## 5 Results and Discussion
### Random Walk Analysis: Information Content Analysis
The flattest is in the case of a partially matched crossover, so this operator may be the most efficient, while in the case of a cycle crossover it may be the most rugged, so this operator may be the worst. The expected partial information content values are 27 (expected partial information content unit) for 2-opt, 28 (expected partial information content unit) for OX, 23 (expected partial information content unit) for CX and 31 (expected partial information content unit) for PMX. The information stability, which shows the largest change in fitness of the neighbors, was given the following values: 7111.15 (information stability unit) for 2-opt, 5809.92 (information stability unit) for OX, 2728.38 (information stability unit) for CX and 5696.12 (information stability unit) for PMX. According to this, the largest change was for 2-opt and the smallest change was for CX. The lower the entropy, information content, density basin information values, the better, because this means that the search is moving in the same direction (increasing or decreasing the fitness value of the neighbor of the current solutions). The entropy values are the followings: for 2-opt 1.5809 (entropy unit) for OX 2.5792 (entropy unit) for CX 2.9458 (entropy unit) and for PMX 2.1070 (entropy unit). According to this, the 2-opt has the smallest entropy and the CX has the largest. The information content values are 0.4101 (information content unit) for 2-opt, 0.8252 (information content unit) for OX, 0.8831 (information content unit) for CX, and 0.6380 (information content unit) for PMX. According to this, the highest value was given by CX and the lowest by 2-opt. The density basin information values are 0.3285 (density basin information unit) for 2-opt, 0.2814 (density basin information unit) for OX, 0.4183 (density basin information unit) for CX, and 0.2888 (density basin information unit) for PMX. The diagram of regularity values for each operator (2-opt, OX, CX, PMX) is shown in Figures 16 and 17 which shows ruggedness. A graph of evolvability portrait values for each operator is shown in Figures 18 and 19, in which we also get a rugged function along the iterations. However, if we plot the values along fitness values, which are shown in Figures 20 and 21. We get a level result (function) that is independent of the fitness value. The higher the value of evolvability, the better the solution, because the more neighbors of the current solution are better than the current solution, so it is more likely to improve during the iteration. In fact, evolvability measures the probability of improvement. \begin{table}
\begin{tabular}{l c} \hline \hline
**Information Content Analysis** & \\ \hline
**Method** & **Optimal Value** \\ \hline Partial Information Content & \\ Expected Partial Information Content & The bigger the better \\ Information Stability & \\ Entropy & \\ Information Content & The smaller the better \\ Density Basin Information & \\ Regularity & \\ Evolvability portrait & High values \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Information content analysis evaluation methodsFigure 16: The regularity in case of 2-opt (**a**) and order crossover operator (**b**). Figure 17: The regularity in case of cycle crossover (**a**) and partially matched crossover operator (**b**). Figure 18: The evolvability along the iterations in case of 2-opt (**a**) and order crossover operator (**b**).