## 5 Conclusions and Future Work  
The corridor planning problem can be addressed as an optimization problem with topological restrictions. This paper presents the SA algorithm's implementation using a variable neighborhood mechanism to generate different alternative routes and select the best one for this problem. By using a guided pseudo-random search approach, the variable neighborhood structure explores alternative routes improving the initial solution.  
Figure 11: Alternate routes for corridors.  
Figure 10: Behavior of the objective function.  
The experimental results demonstrate that implementing the proposed mechanism in SA generates alternative routes with quality and diversity. Likewise, the results obtained by the SA algorithm significantly exceeds 18% over those gotten by the greedy method, this only indicates for comparative purposes that SA obtains optimized routes, but it is not verified that SA gets the best solution. Moreover, the implementation of the proposed neighborhood mechanism outweighs the greedy algorithm in solving large-size problems. Applying a variable neighborhood mechanism in SA allows generating diversity in routes, which is important if it is necessary to choose other alternative paths that respect a corridor's limits. With the results obtained in this work, the objective of finding routes with quality and diversity is met. The SA algorithm solves three practical problems using real topographic data. However, it can be used in a variety of problems finding the shortest route between two points on realistic scenarios.  
Future work can be proposed to develop a method fitting the curves of the impact zone (strip) of the corridor to narrow the search. In this way, it is allowed to explore different alternate routes relatively close to the initial solution without getting too far away. For improving the computation time used to generate an initial solution, it is proposed to implement the techniques used in the MOGADOR method and look for other random mechanisms generating a feasible initial solution in the shortest possible time. The problem needs to be addressed as a multi-objective optimization problem. In addition, it is possible to parallelize the method by its vector nature and the optimization algorithm.  
Something very important for future work is to work on problems by dynamically varying the values of the layers so that the costs of the links change depending on the set of selected links, adapting a greedy uninformed search strategy, the breadth-first-search (BFS) algorithm with the same neighborhood structure procedures used in this work to find multiple solutions and focus on finding multiple global optimal paths.  
Finally, many real problems have GIS information in different formats and scales that could make the spatial analysis complicated. However, it is possible to convert the different data models to a raster format, adapt the different scales to perform complex spatial analysis, and exploit the geographic information available in diverse private and public sources.  
Conceptualization, M.A.C.-C.; investigation, P.M.-B., E.Y.A.-M., B.M.-B., and M.H.C.-R.; methodology, M.A.C.-C., P.M.-B., and R.R.-L.; validation, E.Y.A.-M. and M.H.C.-R.; visualization, B.M.-B.; writing--original draft, M.A.C.-C., P.M.-B., and R.R.-L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by CONACYT under grant PROINNOVA-199685.  
The authors declare no conflict of interest.