Multiple-vector self-adaptation in evolutionary algorithms

Self-adaptation is a common method for learning online control parameters in an evolutionary algorithm. In one common implementation, each individual in the population is represented as a pair of vectors (x, sigma), where x is the candidate solution to an optimization problem scored in terms of f(x), and sigma is the so-called strategy parameter vector that influences how offspring will be created from the individual. Experimental evidence suggests that the elements of sigma can sometimes become too small to explore the given response surface adequately. The evolutionary search then stagnates, until the elements of sigma grow sufficiently large as a result of random variation. A potential solution to this deficiency associates multiple strategy parameter vectors with a single individual. A single strategy vector is active at any time and dictates how offspring will be generated. Experiments are conducted on four 10-dimensional benchmark functions where the number of strategy parameter vectors is varied over 1, 2, 3, 4, 5, 10, and 20. The results indicate advantages for using multiple strategy parameter vectors. Furthermore, the relationship between the mean best result after a fixed number of generations and the number of strategy parameter vectors can be determined reliably in each case.