Journal of Guangdong University of Technology ›› 2022, Vol. 39 ›› Issue (05): 61-67.doi: 10.12052/gdutxb.220067

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An Improved Lagrange Relaxation Algorithm for Green Vehicle Routing Problem

Xu Lin-hao1, Qian Bin1, Hu Rong1, Yu Nai-kang2   

  1. 1. School of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China;
    2. School of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China
  • Received:2022-04-01 Published:2022-07-18

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Abstract: To address the green capacitated vehicle routing problem (GCVRP), a mixed integer programming (MIP) model is established to minimize the total freight cost, and an improved Lagrange relaxation algorithm (ILRA) is proposed to solve the problem. Firstly, the dual problem of the original problem is obtained by Lagrange relaxation technique, and the lower bound of the original problem is obtained by solving the dual problem by subgradient method; Secondly a repair algorithm and a neighborhood search algorithm are designed to obtain the upper bound of the original problem, and then update the multiplier iterative solution; Finally, a simulation experiment is carried out. The experimental results show that 10 tests are carried out on 19 cases of different scales under the same experimental environment. The average gap between the upper and lower bounds of MIP obtained by ILRA is 7.61%, while the average gap obtained by Gurobi solver is 15.47%. Therefore, compared with Gurobi solver, ILRA can obtain high-quality solutions of GCVRP efficiently.

Key words: green capacitated vehicle routing problem, mixed integer programming, improved Lagrange relaxation, lower bound

CLC Number: 

  • TP391.9
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