In an ongoing project, global optimization techniques are applied to achieve a least-cost design of a groundwater management problem which includes not only well network design and construction but also the construction, operation and maintenance of the treatment plant. In particular, branch-and-bound methods combined with outer-approximation techniques guarantee a globally optimal solution to such problems. This approach has been successfully applied in the field. 

In a similar, but quite different, vein another project seeks to find least-cost design scenarios when aquifer parameters are known with uncertainty. Unlike other methods for accommodating parameter uncertainty, this method allows design constraints to be violated, but in so doing the selected design pays a penalty for this violation. The resulting technique, based upon the concept of robust optimization, is very dependent upon the form of the probability distribution assumed for the aquifer parameter uncertainty. Thus the suitability of various distributions is being examined and evaluated as part of this research effort. 

Parameter uncertainty also plays an important role in the least-cost design of groundwater quality monitoring strategies. By taking advantage of our knowledge of the physics of the groundwater system as well as available field data, it is possible to make new or modify existing monitoring network designs to take advantage of our totality of information. The mathematical vehicle that makes this possible is the time-correlated Kalman filter. Thus it has been demonstrated that by formally combining field data and groundwater modeling information significant reductions in monitoring costs are achievable. Idealized problems have been examined to date and a field application is pending. 

The evaluation and utilization of risk in groundwater remediation design is of enormous practical interest because of the potential cost savings a risk-based design can achieve. However, it is widely recognized that current techniques for risk evaluation that depend heavily upon the accurate evaluation of low probability events is of questionable utility. As an alternative to this approach one of our projects is dedicated to the exploration and evaluation of fuzzy set theory and fuzzy logic to evaluate risk and to incorporate it into groundwater remediation and monitoring design. In the proposed model a fuzzy expert system utilizes not only quantitative data but also expert knowledge. Such knowledge is normally available in the form of verbal statements in a natural language. Allowance must be made for the vagueness or fuzziness of many natural-language expressions.  The ongoing research is dedicated to the development and evaluation of an expert shell to assess the health risk at a groundwater contamination site and to provide the necessary design constraints to obtain an optimal risk-based remediation design.