A Survey on
Special Topics on Genetic Algorithm (GA)
by Akira Imada (November 2004)
Data is not a knowledge but just a set of data. To simply put,
Data Mining is to extract a knowledge from a set of data.
Multi Objective GA.
Here, we see two studys where Fuzzy Logic is used in Data Mining based on
Artificial Immune System,
- [1]
Andersson "Applications of a Multi-Objective Genetic Algorithm to
Engineering Design Problems."
In this paper we find a simple algorithm with a pseude code in Section 2.
The point is that after selection of two parents and create one child:
"Find the individual in the entire population that is most similar to the
child. Replace that individual with the new child if the child's ranking is
better, or if the child dominates it."
To know what is "dominate" see, for example
Let me summarize it as
A candidate solution is called a non-dominated iff there is no ohter better
solution w.r.t all the objectives.
Further more [1] refer to [3] as for "how to rank the individual" as follows.
As there is no single objective function to determine the
fitness of the different individuals in a Pareto optimization,
the ranking scheme presented by Fonseca and Fleming is employed,
and the "degree of dominance" in attribute
space is used to rank the population. Each individual is given a rank based on
the number of individuals in the population that are preferred to it, i.e.
for each indi-vidual the algorithm loops through the whole population counting the number of
preferred individuals. "Preferred to" is implemented in a strict Pareto sense, but one
could also combine Pareto optimality with the satisfaction of objective goal levels, as
discussed in Fonseca and Fleming. To be more in detail, see:
Sequential Niching
1. initialize
equate the modified fitness function with the raw fitness function
2. run the gA using the modified fitness function and keep the best
individual found in the run,
3. update the modified fitness function to give a depression in the region
near the best individual producing a new modified fitness function
4. if the raw fitness of the best individual exceeds the solution threshold display this as
a solution.
5 if not all solutions have been found return to step 2.
modify fitness
initially m0 =f
at hte end of each run the best individual sn determin a single-peak derating function g(x,sn)
then M_{n+1} = M_n x G(x,s_n)
as G we have two alternatives
power: G_p(x,s) = (d_{xs}/r)^\alpha if d_{xs}