ADMM-based problem decomposition scheme for vehicle routing problem with time windows

Yu Yao, Xiaoning Zhu, Hongyu Dong, Shengnan Wu, Hailong Wu, Lu Carol Tong, Xuesong Zhou

Research output: Contribution to journalArticle

Abstract

Emerging urban logistics applications need to address various challenges, including complex traffic conditions and time-sensitive requirements. In this study, in the context of urban logistics, we consider a vehicle routing problem with time-dependent travel times and time windows (VRPTW), and the goal is to minimize the total generalized costs including the transportation, waiting time, and fixed costs associated with each vehicle. We adopt a high-dimensional space–time network flow model to formulate an underlying vehicle routing problem (VRP) with a rich set of criteria and constraints. A difficult issue, when solving VRPs, is how to iteratively improve both the primal and dual solution quality in general and how to break the symmetry generated by many identical solutions, particularly with homogeneous vehicles. Along this line, many coupling constraints, such as the consensus constraints across different agents or decision makers, need to be carefully addressed to find high-quality optimal or close-to-optimal solutions under medium- or large-scale instances. Currently, the alternating direction method of multipliers (ADMM) is widely used in the field of convex optimization, as an integration of the augmented Lagrangian relaxation and block coordinate descent methods, for machine learning and large-scale continuous systems optimization and control. In this work, we introduce the use of ADMM to solve the multi-VRP, which is a special case of integer linear programming, and demonstrate a manner to reduce the quadratic penalty terms used in ADMM into simple linear functions. In a broader context, a computationally reliable decomposition framework is developed to iteratively improve both the primal and dual solution quality. Essentially, the least-cost path subproblem or other similar subproblems involving binary decisions can be embedded into a sequential solution scheme with an output of both lower bound estimates and upper bound feasible solutions. We examine the performance of the proposed approach using classical Solomon VRP benchmark instances. We also evaluate our approach on a real-world instance based on a problem-solving competition by Jingdong Logistics, a major E-commerce company.

Original languageEnglish (US)
Pages (from-to)156-174
Number of pages19
JournalTransportation Research Part B: Methodological
Volume129
DOIs
StatePublished - Nov 1 2019

Fingerprint

Vehicle routing
multiplier
Decomposition
Logistics
logistics
costs
Costs
Convex optimization
Electronic commerce
Travel time
commerce
Linear programming
Learning systems
decision maker
penalty
programming
travel
time
traffic
learning

Keywords

  • Alternating direction method of multipliers
  • Problem decomposition
  • Urban logistics
  • Vehicle routing problem with time windows

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation

Cite this

ADMM-based problem decomposition scheme for vehicle routing problem with time windows. / Yao, Yu; Zhu, Xiaoning; Dong, Hongyu; Wu, Shengnan; Wu, Hailong; Carol Tong, Lu; Zhou, Xuesong.

In: Transportation Research Part B: Methodological, Vol. 129, 01.11.2019, p. 156-174.

Research output: Contribution to journalArticle

Yao, Yu ; Zhu, Xiaoning ; Dong, Hongyu ; Wu, Shengnan ; Wu, Hailong ; Carol Tong, Lu ; Zhou, Xuesong. / ADMM-based problem decomposition scheme for vehicle routing problem with time windows. In: Transportation Research Part B: Methodological. 2019 ; Vol. 129. pp. 156-174.
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