Abstract
A hybrid of genetic algorithm and local optimization was tested on a massively multimodal spin-lattice problem involving a huge configuration space. The results are good, and global optima will probably be achieved in a sizeable proportion of cases, especially if a selection scheme is applied that maintains genetic diversity by introducing a spatial separation between the members of the population. If we use single-point cross-over, the performance of the algorithm depends strongly on the order of the units corresponding to individual spins in the bit strings that the genetic part of the algorithm processes. Due to some interplay between the genetic algorithm and local optimization, the best performance is achieved with a peculiar ordering, while the results with the most obvious ordering are much worse. I introduce an ordering-invariant crossover operation that gives excellent performance: it almost always yields states of the lowest energy. I expect this or some similar crossover operation to work well in the hybrid scheme for many other problems as well.
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Pál, K.F. Genetic algorithm with local optimization. Biol. Cybern. 73, 335–341 (1995). https://doi.org/10.1007/BF00199469
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DOI: https://doi.org/10.1007/BF00199469