# An integrated global and local optimization approach for remediation system
design

*C Zheng, PP Wang*

University of Alabama, Department of
Geology, Tuscaloosa, AL 35487, USA
### Abstract:

A global optimization (metaheuristic) method, tabu search, is
integrated with linear programming to solve remediation design problems. This
integrated approach takes advantage of the fact that the global optimization
approach is most effective for optimizing discrete well location variables while
linear programming is much more efficient for optimizing continuous pumping rate
variables. In addition, an efficient forward solution updating procedure is used
to lessen the computational burden of the global optimization approach. With
this procedure, the new solution to a linear flow model perturbed by pumping is
obtained as the sum of a non-perturbed base solution and the solution to the
perturbed portion of the flow system, which can be derived directly without
running the flow model. Numerical results, based on a two-dimensional capture
zone design problem, show that the computation time can be reduced to a small
fraction of that required by the conventional approach, in which a forward
simulation model is run each time the objective function needs to be evaluated.
It is also demonstrated that the maximum number of wells allowed in a given
design has a significant effect on the total remediation costs (the total
remediation costs are nearly doubled when only one well is allowed instead of
the optimal number of six for the test problem). A Monte Carlo analysis, based
on 200 realizations of a log-normally distributed random hydraulic conductivity
field (the variance of LnT =1.0), further reveals that the total remediation
costs determined for the heterogeneous aquifer have a large uncertainty (the
ratio of standard derivation over mean = 0.4). The total remediation costs and
associated uncertainty are also shown to increase with the uncertainty of the
hydraulic conductivity field.

**AGU Index Terms: **1831 Groundwater quality; 1829 Groundwater hydrology;
6344 System operation and management; 6309 Decision making under
uncertainty

**Keywords/Free Terms: **Groundwater modeling,
simulation-optimization approach, tabu search, hydraulic containment

*Water Resour. Res.* 1998WR900032

*Vol. 35 , No. 1 , p. 137
*

*© 1998 AGU*