An Empirical Investigation of an Evolutionary Algorithm's Ability to Maintain a Known Good Solution

We analyze the disruptiveness of four operators in an evolutionary algorithm(\EA") solving a grammar induction problem. The EA in question contains mutation, crossover, inversion, and substitution operators. Grammars are encoded on genotypes in a representation which includes variable-length introns. A repeated measures analysis of variance (\ANOVA") with four factors, the four operators' rates, is used. It is discovered that some operator rates interact, meaning that their eeects on the EA's performance when used together are more than the sum of their individual eeects. In particular, this is found to be true for crossover and mutation, even for a low mutation rate. This suggests that analyzing these operators separately is inadequate, and that operators must be studied in combination, instead of in isolation. 1 Overview The degree to which operators are disruptive is a long-standing question in evolutionary computation. Most often, however, each operator is investigated in isolation, ignoring interactions between the operators. Generally, we would like to know whether a given suite of operators performs well together, and whether combinations of operators interact to produce eeects above and beyond those owing to the operators in isolation. In addition, for evolutionary algorithms (\EA's" hereafter) that have some local search, tuning, or \life history" component to tness evaluation, we would like to know whether the operators are eeective both with and without the local search. An important issue which reeects the disruptiveness of an EA's genetic operators is that of the ability to maintain a solution in the population. That is, if an EA nds a solution better than anything found previously, will this solution continue to be present in the population in the future? If the operators are too disruptive, the novel solution is more likely to be lost. If the operators are not disruptive enough, there is a danger of prematurely converging. We will refer to the ability of an EA to maintain a solution in its population through time as the \robustness" of that EA. In our case, robustness will mean the ability to maintain a solution that is already present in the population, as opposed to the ability to arrive at, xate on, and then maintain such a solution.