Application of Variable Neighborhood Search Algorithms to a Static Repositioning Problem in Public Bike-Sharing Systems

공공 자전거 정적 재배치에의 VNS 알고리즘 적용

Yim, Dong-Soon

  • Received : 2015.07.01
  • Accepted : 2015.11.11
  • Published : 2016.02.29


Static repositioning is a well-known and commonly used strategy to maximize customer satisfaction in public bike-sharing systems. Repositioning is performed by trucks at night when no customers are in the system. In models that represent the static repositioning problem, the decision variables are truck routes and the number of bikes to pick up and deliver at each rental station. To simplify the problem, the decision on the number of bikes to pick up and deliver is implicitly included in the truck routes. Two relocation-based local search algorithms (1-relocate and 2-relocate) with the best-accept strategy are incorporated into a variable neighborhood search (VNS) to obtain high-quality solutions for the problem. The performances of the VNS algorithm with the effect of local search algorithms and shaking strength are evaluated with data on Tashu public bike-sharing system operating in Daejeon, Korea. Experiments show that VNS based on the sequential execution of two local search algorithms generates good, reliable solutions.


Public Bike System;Static Repositioning;Local Search Algorithm


  1. 윤태용, 이상헌, "주기적 다용량 차량경로 문제에 대한 발견적 해법", 한국경영과학회지, 제36권, 제1호(2011), pp.27-38.
  2. 이상헌, 이승원, "시간제약이 있는 차량경로 문제에 대한 개미군집 시스템해법", 한국경영과학회지, 제34권, 제1호(2009), pp.153-165.
  3. Chemla, D., F. Meunier, and R.W. Calvo, "Bike Sharing Systems : Solving the Static Rebalancing Problem," Discrete Optimization, Vol.10(2013), pp.120-146.
  4. Groer, C., B. Golden, and E. Wasil, "A Library of Local Search Heuristics for the Vehicle Routing Problem," Math. Prog. Comp., Vol.2(2010), pp.79-101.
  5. Gaspero, L.D., A. Rendl, and T. Urli, "Constraint-Based Approaches for Balancing Bike Sharing Systems," LNCS, Vol.8124(2013), pp.758-773.
  6. Hansen, P., N. Mladenovic, and J.A.M. Perez, "Variable Neighborhood Search : Methods and Applications," Ann Oper Res, Vol.175(2010), pp.367-407.
  7. Hernandez-Perez, H. and J. Solazar-Gonzalez, "A Branch-and-Cut Algorithm for a Traveling Salesman Problem with Pickup and Delivery," Discrete Applied Mathematics, Vol.145(2004), pp.126-139.
  8. Kloimullner, C., P. Papazek, B. Hu, and G.R. Raidl, "Balancing Bicycle Sharing Systems : An Approach for the Dynamic Case," LNCS, Vol.8600(2014), pp.73-84.
  9. Kochel, P., S. Kunze, and U. Nielander, "Optimal Control of a Distributed Service Systems with Moving Resources : Application to the Fleet Sizing and Allocation Problems," International Journal of Production Economics, Vol. 81(2003), pp.443-459.
  10. Rainer-Harbach, M., P. Papazek, G.R. Raidl, B. Hu, and C. Kloimullner, "PILOT, GRASP, and VNS approaches for the static balancing of bike sharing systems," Journal of Global Optimization, (2014), pp.1-33.
  11. Raviv, T. and O. Kolka, "Optimal Inventory Management of a Bike-Sharing Station," IIE Transactions, Vol.45, No.10(2013), pp.1077-1093.
  12. Raviv, T., M. Forma, and I.A. Tzur, "Static Repositioning in a Bike-Sharing System : Models and Solution Approaches," EURO J. Trasnp Logist, Vol.2 , No.3(2013), pp.187-229.
  13. Sayarshad, H., S. Avassoli, and F. Zhao, "A Multi-periodic Optimization Formulation for Bike Planning and Bike Utilization," Applied mathematical Modeling, Vol.36(2012), pp.4944-4951.