreciation, depreciation and
repair cost. Pre-processing algorithm 2 is best
equipped to deal with these variations as the number
of bridges repaired is not static (as is the case in pre-
processing algorithms 3 and 4).
A post-processing algorithm was devised to
improve upon the genetic algorithm solution. While
the algorithm was implemented and preliminary
tests showed that it was successful in improving
upon the solution obtained by the genetic algorithm,
more testing is required with a wider range of
conditions to confirm that the post-processing
algorithm is effective.
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