APPROXIMATE MIXED-INTEGER NONLINEAR-PROGRAMMING METHODS FOR OPTIMAL AQUIFER REMEDIATION DESIGN

An optimal aquifer remediation design model employing a nonlinear prog ramming algorithm was developed to find the minimum cost design of a p ump-and-treat aquifer remediation system. The mixed-integer nonlinear programming model includes the discontinuous fixed costs of system con struction and installation as well as operation and maintenance. The f u;ed cost terms in the objective function have been approximated by co ntinuous functions of the decision variables using a polynomial penalt y 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 d esign problem show that a combined well field and treatment process mo del that includes fixed costs has a significant impact on the design a nd cost of aquifer remediation systems, reducing system costs by using fewer, larger flow rate wells. Previous pump-and-treat design formula tions 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 res ults were compared to two alternative approximate mixed-integer nonlin ear programming methods for solving optimal aquifer remediation design problems, the pseudo-integer method and the exponential penalty coeff icient method. The polynomial penalty coefficient method obtains the s ame solutions and performs as well as or better than the exponential p enalty coefficient method. The polynomial penalty coefficient method a lmost always results in better, less expensive designs and requires si gnificantly less computer time than the pseudo-integer method.