Risk based groundwater remediation design using a tunneling optimization algorithm

The uncertainty in hydraulic conductivity has been incorporated into an optimization scheme for groundwater remediation design. The approach involves the generation of a set state-variable realizations using hydraulic conductivity values drawn from a known probability distribution. Given a possible remediation design, violations of preset constraints for each scenario incur penalty costs. These costs are added to the objective function. This optimization technique is an effective way to account for uncertainty of the hydraulic conductivity. The objective function for a pump-and-treat remediation design subject to gradient constraints, is convex, and one optimal solution exists for this problem. The objective function subject to concentration constraints, however, is non-convex with multiple local minimums within the feasible region. An innovative method of optimization for non-convex problems is implemented in this paper. This method, called the tunneling method, determines the global optimal solution of an objective function with multiple local optima.