Optimized calibration is conducted by satisfying two type constraints, the hydraulic system constraints and calibration parameter bound constraints. The system constraints are a set of implicit equations that ensure the conservation of flow continuity at nodes and energy for the loops within a water distribution system. Each trial solution generated by the GA is analyzed using Bentley WaterGEMS hydraulic network solver.

The calibration bound constraints are used to set the minimum and maximum limits for the pipe roughness coefficients and junction demand multiplier. They are given as follows:

Pipes that have the same physical and hydraulic characteristics are allowed to be grouped as one calibration link, and one new roughness coefficient or one roughness coefficient multiplier is assigned to all the pipes in the same group. Junctions that have the same demand patterns and within a same topological area can also be aggregated as one calibration junction to which a same demand multiplier is calculated and assigned. Calibration parameters are bounded by prescribed upper and lower limits and adjusted with a user-prescribed incremental value. For example, a Hazen-Williams C value for a pipe or a group of pipes will be computed within a range of 40 to 140 and by an increment of 5. Demand multipliers may range from 0.8 to 1.2 by 0.1. Parameter aggregation is useful at reducing the calibration dimension, however caution needs to be exercised when grouping pipes and junctions, as this may affect the accuracy of the model calibration.