This paper proposes a novel strategy for solving the vehicle routing problem with capacity constraints by applying the Multiverse Optimizer (MVO) algorithm. Inspired by the principles of the multiverse theory, MVO simulates the movement of candidate solutions through metaphorical white holes, black holes, and wormholes to enhance the exploration and exploitation processes. The white hole mechanism supports global exploration, while the black hole and wormhole components help refine and converge toward optimal routes. The proposed method enables a practical trade-off between delivery time and operational costs, making it suitable for real-time logistics planning. A case study involving 20 customer locations illustrates the effectiveness of the approach, achieving a total delivery duration of 4.4 h and an overall cost of $261.59.

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A Multiverse Optimizer for Time–Cost Trade-Off of Vehicle Routing Problem

  • Vu Hong Son Pham,
  • Van Nam Nguyen,
  • Nghiep Trinh Nguyen Dang,
  • Thuy Dung Dau

摘要

This paper proposes a novel strategy for solving the vehicle routing problem with capacity constraints by applying the Multiverse Optimizer (MVO) algorithm. Inspired by the principles of the multiverse theory, MVO simulates the movement of candidate solutions through metaphorical white holes, black holes, and wormholes to enhance the exploration and exploitation processes. The white hole mechanism supports global exploration, while the black hole and wormhole components help refine and converge toward optimal routes. The proposed method enables a practical trade-off between delivery time and operational costs, making it suitable for real-time logistics planning. A case study involving 20 customer locations illustrates the effectiveness of the approach, achieving a total delivery duration of 4.4 h and an overall cost of $261.59.