Dynamic optimal groundwater management considering fixed and operation costs for an unconfined aquifer

The simulation and planning of unconfined aquifers are much more complex than those of confined aquifers because the former are nonlinear. However, unconfined aquifers are important in groundwater management because they are the upper aquifers of a groundwater system. Computing an optimal strategy for the management of a groundwater system is a nonlinear, discrete and dynamic optimization problem if the total costs include both fixed and operating. The nonlinearity is caused by the objective function and the simulation of the groundwater flow of an unconfined aquifer. The computational difficulty makes conventional groundwater management models unable to solve the problem without simplification. Therefore, this investigation proposes a groundwater management model that can determine the optimal network and pumping rates of the pumping wells by simultaneously considering fixed and operating costs. The proposed model involves a novel hybrid algorithm that combines the Genetic Algorithm (GA) and Constrained Differential Dynamic Programming (CDDP), a kind of the optimal control theorem. The main part of the hybrid algorithm is the GA, in which each chromosome represents a potential network design of the pumping wells. The CDDP is used to compute the optimal pumping rates and operating costs associated with each pumping network. A two dimensional finite element model is embedded in the CDDP to simulate the groundwater flow. Hypothetical cases are considered to demonstrate the computational capability. The results of the simulation reveal that the proposed algorithm can solve the complex problem using affordable computation resources. Comparing the management strategy obtained by the proposed algorithm with that computed using an algorithm that considers only the operating cost indicates that the proposed algorithm significantly reduces the costs of implementing management strategy. Accordingly, the proposed model can be employed to obtain a cost-effective strategy, including network design and pumping policy, for managing a groundwater system.