A Priori Comparison of Binary Crossover Operators: No Universal Statistical Measure, But a Set of Hints

The choice of an operator in evolutionary computation is generally based on comparative runs of the algorithms. However, some statistical a priori measures, based on samples of (parents-oospring), have been proposed to avoid such brute comparisons. This paper surveys some of these works in the context of binary crossover operators. We rst extend these measures to overcome some of their limitations. Unfortunately, experimental results on well-known binary problems suggest that any of the measures used here can give false indications. Being all deened as averages, they can miss the important parts: none of the tested measures have been found to be a good indicator alone. However, considering together the mean improvement to a target value and the Fitness Operator Correlation gives the best predictive results. Moreover, detailed insights on the samples, based on some graphical layouts of the best oospring tnesses, seem to allow more accurate predictions on the respective performances of binary crossover operators.