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  • According to the formulation, a local search of students and stops is done to identify and sort possible solutions. Thereafter, a list is created that transverses respective savings using an objectives function, which leads to execution of list in decreasing values (Schittekat et al.523). The objective functions of the GRASP + VND formulation seeks to shorten the distance that all the buses travel in a single trip and enforce the trans-version of buses entering specific stages. (Schittekat et al. 524). As developed, the constraints of the model include imposing the connectivity of a single bus (Schittekat et al. 524). The decision to use the formulation depends on the idea that if well implemented, will let only one bus visit a stop, the stop should not contain more students than a bus can carry and a bus should pass only a single route.

According to the formulation, a local search of students and stops is done to identify and sort possible solutions. Thereafter, a list is created that transverses respective savings using an objectives function, which leads to execution of list in decreasing values (Schittekat et al.523). The objective functions of the GRASP + VND formulation seeks to shorten the distance that all the buses travel in a single trip and enforce the trans-version of buses entering specific stages. (Schittekat et al. 524). As developed, the constraints of the model include imposing the connectivity of a single bus (Schittekat et al. 524). The decision to use the formulation depends on the idea that if well implemented, will let only one bus visit a stop, the stop should not contain more students than a bus can carry and a bus should pass only a single route.

  • Category:
    Geography
  • Document type:
    Assignment
  • Level:
    Undergraduate
  • Page:
    1
  • Words:
    373

Review of Formulation: GRASP + VND

In their research study, ‘A Metaheuristic for the School Bus Routing Problem with Bus Stop Selection,’ Schittekat, Kinable, Sorensen, Sevaux, Spieksma and Springael came up with a formulation to solve bus route generation and bus stop selection. The developed formulation, GRASP + VND Metaheuristic uses a GRASP Construction Phase and Variable Neighborhood Descent (VND) by selecting elements and adding them to a Restricted Candidate List (RCL) (Schittekat et al. 521). The first step in this process is to ensure that buses visit all stops in various routes (Schittekat et al. 521). After the integration of the two phases, the GRASP phase moves away from the VND phase and dumps the RCL in favor of a Roulette Wheel Selection procedure. Using a pseudo-code, the GRASP removes and inserts bus stops within a route, removes and inserts them between routes, replaces the stops and finally removes those that do not fall along formed rectangular route (Schittekat et al. 522). Using the following LP formulation, the GRASP + VND approach gives n extra constraints that suit the formulation to larger instances.

ui
þ uj
þ nxij
6 n
1 8i; j ¼ 2; . . . ; n; i – j ð16Þ

According to the formulation, a local search of students and stops is done to identify and sort possible solutions. Thereafter, a list is created that transverses respective savings using an objectives function, which leads to execution of list in decreasing values (Schittekat et al.523). The objective functions of the GRASP + VND formulation seeks to shorten the distance that all the buses travel in a single trip and enforce the trans-version of buses entering specific stages. (Schittekat et al. 524). As developed, the constraints of the model include imposing the connectivity of a single bus (Schittekat et al. 524). The decision to use the formulation depends on the idea that if well implemented, will let only one bus visit a stop, the stop should not contain more students than a bus can carry and a bus should pass only a single route.

Works Cited

Schittekat, Patrick, et al. «A Metaheuristic for the School bus Routing Problem with Bus Stop

Selection.» European Journal of Operational Research 229.2 (2013): 518-528. Web.