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7.7 Automated Optimization 239

Original concentrations

Reacted concentrations

Transport through system

Figure 7.6 Lagrangian Time-Driven Method (TDM)

as in Eulerian methods, the concentration and size of water parcels are tracked as they
travel through the pipes. With each time step, the farthest upstream parcel of each pipe
elongates as water travels into the pipe, and the farthest downstream parcel shortens as
water exits the pipe.
Similar to the discrete volume method, the reactions of a constituent within each par-
cel are calculated, and the mass and flow entering each node are summed to determine the
resulting concentration. If the resulting nodal concentration is significantly different from
the concentration of a downstream parcel, a new parcel will be created rather than elongat-
ing the existing one. These calculations are repeated for each water quality time step until
the next hydraulic change is encountered and the procedure begins again.

7.7 AUTOMATED OPTIMIZATION
WaterGEMS has the capability to optimize a model based on field data or design criteria.
Oftentimes, water utility managers will use a model to make design decisions or gather
field data to calibrate a model. This process is typically a trial-and-error approach in which
the modeler will modify a few parameters in a model to either compare design solutions
based on cost or benefit, or have the model better predict the real conditions. Because this
can be very time consuming, WaterGEMS has the capability to create many potential solu-
tions and provide a measure of which solution is the “better” solution based on specific
boundary conditions and input criteria.
WaterGEMS employs a genetic algorithm search method to find “better” solutions
based on the principles of natural selection and biological reproduction. This genetic algo-
rithm program first creates a population of trial solutions based on modeled parameters.
The hydraulic solver then simulates each trial solution to predict the hydraulic grade line
(HGL) and flow rates within the network and compares them to any input criteria. Based
on this comparison, a goodness-to-fit value is assigned. This information is now used to
create a new population of trial solutions. These solutions are then again used to find new
solutions. The program compares these solutions to the specific boundary conditions and
input criteria until the goodness-to-fit value is optimized. In other words, comparisons are
made until no better solution can be generated.

7.7.1 Model Calibration

Model calibration is the process of modifying parameters or values in a model so it better
matches what is happening in the real system. The calibration of water distribution models
is very complicated. Many values and parameters that are unknown are needed at any one
time to reduce the discrepancy between the model and the real system. Oftentimes the pipe