Extending self-adaptation in evolutionary algorithms

Self-adaptation in evolutionary algorithms concerns processes in which individuals incorporate information on how to search for new individuals. Instead of detailing the means for searching the space of possible solutions a priori, a process of random variation is applied both in terms of searching the space and searching for strategies to search the space. 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 a funtion f(x), and sigma is the so-called strategy parameter vector that influences how offspring will be created from the individual. Typically, a describes a variance or covariance matrix under Gaussian mutations. Experimental evidence suggests that the elements of sigma can sometimes become too small to explore the given search space adequately. The evolutionary search then stagnates until the elements of sigma grow sufficiently large as a result of random variation. Several methods have been offered to remedy this situation. This paper reviews recent results with one such method, which 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 on four 10-dimensional benchmark functions are reviewed, in which the number of strategy parameter vector 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.