Approximate Mixed‐Integer Nonlinear Programming Methods for Optimal Aquifer Remediation Design

An optimal aquifer remediation design model employing a nonlinear programming algorithm was developed to find the minimum cost design of a pump‐and‐treat aquifer remediation system. The mixed‐integer nonlinear programming model includes the discontinuous fixed costs of system construction and installation as well as operation and maintenance. The fixed cost terms in the objective function have been approximated by continuous functions of the decision variables using a polynomial penalty coefficient method resulting in a nonlinear programming formulation of an otherwise mixed‐integer nonlinear programming model. Results of applying the new polynomial penalty coefficient method to an example design problem show that a combined well field and treatment process model hat includes fixed costs has a significant impact on the design and cost of aquifer remediation systems, reducing system costs by using fewer, larger flow rate wells. Previous pump‐and‐treat design formulations have resulted in systems with numerous, low flow rate wells due to the use of simplified cost functions that do not exhibit economies of scale or fixed costs. The polynomial penalty coefficient method results were compared to two alternative approximate mixed‐integer nonlinear programming methods for solving optimal quifer remediation design problems, the pseudo‐integer method and the exponential penalty coefficient method. The polynomial penalty coefficient method obtains the same solutions and performs as well as or better than the exponential penalty coefficient method. The polynomial penalty coefficient method almost always results in better, less expensive designs and requires significantly less computer time than the pseudo‐integer method.