# Metaheuristic with Cooperative Processes for the University Course Timetabling Problem
## 5 Conclusions  
It is concluded that applying processes cooperation in SACP, through addressing of the solutions of each process using the Hamming distance in each iteration of the algorithm, allows improving the final result obtained.  
Optimizing values in the soft constraints with SACP for large problems has a different complexity since the degree of difficulty in optimization increases in the order of Soft3 \(->\) Soft1 \(->\) Soft2 for large01 and in the order of Soft1 \(->\) Soft3 \(->\) Soft2 for large02.  
The efficacy of SACP is the highest compared to five heuristics proposals found in the literature, ACO, GA ILS, TS and SA. SACP always achieves first place in all revised instances (average ranking). Furthermore, in some cases, some algorithms in the literature do not find a solution for large instances (ACO, GA and SA), which does not happen in SACP because it always finds solutions for any instance.  
Statistical analysis shows that, in the SACP comparison with each of the other algorithms, there are differences in the effects of SACP with the other algorithms compared because the p-value does not exceed the significance level of 0.05. In the case of the p-value obtained with respect to SA, it exceeds the significance value of 0.05 for very little. Added to this, SACP has a better average rank than SA and SA also does not obtain results for any of the large problems. In the case of SACP, in all the executions carried out by the algorithm, feasible results are obtained for the large problems. SACP efficiency is very good when using a single node in the cluster, but it is quickly reduced by having to use more than one node in the cluster, further added to the communication between processes that each iteration of the algorithm requires to apply processes cooperation.  
The limitations found for this work were that no more test instances were found for the presented optimization model with which more results could be presented, nor were other works found that will present other optimization methods to compare the efficacy of SACP.  
In future works, the aim will be to improve the speedup by applying better communication between cluster nodes with the infinband network. A better and more efficient compiler such as INTEL will also be used instead of the free GNU compiler.  
Some future needs are the elaboration of new test instances of the optimization model and the development of heuristics of populations that present results for the optimization model presented in this work with which more robust comparative tests can be carried out.  
Figure 15: SACP speedup for large UCTP problems.  
**Author Contributions:** Conceptualization, M.H.C.-R. and M.A.C.-C.; methodology, F.A.-P. and J.d.C.P.-A.; software, M.A.C.-C.; validation, M.H.C.-R., E.Y.A.-M. and B.M.-B.; formal analysis, J.E.-U.; investigation, B.M.-B. and J.E.-U.; writing--original draft preparation, M.A.C.-C. and E.Y.A.-M.; writing--E.Y.A.-M. and J.d.C.P.-A.; supervision, F.A.-P.; project administration, M.A.C.-C.; funding acquisition, M.A.C.-C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by CONACYT grant number 317029.  
Not applicable.  
The authors declare no conflict of interest.