A further 50 runs were conducted (using the same initial populations) and no fitness selection. Unsurprisingly no run found a solution and the maximum, mean and other fitness statistics fluctuate a little but are essentially unchanged (cf. Figure 4). Similarly program size statistics fluctuate but are essentially the same as those of the initial population (cf. Figure 5). This is in keeping with results with no selection reported in [2, page 112,]. Given crossover produces random changes in length we might have expected the spread of lengths to gradually increase. This is not observed. The slow fall in maximum program size can be seen in Figure 5. There is also a small fall in mean standard deviation from 32.8 in the initial population to 27.3 at the end of the runs.
Figure 4: Evolution of maximum and population mean of food eaten. Error bars indicate one standard deviation. Means of 50 runs comparing tournament sizes of 7 and 1.
Figure 5: Evolution of maximum and population mean program length. Error bars indicate one standard deviation. Solid line is the length of the ``best'' program in the population. Means of 50 runs comparing tournament sizes of 7 and 1.