Dynamic optimal groundwater management with inclusion of fixed costs

Obtaining optimal solutions for groundwater resources planning problems, while simultaneously considering both fixed costs and time-varying pumping rates, is a challenging task. Application of conventional optimization algorithms such as linear and nonlinear programming is difficult due to the discontinuity of the fixed cost function in the objective function and the combinatorial nature of assigning discrete well locations. Use of conventional discrete algorithms such as integer programming or discrete dynamic programming is hampered by the large computational burden caused by varying pumping rates over time. A novel procedure that integrates a genetic algorithm (GA) with constrained differential dynamic programming (CDDP) calculates optimal solutions for a groundwater resources planning problem while simultaneously considering fixed costs and time-varying pumping rates. The GA determines the number and locations of pumping wells with operating costs then evaluated using CDDP. This study demonstrates that fixed costs associated with installing wells significantly impact the optimal number and locations of wells.