An iterated local search algorithm for the vehicle routing problem with convex time penalty functions

  • Authors:

  • Toshihide Ibaraki;Shinji Imahori;Koji Nonobe;Kensuke Sobue;Takeaki Uno;Mutsunori Yagiura

  • Affiliations:

  • Department of Informatics, School of Science and Technology, Kwansei Gakuin University, Sanda 669-1337, Japan;Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan;Department of Engineering and Design, Faculty of Engineering and Design, Hosei University, Tokyo 102-8160, Japan;Toyota Motor Corporation, Toyota 471-8571, Japan;National Institute of Informatics, Tokyo 101-8430, Japan;Department of Computer Science and Mathematical Informatics, Graduate School of Information Science, Nagoya University, Nagoya 464-8603, Japan

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2008

Quantified Score

Hi-index 0.04

Visualization

Abstract

We propose an iterated local search algorithm for the vehicle routing problem with time window constraints. We treat the time window constraint for each customer as a penalty function, and assume that it is convex and piecewise linear. Given an order of customers each vehicle to visit, dynamic programming (DP) is used to determine the optimal start time to serve the customers so that the total time penalty is minimized. This DP algorithm is then incorporated in the iterated local search algorithm to efficiently evaluate solutions in various neighborhoods. The amortized time complexity of evaluating a solution in the neighborhoods is a logarithmic order of the input size (i.e., the total number of linear pieces that define the penalty functions). Computational comparisons on benchmark instances with up to 1000 customers show that the proposed method is quite effective, especially for large instances.