1. Fitness Cases Are input-output pairs describing the output a program should produce given the particular input value. The fitness of an individual is usually a function of the output produced by the individual and the target value for each fitness case. The success of the GP system is to some extent dependant on the choice of fitness cases.

2. Example of Fitness Cases Inputs: x Target Value 1 0 2 3 3 8 4 15 5 24

3. Fitness Functions Fitness functions calculate fitness measures. Fitness measures are used by selection methods to choose parents. Commonly used fitness functions: How well the individual solves the problem. A minimization of the size of the programs induced. A minimization of the run time of the programs. A minimization of the cost of solving the problem. Multi-objective fitness functions.

4. Measures of Fitness Raw Fitness Standardized Fitness Adjusted Fitness Normalized Fitness Hits Ratio Calculated when using the fitness proportionate selection method

5. Raw Fitness Indicates how promising an individual is. Depending on the problem a better raw fitness may be a smaller value, e.g. the fitness error or a bigger value, e.g. the amount of found eaten by the artificial ant in the artificial ant problem. A commonly used raw fitness function is the error function:

6. Standardized Fitness Standardized fitness s(i,t) describes the raw fitness so that a lower numerical value is always better. The best value of the standardized fitness is zero. In problems where a smaller fitness value means a better fitness the standardized fitness and the raw fitness are equal, i.e. s(i,t) = r(i,t). In problems where the a larger value is a better fitness the standardized fitness is calculated by subtracting the raw fitness from the maximum raw fitness value that can be attained.

7. Adjusted Fitness The range of the adjusted fitness is zero to one. The adjusted fitness is higher for fitter individuals of the population. The adjusted fitness is calculated by incrementing the standardized fitness by one and taking the inverse of the incremented value.

8. Normalized Fitness The normalized fitness of an individual is the individuals adjusted fitness divided by the sum of the adjusted fitness for all elements of the population. The normalized fitness lies between zero and one. It is larger for fitter individuals in the population. The sum of the normalized fitness values for each individual in the population is one.

9. Hits Ratio Is the number of fitness cases for which the value produced by an individual is the same or within a specified bound of the target value for each fitness case. Is used to determine whether a solution has been found.

10. Example Individual: Bound: 0.01 Fitness cases: InputTarget Value ProducedError By Individual 1011 2341 3891 415161 524251 Raw Fitness: 5 Standardized Fitness: 5 Adjusted Fitness: 0.17 Hits Ratio: 0

11. Aspects to Vary Fitness cases Fitness function GP parameters: Bound