Dimitrios K. Karpouzos

A multipopulation genetic algorithm to solve the inverse problem in hydrogeology

The inverse problem of groundwater flow is treated with an automatic method that can produce several alternative solutions at once. During their joint optimization, these solutions can exchange information in order to maintain some diversity and thus avoid a systematic premature convergence toward a single local minimum. Although genetic algorithms are capable of doing this, they have not often been used in groundwater inverse optimization. First, a specific multipopulation genetic algorithm is developed. It is then tested on two synthetic cases of steady state flow with transmissivity values extending over 4 orders of magnitude. The first test is nonparametric and optimizes as many parameters as those used to define the reference case. The second test uses a sort of “pilot point” parametrization. The optimization is carried out on a limited number of perturbations that are interpolated and superimposed on an initial transmissivity field. In view of the good quality of the results, these initial attempts provide incentives to further develop genetic algorithms in groundwater inverse problems.

Combined use of BEM and genetic algorithms in groundwater flow and mass transport problems

The boundary element method (BEM) can be used very efficiently, in solving groundwater flow problems. Genetic algorithms (GAs) constitute a very efficient optimization tool. In this paper, BEM and GAs have been combined to find optimal solutions in three classes of commonly encountered groundwater flow and mass transport problems: (a) determination of transmissivities in zoned aquifers (inverse problem), based on a restricted number of field measurements; (b) minimization of pumping cost from any number of wells under various constraints; and (c) hydrodynamic control of a contaminant plume, by means of pumping and injection wells. Application examples show that the proposed combination is very efficient in optimizing development and protection of groundwater resources.

A Set of New Benchmark Optimization Problems for Water Resources Management

In this paper, we introduce four new benchmark problems, which are based on rather common optimization issues of water resources management. These problems have the following features: a) adjustable difficulty, to cover a wide range of common engineering problems b) physical background familiar to scientists working on water resources management c) known global optimal solution and known range of values of the objective function d) easy application and e) low computational volume (analytical solution of the respective groundwater flow model). First we calculate the optimal solutions of these problems and then we evaluate their difficulty and their suitability as benchmarking tools, based on theoretical considerations and on the performance of a genetic algorithm and a simulated annealing code in finding their optimal solutions. Results show that the proposed set of benchmark problems is useful for evaluating heuristic optimization codes in the field of water resources management.