Information Technology Reference
In-Depth Information
management problems; and Groundwater quality management problems. The first
group deals with the solution of parameter estimation problems defined above. It aims
to determine some hydro-geological parameter values through inverse modeling ap-
proach. The second group deals with the solution of groundwater hydraulic manage-
ment problems. The typical problems for this group are to maximize the total yield of
the aquifer system; or to minimize the total pumping costs to satisfy the given water
demand [4]. In the last group, the main objective is to solve the groundwater quality
management problems based on the historical observation data. Two typical problems
for this group are to solve the contaminant source identification problems [5], and to
determine the best remediation strategy to clean up the aquifer system [6]. Note that
the groundwater parameter estimation problem described in the first group must be
solved before solving the groundwater hydraulic and quality management problems
since hydro-geological parameter distributions are required to solve the governing
flow and transport equations.
The optimization problems dealing with the groundwater modeling usually have
non-linear and non-convex solution spaces [7]. For such problems, finding a global
optimum solution is not an easy task using traditional optimization algorithms since
they require some derivatives and initial values [6-8]. Therefore, meta-heuristic algo-
rithms are usually preferred for the solution of optimization problems dealing with
groundwater modeling.
Recently, Geem et al. [9] developed the meta-heuristic Harmony Search (HS) op-
timization algorithm which is based on the musical process of searching for a perfect
state of harmony. In the HS algorithm, musicians try to find the musically pleasing
harmony by performing several improvisations. The quality of the generated harmo-
nies is determined by aesthetic or artistic standards. In the optimization process, a
global optimum solution may be found by performing several iterations through dif-
ferent values of decision variables. The quality of the obtained solutions is evaluated
by an objective function. These are the main similarities between the musical im-
provisation and optimization. The main advantages of HS are: 1) HS does not require
complex mathematical calculations; 2) Programming HS is simple; 3) HS does not
require specifying the initial value settings; 4) HS can handle both discrete and
continuous decision variables without requiring gradients.
The objective of this chapter is to review the application of the HS optimization al-
gorithm to the solution of groundwater parameter structure identification problems. In
order to evaluate the performance of the HS algorithm, two published papers were
examined. The first paper [10] solves the parameter structure identification problem
using a combinatorial optimization scheme in which a Genetic Algorithm (GA) is
combined with a grid search and a quasi-Newton optimization algorithm. The second
paper [11] solves the same problem using HS based optimization model. The obtained
results indicate that HS requires fewer simulation runs and yields the same or better
solutions than GA.
The remainder of this chapter is organized as follows: first, the main structure and
computational structure of the HS algorithm is presented; second, how to apply the
HS algorithm to the solution of inverse parameter structure identification problem is
described; and finally, a comparison of HS and GA is performed.
Search WWH ::
Custom Search