**5. Application of simulated annealing for monitoring network design**

Monitoring network design in the context of groundwater quality management essentially means specifying the spatial location of monitoring wells and frequency of sampling. Since this is one of the most cost intensive part of most contaminated groundwater remediation problems, an efficient and cost effective design of monitoring network is essential. Monitoring of groundwater quality may be necessitated by a variety of objectives such as:


14 Will-be-set-by-IN-TECH

larger simulation runs. Because of the erroneous measurement data this problem may be ill-posed and the solution may not be unique. Therefore, lower objective function values do

In order to test the effectiveness of the competing methods based on accuracy of solutions produced, reconstructed release histories were compared to the actual release history after every set of 10,000 transport simulation runs. The results are shown in Figure 6. It can be seen that ASA based method is more efficient compared to GA based method after 10,000 and 20,000 simulation runs. However, as the execution time increases further with increase in number of simulation runs, the release histories produced by both methods become similar. This is also confirmed from the calculated values of NAEE presented in Table 4. As the execution time increases, the NAEE of ASA based method appears to increase only slightly. This could be due to statistical variation in the five different solutions and may be attributed to the input data error. Averaging over larger number of solutions may modify this inference. NAEE of GA based method consistently improves. However, the NAEE values obtained using

not always mean accurate reconstruction of the release histories.

**Figure 6.** Reconstructed Release Histories using the competing methods

**Table 4.** Normalized Absolute Error of Estimation

No. Of Simulation Runs NAEE (%)

GA ASA 6.86 4.25 6.53 4.18 5.82 3.83 4.26 3.62

ASA is still better in comparison.

4. Hydro-geological parameter estimation

Irrespective of the various objectives, the problem of monitoring network design can be formulated as an optimization problem [8, 20]. While designing a monitoring network for estimating unknown groundwater source characteristics, the objective of optimization can be to maximize the reliability of estimated source characteristics or to minimize the total number of monitoring locations in the network or both. Compliance monitoring is aimed at minimizing the area of contamination when the contamination is first detected at monitoring network or maximizing the probability of detection of contaminant in groundwater. Often, only the average values of hydro-geological parameters of the aquifer are known. This results in uncertainty in the modeling results. In order to better characterize an aquifer, spatial distribution of hydro-geological properties should be specified. This objective can be achieved by sampling hydro-geologic parameter at sufficient locations such that the interpolated values can represent actual hydrological parameters accurately. The objective of optimization in this case is to find the minimum number of samples required to accurately represent a population of random hydro-geological parameter values. In all such cases, Adaptive Simulated Annealing can be efficiently used as the tool for optimization. Our attempts to develop classical simulated annealing algorithm for optimal design of a dedicated monitoring network for enhancing the efficiency of source identification was successful to a large extent. However, the mixed integer nature of the decision variables in a monitoring network design problem makes the application of classical simulated annealing algorithm a bit constraining. Adaptive Simulated Annealing is more suitable to solve this monitoring network design problems.
