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From: hariram@netcom.com (Harihanane Ramasamy)
Subject: Pareto optimality and genetic algorithm
Message-ID: <hariramDwtn5s.H1u@netcom.com>
Organization: NETCOM On-line Communication Services (408 261-4700 guest)
Date: Wed, 28 Aug 1996 00:10:40 GMT
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Recently there were lot of talk about genetic algorithm to 
multiobjective functions especially when they conflict each other.
I presented the following abstract in Protein Science and ICJAMM.

I implemented the algorithm and have obtained positive results. I 
acm currently working on testing other problems

Please give me feedback on this.

Thanks

hari
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An extended Genetic Algorithm

    A new genetic algorithm to search through the solution space
towards problems characterized with multi-objective functions that 
conflict each other is proposed. Such problems have charactersitics 
of "Pareto optimality".

    In this method, we address the issue by choosing a class of
problem (lattice search) with two conflicting objective functions.
A set of genetic algorithms have been developed, which uses
two fitness criteria to search through a model system's conformational
space on a three dimensional lattice.  In one case, two populations
"evolved" under the independent fitness criterion, allowing only
"mutations" and "selective reproduction".  "Recombination" was allowed
between the two, where the recombined partial solutions are selected
for fitness in their respective populations.

   The lattice is a simple "Knight-move" 2x1 rectangular lattice and
the model system is composed of a linear chain of 2x1 planes connected
at a single corner. "Mutations" are drawn from a set of six relative
neighboring plane lattice orientations.  Motivation for this model is
taken from the biological protein structure problem, where a protein
can be considered a simple linear chain of peptide planes (amino
acids) connected with two rotational degrees of freedom.  The design
of the two fitness functions was also motivated from this applied
problem. Folding of a protein chain may be considered a simple min-max
optimization of finding the structure that minimizes the number of
exposed hydrophobic amino acids and maximizes the number of peptide
chain Hydrogen bonds.  Test cases with solution space ranging from
6^26 to 6^53 resulted in intriguing lattice topologies, which look
very much like the restricted set of real world protein structures,
and thus supporting the utility of using conflicting fitness criteria
when they are potentially incongruent force "compromise" solutions.

   We are currently investigating the relative conformational search
efficiency and convergent behavior of this algorithm on other similar
problems.


