2 Empirical Analysis of Diversity Measures

The Artificial Ant, Even-5-Parity, and symbolic regression problems (using the Quartic polynomial and Rastrigin function) were introduced in Chapter 2. The problems are used here to explore diversity measures and the relationship between diversity and fitness. Table 4.1 contains the problem and experiment parameters for the following empirical investigation. These parameters were selected as they are commonly used in the literature and in many similar empirical studies. Note that the function set used here is typical for the Rastrigin function, whereas the Quartic problem typically only uses addition, subtraction, multiplication and division. The same function set are used for both to be consistent and do not use any ephemeral random constants. The Rastrigin problem is likely to be more difficult to solve without using ephemeral random constants. All experiments in this thesis were carried out using a modified version of the ECJ framework [Luke, 2004] and the Mersenne Twister random number generator [Matsumoto and Nishimura, 1998].

Table 4.1: Experiment and problem parameters for the Ant, Parity, Quartic and Rastrigin diversity measure experiments. These parameters settings represent the commonly used settings in the literature for these problems. The division and log functions are protected, as described in Chapter 2.

Evolutionary algorithm	Generational
Population size	500
Stopping criterion	Maximum generation = 51
Function sets
Ant	if_food_ahead, progn2, progn3
Parity	and, or, nand, nor
Quartic, Rastrigin	+ , -, *, p/, sin, cos, exp, log
Terminal sets
Ant	left, right, move
Parity	D1, D2, D3, D4, D5
Quartic, Rastrigin	x
Tree generation	Ramped half-n-half
Initial depth	4
Maximum depth	10
Subtree crossover probability	1.0
Subtree crossover internal node selection prob.	0.9
Mutation probability	0.0
Selection method, size	Tournament selection, size 4