XVIII International Conference on Water Resources
CMWR 2010
J. Carrera (Ed)
CIMNE, Barcelona 2010
DETERMINING PUMPING SCHEMES AND QUANTIFYING THE
IMPACT OF COMPUTATIONAL RESOLUTION USING A MIXED
INTEGER HYBRID OPTIMIZATION TECHNIQUE
Genetha A. Gray*, Kathleen R. Fowler† and Matthew W. Farthing‡
*
Sandia National Laboratories, Predictive Simulation R&D
P.O. Box 969, MS9159 Livermore, CA 94551-0969 USA
e-mail: gagray@sandia.gov
†
Clarkson University, Dept of Math and Computer Science
Box 5815, Potsdam, NY 13699-5815 USA
e-mail: kfowler@clarkson.edu, web page: http://people.clarkson.edu/~kfowler
‡
Coastal and Hydraulics Laboratory, US Army Corp of Engineers ERDC
3909 Halls Ferry Road, Vicksburg, MS 39180 USA
e-mail: Matthew.W.Farthing@usace.army.mil
Summary. Simulators are a useful tool for the study and behavior prediction of water
management scenarios. Moreover, simulation can paired with optimization in order to design
and control systems at minimum cost. This pairing of optimizer and simulator can introduce a
number of challenges to obtaining reasonable solutions. The objective function and
constraints rely on output from the simulator, and the simulator often requires the numerical
solution to a system of nonlinear partial differential equations. Various assumptions can be
made to simplify either the objective function or the physical system so that gradient-based
methods apply, however the incorporation of realistic objection functions can be
accomplished given the availability of derivative-free optimization methods. In this paper, we
will describe a means of hybridizing multiple derivative-free approaches in order to take
advantage of the benefits of multiple methods and more efficiently solve the problem.
We specifically target the mixed integer problem (MINLP) formulation of pumping scheme
determination. Here, the integer parameters represent the number of wells and the continuous
parameters represent the location and outputs of the wells. To address the needs of MINLPs, a
hybrid of a derivative-free sampling method and a genetic algorithm (GA) is constructed. The
GA carries forward a population of points that are iteratively mutated, merged, selected, or
dismissed. In the hybrid, the GA governs point survival, mutation, and merging as an outer
iteration. Then, during an inner iteration, individual points may improve themselves via a
local sampling optimization method applied to the real variables, with the integer variables
held fixed. The resulting algorithm is called EAGLS, Evolutionary Algorithm Guiding Local
Search. Here, we demonstrate EAGLS on challenging benchmark water supply problem and
consider performance for a range of simulation conditions, from under-resolved to highly
resolved.