# Metaheuristic with Cooperative Processes for the University Course Timetabling Problem
## 4 Computational Results
### Landscape and Efficacy of SACP  
An analysis of the UCTP landscape was performed for the two large-type instances. The landscape is presented based on three variables, the OF objective function, the Hamming distance and the elapsed time in the SACP execution, which is a function of the \(NR\) that is executed in SACP. The execution time was about 8000 s.  
Figure 5 presents the landscape for the instance large01 without applying cooperation between processes. It is observed that, with greater distance Hamming, the behavior of the solutions obtained as a function of time generates lower quality in the evaluation of the objective function with Equation (1). In addition, similarly, a shorter Hamming distance impacts on the behavior of the solutions obtained as a function of time generating a higher quality in the evaluation of the objective function. However, there are solutions that, despite having a large Hamming distance, the quality of their result is very good; the same happens when the Hamming distance is small. It is observed that, between a Hamming distance of 300 to 400, there is a path in which no peaks appear in the landscape. The opposite occurs when the Hamming distance is less than 300 and greater than 500. Figure 5 presents the landscape for the instance large02 without applying the cooperation among processes. Here, there is no clear behavior depending on the distance. As in large01, there are solutions that, despite having a large Hamming distance, the quality of their result is very good. The same happens when the Hamming distance is small. It is also observed that near to a Hamming distance of 400 there is a path in which no peaks appear in the landscape. The opposite occurs when the Hamming distance is less than 300 and greater than 500. Figure 5: SACP with 48 processes generating the landscape without applying cooperation between the processes. Results of 30 tests. (**a**) Instance large01. (**b**) Instance large02. Figure 6 presents the landscape for the instances large01 and large02 applying cooperation between the processes. Figure 6a presents the landscape for instance large01 applying processes cooperation. It is observed that, with greater distance Hamming, the behavior of the solutions obtained as a function of time generates more clearly lower quality in the evaluation of the objective function with the Equation (1), unlike when there is no processes cooperation. In addition, at a shorter Hamming distance throughout the time interval, the behavior of the solutions obtained as a function of time generates the highest quality in the evaluation of the objective function. Moreover, if we compare Figure 6a,b, it can be observed that the value of the objective function has better quality throughout the interval of time from the application of the cooperation of processes that starts on the surface marked in blue (Figure 6b). It is observed that the best solutions obtained with cooperation are presented when the value of the Hamming distance is close to zero and in the SACP execution time limit. Figure 6b presents the landscape for the instance large02 applying cooperation among processes. It is observed that, with greater distance Hamming, the behavior of the solutions obtained as a function of time generates more clearly lower quality in the evaluation of the objective function with Equation (1), unlike when there is no processes cooperation. In addition, at a shorter Hamming distance throughout the time interval, the behavior of the  
Figure 6: SACP with 48 processes generating the landscape applying cooperation between the processes. Results of 30 tests. (**a**) Instance large01. (**b**) Instance large02. Figure 7a presents the effect of processes cooperation for the large01 problem, when SAP (simulated annealing with processes) without processes cooperation and when SACP with processes cooperation are applied. The graph presents infinity of points with blue and red colors.