14. Experimenting with Symbolic Regression

The purpose of this topic is to
- Gain more hands on experience working with a genetic programming
- Think about multi-objective problems

14.1. Run on Multiple Instances

A total of 20 instances are made available on the GitHub repository
All instances are made up of tabular data where the rows are observations and columns are the variables
The dependant variable is always the last column
Many of these instances are more than two or three dimensions, so visualizing and plotting the data may be difficult
Each of these instances were generated by some function
Further, normally distributed noise was added to each data point
The goal is to find the function that was used to generate each instance

The language that is included in the provided code may not be sufficient to effectively model the data
Try changing the language by adding or removing some operators
Also consider adding floating point numbers as constants

A strategy for managing bloat is to add negative selection pressure to larger chromosomes
- Given chromosomes with similar or identical fitness values, it is better to select those with smaller trees
Try adding tree size as part of the fitness measure and see if this helps simplify the generated chromosomes
- Going through DEAP’s documentation will be helpful for learning how to do this
  Defining a fitness that has more than one objective
  
  Having a fitness function return multiple values