Recorded Step Directional Mutation for Faster Convergence

Two meta-evolutionary optimization strategies described in this paper accelerate the convergence of evolutionary programming algorithms while still retaining much of their ability to deal with multi-modal problems. The strategies , called directional mutation and recorded step in this paper, can operate independently but together they greatly enhance the ability of evolutionary programming algorithms to deal with fitness landscapes characterized by long narrow valleys. The directional mutation aspect of this combined method uses correlated meta-mutation but does not introduce a full covari-ance matrix. These new methods are thus much more economical in terms of storage for problems with high dimensionality. Additionally, directional mutation is rotationally invariant which is a substantial advantage over self-adaptive methods which use a single variance per coordinate for problems where the natural orientation of the problem is not oriented along the axes. Step-recording is a subtle variation on conventional meta-mutational algorithms which allows desirable meta-mutations to be introduced quickly. Directional mutation, on the other hand, has analogies with conjugate gradient techniques in deterministic optimization algorithms. Together, these methods substantially improve performance on certain classes of problems, without incurring much in the way of cost on problems where they do not provide much benefit. Somewhat surprisingly their effect when applied separately is not consistent. This paper examines the performance of these new methods on several standard problems taken from the literature. These new methods are directly compared to more conventional evolutionary algorithms. A new test problem is also introduced to highlight the difficulties inherent with long narrow valleys.