Results

**1 - 2**of**2**### Table 5: Results for the Artificial-Ant benchmark. Given are the overall number of trials and the number (no.) and percentage (fraction) of successful ones.

"... In PAGE 8: ...2 Results The results demonstrate that none of the benchmarks is difficult for graph GP. Espe- cially the results for the Artificial-Ant problem are remarkable, see Table5 , since basic GP algorithms are not much better than random search on this task (Langdon and Poli, 1998). Our own experiments with a tree-based GP system show success rates of only seven percent (Niehaus, 2003).... ..."

### Table 2 shows the operator probabilities used. The nop operation is the only func- tion associated with a (1, 1)-vertex in the Two-Boxes task and it is only needed by the random graph generator during the initialization of the population (cf. Niehaus, 2003). Thus, probabilities of vertex-operators are low. Furthermore, the Two-Boxes bench- mark is the only problem for which we require acyclic graphs. Hence, the probability of applying the operator cycle is set to zero and xover is configured not to create cycles. The remaining parameters are given in Figure 3. Note that going from a tree to a graph representation has changed the function set only as far as the switch from a functional to an imperative algorithmic approach are concerned.

"... In PAGE 8: ...Problem vmut vdel vins vmov pdel pins cycle xover no op. Artificial-Ant 12 % 12% 12 % 12 % 12 % 12 % 12 % 12 % 4 % Lawn-Mower 12 % 12% 12 % 12 % 12 % 12 % 12 % 12 % 4 % Two-Boxes 24 % 2 % 0 0 24 % 24 % 0 24 % 4 % Table2 : Operator probabilities used in the experiments. The probability of performing no variation (no op.... ..."

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