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Research Mentor

Dr.Sanza T. Kazadi
Jisan Research Institute
JRI Research Mentor
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People constantly require methods of generating optimal configurations of complex systems. Many methods have been created for this purpose, such as genetic algorithms, simulated annealing algorithms, and taboo search. Recently, a new method of functional optimization based upon the use of conjugate schema has been proposed. This search algorithm is part of a larger class of elimination algorithms (not to be confused with branch-and-bound) for searching large-dimensional spaces for optimal solutions.

One specific use of optimization methods is in protein design, where the physical attributes of the system are fixed enough to attempt a branch-and-bound method of optimization. In protein design, a protein backbone is given, and the search algorithm is used to determine the rotamers (side chains) and rotamer positions that would yield the optimum protein, or protein with the minimum amount of energy. This problem has been difficult to tackle because of the vast number of possible rotamer positions and identities.

Conjugate schema are a relatively new concept first applied to genetic algorithms. These mathematical structures allow one to determine the subspaces of a given search space which are functionally disparate from others. This allows one to optimize disparate subspaces separately, treating the cross product as a direct product, and effectively reducing the size of the search space.

We have already successfully tested a conjugate schema based search algorithm on a real protein design problem and several random data sets of the same format. The real protein design data were reduced from 71 million possibilities to 3, with retention of the minimum (what we were searching for). The random data were reduced by a minimum of 93 percent. We have also explored other applications of conjugate schema, such as correlated ring lattices, otherwise known as "neighbor rings." Currently work includes the generation of a general algorithm, and its application to artificially generated protein data.


S. Rhee, J. Chung, S. Kazadi, H. Lin. Conjugate Schema-Based Search, JRI Technical Report 1, 1999.

S. Kazadi, H. Lin, P. Hung, D. Lee, D. Tsikata, J. Ogita, V. Huang. Conjugate Schema in the HP Heteropolymer Model of Protein Folding and Protein Design, Complexity International, v7, 1999.(postscript) (PDF)

Kazadi, S. Conjugate Schema and Basis Representation of Crossover and Mutation, Evolutionary Computation, v6(2), 129-160, 1998.(postscript) (PDF)

Kazadi, S. Conjugate Schema in Genetic Search. Proceedings of the Seventh International Conference on Genetic Algorithms, San Mateo, CA, Morgan Kaufmann Publishers, pp. 10-17, 1997.(postscript) (PDF)

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