The problem with a self-adaptative mutation rate in some environments: a case study using the shaky ladder hyperplane-defined functions

Dynamic environments have periods of quiescence and periods of change. In periods of quiescence a Genetic Algorithm (GA) should (optimally) exploit good individuals while in periods of change the GA should (optimally) explore new solutions. Self-adaptation is a mechanism which allows individuals in the GA to choose their own mutation rate, and thus allows the GA to control when it explores new solutions or exploits old ones. We examine the use of this mechanism on a recently devised dynamic test suite, the Shaky Ladder Hyperplane-Defined Functions (sl-hdf's). This test suite can generate random problems with similar levels of difficulty and provides a platform allowing systematic controlled observations of the GA in dynamic environments. We show that in a variety of circumstances self-adaptation fails to allow the GA to perform better on this test suite than fixed mutation, even when the environment is static. We also show that mutation is beneficial throughout the run of a GA, and that seeding a population with known good genetic material is not always beneficial to the results. We provide explanations for these observations, with particular emphasis on comparing our results to other results [2] which have shown the GA to work in static environments. We conclude by giving suggestions as to how to change the simple GA to solve these problems.