Conscious Exploration of Alpha-Cuts in the Parametric Solution of the School Bus Routing Problem with Fuzzy Walking Distance

Combinatorial optimization problems allow for modeling multiple situations in which proper allocation of resources is needed. For some real-world problems, the use of fuzzy elements in the models allows for incorporating certain levels of uncertainty to better approximate such real-world situations. One way to solve combinatorial optimization problems with fuzzy elements is the parametric approach, where it is necessary to define how to explore different relaxation levels using alpha-cuts. Researchers tend to select such alpha-cuts uniformly. The current investigation proposes a novel strategy for selecting alpha-cuts in the School Bus Routing Problem with fuzzy students' maximum walking distance. This proposal bases its foundations on the number of student-bus stop pairs available according to the different levels of relaxations allowed. Results demonstrate how the proposed strategy gives attractive solutions with more diverse trade-offs, contrasted with other methods in the literature. Furthermore, it decreases the computational cost for those instances where the maximum relaxation does not provide new pairs of students-bus stops.