Biology Reference
In-Depth Information
During the past five decades, the field of global optimization has
been growing at a rapid pace and many new theoretical, algorithmic, and
computational contributions have resulted (Horst and Pardalos, 1995).
Global optimization is concerned with the computation and characteriza-
tion of global minima (or maxima) of nonlinear functions. Global opti-
mization problems are widespread in the mathematical modeling of
real-world systems for a very broad range of applications. The majority of
problems can be described as some form of global optimization proce-
dures. In the gene selection problem, one would need to find out how to
form gene subsets to obtain the optimum classification response — chang-
ing one gene element in a given subset may improve the classification per-
formance of the subset at one testing sample, but worsen it at another.
An objective function is necessary to evaluate how close each gene
subset gets to the target requirement. The gene selection process involves
finding the gene subset that corresponds to the minimum (or maximum)
of the objective function. Plotting the objective function against the gene
search space of each gene element in the gene subset, one axis per gene
element would be needed, plus the orthogonal axis for the objective function.
The objective function plot would appear as a multi-peak, multi-variable
plot. Because there is an enormous number of interrelated possible gene
combinations, the best gene subset cannot be found by any simple
process. It is not obvious how to select the genes analytically to find the
best solution. The methods currently used in gene selection — such as
clustering, neighborhood analysis, and genetic algorithms (GAs) —
almost all depend on a starting condition, either selected by the user or
generated internally by the program, that is sometimes not obvious.
Changing the initial conditions will give a different result, and one has no
way of knowing how much improvement could be effected.
Currently available multi-variable optimization algorithms for select-
ing the gene subset may not give optimum solutions. Usually, those algo-
rithms obtain their final solutions either from optimizing a starting guess
or by techniques which may or may not involve a pseudo-random process
that gives different answers every time, depending upon the initial condi-
tions. A true global optimization algorithm should always find the very
best solution possible within the boundary conditions stipulated. The pos-
sibility of creating a true global optimization algorithm for a large number
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