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Full-Text Articles in Physical Sciences and Mathematics
The Eigenvalues Of A Tridiagonal Matrix In Biogeography, Boris Igelnik, Daniel J. Simon
The Eigenvalues Of A Tridiagonal Matrix In Biogeography, Boris Igelnik, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
We derive the eigenvalues of a tridiagonal matrix with a special structure. A conjecture about the eigenvalues was presented in a previous paper, and here we prove the conjecture. The matrix structure that we consider has applications in biogeography theory.
A Dynamic System Model Of Biogeography-Based Optimization, Daniel J. Simon
A Dynamic System Model Of Biogeography-Based Optimization, Daniel J. Simon
Electrical and Computer Engineering Faculty Publications
We derive a dynamic system model for biogeography-based optimization (BBO) that is asymptotically exact as the population size approaches infinity. The states of the dynamic system are equal to the proportion of each individual in the population; therefore, the dimension of the dynamic system is equal to the search space cardinality of the optimization problem. The dynamic system model allows us to derive the proportion of each individual in the population for a given optimization problem using theory rather than simulation. The results of the dynamic system model are more precise than simulation, especially for individuals that are very unlikely …