Implementation of the Metaheuristic GRASP Applied to the School Bus Routing Problem

Abstract

The school bus problem routing (SBRP) is an important practical problem studied in combinatorial optimization of operational research. It is formulated through a set of stops, buses, schools and garage, where from these sets, we seek to create optimized routes to reduce the operating cost of the service. This paper presents a solution to the SBRP, using the GRASP applied to a real problem. This meta-heuristic is divided into two stages: the construction of a viable solution and followed by a Local Search procedure. These two phases are repeated in each iteration. In the construction phase, a greedy and random function is used to construct an initial solution. It is also presented compared to the widely used heuristic and good results in the literature.

Shuttle bus service routing: A systematic literature review

“…# of bus [15], [31]- [33], [36]- [38], [47], [49], [53], [58], [61], [74], [75], [80] min. total travel distance [9], [10], [12], [14], [15], [17], [18], [25], [31], [32], [34], [36]- [38], [41], [47], [49], [52], [53], [62]- [65], [67], [71], [74], [77]- [79], [82] min. # of travelling time [18], [19], [23], [24], [30], [32], [33], [35], [36], [39], [42],…”

“…Commercial Solvers [8]- [13], [22], [28]- [46] Constraint Programming [46] Genetic Algorithm [14]- [16], [47]- [56] Tabu Search Algorithm [17]- [20], [22], [39], [42], [57]- [60] Clark&Wright Savings Algorithm [33], [61], [62] Maximin [63] K-means [14], [63]- [65] Fuzzy C-means [63], [65] Competitive Learning [63] Ant Colony Algorithm (ACO) [27], [35], [63], [66], [67] Evolutionary Algorithm [28], [58], [68] Greedy Algorithm [25], [34], [57], [69]- [71] Simulated Annealing [19], [20], [31], [36], [41], [43] Local Search [15], [19],…”

A Heuristic Algorithm for School Bus Routing with Bus Stop Selection

“…The proposed heuristic algorithm as well as the MIP model formulation presented in this paper can be extended to other SBRP variants. One such variant is the heterogeneous fleet, in which buses are characterized by different capacities, as studied in [17,20,24] amongst others. Another potential future development is the consideration of multi-tripping where several routes, possibly pertaining to different schools, are merged so that buses are able to perform multiple routes successively.…”

“…The majority of the publications on school bus routing also deal with the single-school SBRP (e.g. [20,22,24]). Here, we cover the first three subproblems stated above.…”

A Relation of Dominance for the Bicriterion Bus Routing Problem

“…The problem is widely studied and a review of papers on SPRP solutions is presented by Park and Kim (2010). The work on solving the problem has continued by the adaptation of various methods such as the branch-and-cut algorithm (Riera-Ledesma and Salazar-González, 2012), ant colony optimization (Addor et al, 2013;Arias-Rojas et al, 2012;Bronshtein and Vagapova, 2015;Yigit and Unsal, 2016), simulated annealing (Manumbu et al, 2014), the genetic algorithm (Sghaier et al, 2013), tabu search (Pacheco et al, 2013), the GRASP (greedy randomized adaptative search procedure) metaheuristic (Siqueira et al, 2016), the time saving heuristic (Worwa, 2014), the harmony search heuristic (Kim and Park, 2013), or the column-generation-based algorithm (Caceres et al, 2014). In the work of Chen et al (2015) two algorithms for solving the SBRP are proposed: an exact method of mixed integer programming (MIP) and hybrid simulated annealing with the local search metaheuristic.…”