A simulated annealing algorithm for the capacitated vehicle routing problem with two-dimensional loading constraints

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

123 Scopus Citations
View graph of relations


  • Lijun Wei
  • Zhenzhen Zhang
  • Defu Zhang
  • Stephen C. H. Leung

Related Research Unit(s)


Original languageEnglish
Pages (from-to)843-859
Journal / PublicationEuropean Journal of Operational Research
Issue number3
Online published25 Aug 2017
Publication statusPublished - 16 Mar 2018


This paper studies the well-known capacitated vehicle routing problem with two-dimensional loading constraints (2L-CVRP). It requires designing a set of min-cost routes, starting and terminating at the central depot, to satisfy customer demands which involve a set of two-dimensional, rectangular, weighted items. A simulated annealing algorithm with a mechanism of repeatedly cooling and rising the temperature is proposed to solve the four versions of this problem, with or without the LIFO constraint, and allowing rotation of goods or not. An open space based heuristic is employed to identify the feasible loading patterns. In addition, the data structure Trie is used to accelerate the procedure by keeping track of the packing feasibility information of routes examined, and also by controlling the effort spent on different routes. The proposed algorithm is tested on the widely used instances of 2L-CVRP. The results show that our approach outperforms all existing algorithms on the four problem versions, and reaches or improves the best-known solutions for most instances. Furthermore, we compared the impact of different loading constraints, and observed some interesting results.

Research Area(s)

  • 2L-CVRP, Packing, Rotation, Routing, Simulated annealing

Citation Format(s)