3 Binomial-3

Daida et al. (2001) provided a thorough investigation of why increasing the ephemeral constant range makes the Binomial-3 problem `harder'. The authors draw attention to the inter-play between content and context of functions and terminals in the representation. Many different solutions exist to the Binomial-3 problem and combining parts of different solutions does not always make sense. A level of deception exists that is similar to the Ant problem, due to the many different solutions. However, in the Ant problem the functions and terminals preserve, to some degree, semantic meaning in different contexts. Moving constants and arithmetic functions between programs in Regression problems does not ensure their meaning in new contexts. A DAG (directed acyclic graph) representation of genetic programming was used on a Regression problem [Monsieurs and Flerackers, 2003] where the author introduced a diversity method that was also highly elitist. Performance showed that best fitness was achieved much faster with smaller population sizes using the elitist diversity measure.

Regression problems appear to pose a two-fold problem, finding a good approximation to fit the data points and attempting to reduce semantic changes of nodes during crossover. In this case, increasing genetic diversity could increase the chance that crossover will have problems with nodes changing context. A converged population may contain fewer nodes but with similar contexts and improve search performance. However, too little or too much selection or diversity would cause problems as well, making this a complex problem domain.