SMART Operator Application

 

This chapter has used the simplest application of the SMART operator population to the main population: each operator gets R recombination attempts (equation 3.1).

There are several other options, which offer potential improvements to the paradigm. First, let us review why this simple strategy should work at least as well (baring over-greediness) as using only random recombination. Any SMART operator that doesn't act gets zero fitness, but the programs that were input are randomly recombined anyway. So the inactive SMART operators do not pose a fitness disadvantage (relative to random operators) to the main population. All SMART operators are given the random operator as a safety net (SA-8). This means that it is trivial for SMART operators to do at least as well as the random operator would do. Depending on the representation and recombination styles for the SMART operators, only a small fraction of the population will do something and not use the safety net primitive. It is only this small fraction of the SMART operator population that stands a chance of bringing the population's total recombination performance down below that of the random recombination strategy.

Here is an example of another strategy: conservative SMART operator reapplication. FPR below stands for Fitness Proportionate Reproduction.

1. Save main population state
2. Perform Main population FPR and recombination using all SMART operators
3. Test the fitness of each program in the main population
4. Use relative main population fitnesses from 1 and 3 to get SMART operator fitnesses.
5. Perform FPR and recombination on the SMART operators
6. Return the main population to its saved step 1 state.
7. Perform Main population FPR and recombination using the K best SMART operators.
8. Test fitness of main population programs
9. Start Generation X+1. Goto step 1

Up to step 5 this process is exactly the strategy described in section 3.4. A natural question is, ``In step 4, why not save the better individuals and integrate them with the main population in step 7?'' The reason is that without very clever program difference-measures this strategy can quickly kill diversity.

This strategy has the advantage of only the most skillful SMART operators having a real effect on the main population's journey through fitness landscape. The cost for this is a slow down of a factor two. In our limited experience with conservative reapplication, this cost is often made up for either with an earlier generation at which the population reaches some particular level of fitness, or with the increased fitness maximum the population achieves.