SECOND-ORDER CONE OPTIMIZATION APPROACH TO GROUNDWATER QUANTITY MANAGEMENT

J.M. Ndambuki,∗ T. Terlaky,∗∗ C.B.M. Stroet,∗∗∗ and E.J.M. Veling∗∗∗

Keywords

Optimization, modelling, second order cone, stochastic, multi- objective, groundwater ∗ Vaal University of Technology, Private Bag X021, Vanderbijl- park 1900, South Africa; e-mail: jmndambuki@yahoo.co.uk ∗∗ McMaster University, 1280 Main Street West, Hamilton, On- tario, Canada, L8S 4LT; e-mail: terlaky@mcmaster.ca ∗∗∗ Delft University of Technology, Stevinweg 1, NL-2628 CN Delft, The Netherlands; e-mail: ed.veling@citg.tudelft.nl Recommended by Dr. Syed Rizwan

Abstract

As demand for potable water increases due to either increase in world population, contamination of surface water bodies or both, groundwater aquifers are constantly being viewed as the ultimate alternative source for additional quantities. Moreover, as these aquifers get exploited, it is becoming mandatory to incorporate man- agement schemes to ensure sustainable exploitation of such sources. However, because of the complexity of the earth material that forms such aquifers, it has become evident that deterministic management approaches are not suitable for designing such management schemes. This has resulted in researchers developing stochastic management methodologies which recognize the fact that measurement data used to characterize the groundwater aquifers is not only scarce but also uncertain due to, for example, measurement errors. The most popular approach of addressing this uncertainty has been through the Monte Carlo approach and its variants. However, Monte Carlo approach is CPU intensive and therefore only a few realizations can be considered. In this paper, we introduce a novel optimization technique which explicitly takes into account the uncertainty in the hydraulic conductivity of a groundwater aquifer. In this approach, we transform the uncertain groundwater management problem into a Second Order Cone Optimization problem which is then solved. Furthermore, we extend the methodology to address both a single objective and multi-objective groundwater quantity optimization in the presence of uncertainty. Results from an hypothetical example demonstrate that solutions obtained through this approach are ro- bust, meaning that small perturbations in the hydraulic conductivity values will not aﬀect the optimal solutions computed.