General Upper Bounds on the Running Time of Parallel Evolutionary Algorithms
This work provides theoretical tools for optimizing parallel evolutionary algorithms, which is incremental for researchers and practitioners in evolutionary computation.
The authors tackled the problem of analyzing the running time of parallel evolutionary algorithms with spatially structured populations, developing a method based on the fitness-level approach to derive upper bounds on expected parallel running time and estimate speedup, with example applications showing that speedup increases with topology density and sparse topologies like ring graphs can achieve significant speedup without substantially increasing function evaluations.
We present a new method for analyzing the running time of parallel evolutionary algorithms with spatially structured populations. Based on the fitness-level method, it yields upper bounds on the expected parallel running time. This allows to rigorously estimate the speedup gained by parallelization. Tailored results are given for common migration topologies: ring graphs, torus graphs, hypercubes, and the complete graph. Example applications for pseudo-Boolean optimization show that our method is easy to apply and that it gives powerful results. In our examples the possible speedup increases with the density of the topology. Surprisingly, even sparse topologies like ring graphs lead to a significant speedup for many functions while not increasing the total number of function evaluations by more than a constant factor. We also identify which number of processors yield asymptotically optimal speedups, thus giving hints on how to parametrize parallel evolutionary algorithms.