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A set-covering based heuristic algorithm for the periodic vehicle routing problem.

V Cacchiani1, V C Hemmelmayr2, F Tricoire3

  • 1DEIS, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy.

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Summary
This summary is machine-generated.

A new hybrid optimization algorithm effectively solves the periodic vehicle routing problem (PVRP) by combining heuristic and exact methods. It achieves new best solutions on benchmark instances, demonstrating its efficiency for complex routing challenges.

Keywords:
Column generationMatheuristicsPeriodic vehicle routing

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Area of Science:

  • Operations Research
  • Combinatorial Optimization
  • Logistics and Supply Chain Management

Background:

  • The periodic vehicle routing problem (PVRP) is a complex generalization of the vehicle routing problem (VRP).
  • Existing methods struggle with the intricate constraints of customer visit frequencies and vehicle capacities over a planning horizon.

Purpose of the Study:

  • To develop and validate a novel hybrid optimization algorithm for mixed-integer linear programming problems.
  • To apply the algorithm to the periodic vehicle routing problem (PVRP) as a case study, demonstrating its effectiveness.

Main Methods:

  • A hybrid optimization algorithm embedding heuristic and exact components.
  • Utilizes linear programming (LP) relaxation solved via column generation with heuristic column generation (iterated local search).
  • Employs LP-solution-guided local search techniques, including column fixing/releasing and a tabu list.

Main Results:

  • The algorithm demonstrates effectiveness in producing high-quality solutions for PVRP benchmark instances.
  • Achieved new best-known solutions on tested PVRP and periodic traveling salesman problem (PTSP) instances.
  • Outperforms state-of-the-art algorithms on benchmark and realistic PVRP instances.

Conclusions:

  • The proposed hybrid optimization algorithm is highly effective for solving the periodic vehicle routing problem.
  • The method's ability to find new best solutions highlights its potential for complex logistics optimization.
  • The algorithm shows broad applicability, performing well on both standard and realistic PVRP and PTSP instances.