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An ACO Algorithm for the Bi-objective School Bus Routing Problem

KONG Yunfeng;NIU Ning;CHEN Xiaopan;HOU Yane;Key Laboratory of Geospatial Technology for Middle and Lower Yellow River Regions,Ministry of Education ,Henan University;Geography and Planning School of Sun Yat-Sen University;College of Computer and Information Engineering,Henan University;  
The school bus routing problem(SBRP)seeks to plan an efficient route schedule of a fleet of school buses that pick up students and deliver them while satisfying various constraints.Most of existing SBRP algorithms focus on reducing the total bus travelling distance instead of reducing the number of buses required.Considering that the cost of bus purchase and maintenance accounts for a large percentage in school bus operations,this paper proposes an ant colony optimization(ACO)algorithm for the bi-objective SBRP.The optimization objectives are to minimize the number of buses required and the total traveling distance.The key algorithm procedures such as the bus route construction,the ant pheromone setting and updating,and the local search for solution improvement are discussed in details.The proposed algorithm is tested on a set of benchmark instances.The computational results show that the local search procedure embedded in ACO is capable of improving the solution quality significantly.The performance of the algorithm is also verified by comparing it with the IBM ILOG CPLEX optimizer.For the small instances that CPLEX can obtain the optimal number of required buses,our algorithm can also find the minimum number of required buses.While for the large instances,our algorithm outperforms CPLEX in terms of solution quality and computation time.
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