Keywords: artificial neural networks, differential evolution, agricultural nitrate pollution, soft-computing methodologies.

The formulation of complex management problems that take place in nature requires a large number of decision variables for the accurate representation of the physical system's conditions. Also, the optimal solution demands a large amount of computational time. The multi-dimensionality issues raised in the majority of environmental management problems are overcome using derivative-free optimization methodologies. Versatility, ease of implementation, robustness, fully automated implementation and ease of parallel computing are their characteristics that make them extremely powerful for the solution of complex environmental management problems.

In this paper, a differential evolution (DE) algorithm is combined with two types of artificial neural network (ANN) models (radial basis functions network and multi layer perceptron) in order to find the optimal pumping rates for a number of remediation wells, used for the containment of a contaminant plume in an aquifer. The ANN models are used as local surrogate models of the cost function for the optimization procedure in order to replace the costly exact computations of the flow field by inexact but fast approximations. The exact computation of the cost function is performed using the numerical solution of the flow equations for a period of 15 years in an unstructured grid. The large computation time needed for the evaluation of each candidate solution in the optimization procedure and the large number of evaluations imposed by the differential evolution algorithm result in a very costly procedure in terms of computation time, which can be accelerated by the use of sufficient approximation models. The paper presents how the suggested methodology is used to provide optimal strategies for the solution of high-risk contamination problems in physical systems such as the nitrate pollution in high-value agricultural land.

The first model managed to accelerate the optimization procedure with respect to the original DE algorithm without any approximation model. On the contrary the second approximation model failed to enhance the convergence rate of the algorithm, and this is attributed to the fact that no effort was spent to optimize its architecture and training procedure, which is left for future studies. The more automatic (and effective) use of the RBFN model shows its superiority with respect to the second model. Concerning the environmental problem at hand, the imposed maximum values of the pumping rates proved insufficient to assure the fulfilment of the imposed constraints for all observation locations. Additionally, a single remediation well is actually activated in the optimal solution, having as a result that large quantities of nitrates are still present within the plume. However, the primary goal of the design is obtained since further spreading of the nitrate pollution is avoided.

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