Hybrid variable neighborhood search for solving school bus-driver problem with resource constraints

The School Bus-Driver Problem with Resource Constraints (SBDP-RC) is an optimization problem with many practical applications. In the problem, the number of vehicles is prepared to pick a number of pupils, in which the total resource of all vehicles is less than a predefined value. The aim is to find a tour minimizing the sum of pupils’ waiting times. The problem is NP-hard in the general case. In many cases, reaching a feasible solution becomes an NP-hard problem. To solve the large-sized problem, a metaheuristic approach is a suitable approach. The first phase creates an initial solution by the construction heuristic based on Insertion Heuristic. After that, the post phase improves the solution by the General Variable Neighborhood Search (GVNS) with Random Neighborhood Search combined with Shaking Technique. The hybridization ensures the balance between exploitation and exploration. Therefore, the proposed algorithm can escape from local optimal solutions. The proposed metaheuristic algorithm is tested on a benchmark to show the efficiency of the algorithm. The results show that the algorithm receives good feasible solutions fast. Additionally, in many cases, better solutions can be found in comparison with the previous metaheuristic algorithms.