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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.
2 A HYBRIDIZED GA FOR COST
ESTIMATION IN A BMS
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
restraints.
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 X−1. 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
A HYBRIDIZED GENETIC ALGORITHM FOR COST ESTIMATION IN BRIDGE MAINTENANCE SYSTEMS
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