Problem

When calibrating a WaterGEMS model in Darwin Calibrator, "Fitness" values are presented in the calibration solution results.

What does the fitness mean and what is a good value for it? How do I know if a solution is acceptable based on the fitness?

Solution

Fitness numbers are just relative numbers, useful for comparing different solutions for a given Calibration run in a given model. For example in the screenshot above, an optimized run is set to save three solutions, and the fitness values shown for each solution enable you to compare them. Generally speaking you want them to be as low as possible but their value depends on things like size of system, number of points, quality of data, etc.

There isn't a set rule of thumb for what a "good" fitness value is, aside from knowing that the lower the fitness number, the better (closer to field data.) You may need to use some engineering judgment to assess your calibration results. You can examine the detailed solution results (model results vs field data, modified roughness/demand/status), and/or export the solution to the model and take a closer look. You may conclude that the results are good, with possibly a few manual tweaks. Or, you might decide that further calibration is necessary, to get the fitness even lower.

The Help documentation has further details on the formulas used to calculate the values. From the help topic "GA-Optimized Calibration Tips",

The GA calculates fitness of each trial solution according to the defined objectives for the optimization problem. GA only uses objective means to decide what constitutes a fit solution and what constitutes a less fit solution. The GA has no way of subjectively assessing a solution other than the methods (weightings) built into the definition of the fitness calculation. The best solution found by a GA shouldn’t be blindly accepted as being correct. To any single optimization problem there are likely to be many solutions that closely match the required objectives. Due to the fact that the GA has no concept of what constitutes a fit solution, other than its performance against the defined objectives, the GA may produce solutions that are impractical. That is, the GA cannot think for the engineer, it can only search the combination of choices that are presented to it. If the engineer doesn’t provide the GA with high quality data and enough or sufficiently flexible options to consider, then the GA may not be able to find a satisfactory solution. Conversely if the GA is presented with too many possibilities to try (e.g., in Darwin Calibrator, if you define excessively large adjustment group ranges combined with small adjustment increments and a large number of adjustment groups), then the efficiency of the GA search is reduced, and the likelihood that the GA will find the correct answer is also greatly reduced. GA is a highly sophisticated search technique, but despite all of its great features, GA still must be used with a degree of engineering judgment and skill. Only then can the engineer expect the GA to find solutions that are not only fit but are practical and likely to represent the real life situation as accurately as possible.

Calibration Criteria (Head/flow per fitness point)

In the "Calibration Criteria" tab of your Calibration study, you will see default values for "Head per fitness point" and "Flow per fitness point" which are related to how the fitness is calculated.

These values are fairly arbitrary. In US units they are nice round numbers (1.0 ft and 10.0 gpm), and the values in metric units are simply converted from the default US units.

The main thing to consider is their size relative to each other. So what we are saying is that, in terms of calibration, a pressure within 0.3 m (the default Head per fitness point) of a measured pressure is as good as a flow within 0.63 l/s (the default Flow per fitness point) of a measured flow.

These Head and Flow per fitness point values (if you analyze the Fitness equation) are weighting factors for Pressure/HGL and Flow that are used in order to indicate the relative importance or impact of each type of difference between field data and model results.

In consequence and in addition to some statistics criterions, in order to define these weighting factors (instead default values) you must consider the precision (max. error for an established range of measurement) of the devices used to obtain field data. For example, if you used an insertion water flow meter (low accuracy) it may not make sense to define a Flow per fitness point lower than the accuracy of this instrument. The situation is different if you use an accurate/expensive electromagnetic flow meter for example.

See Also

Using Darwin Calibrator

Water Model Calibration Tips

(Forum post) Darwin Calibrator Fitness Number

(Forum Post) Darwin Calibrator Fitness Number

(Forum post) Head and Flow per fitness point