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A Parallel Monte-Carlo Tree Search-Based Metaheuristic For Optimal Fleet Composition Considering Vehicle Routing Using Branch & Bound

T. M. J. T. Baltussen, M. Goutham, M. Menon, S. G. Garrow, M. Santillo, S. Stockar

TL;DR

The paper tackles FSMVRPTW by jointly optimizing heterogeneous fleet composition and routing under time windows, a problem that combines fixed and operational costs. It introduces a parallel hybrid optimizer that couples a Monte-Carlo Tree Search-based metaheuristic (UCT-MH) with an incremental Branch & Bound (B&B) framework, where MCTS guides fleet sizing and provides upper bounds to accelerate the exact search. Key contributions include an exact incremental B&B for the RAP with a nested TSPTW, the UCT-MH metaheuristic for fleet design, and a hybrid schema that warm-starts and tightens the global search, dramatically reducing computation time. Empirical results show substantial speedups (up to 86.5%) and feasibility improvements on real-life case studies, enabling larger FSMVRPTW instances and outperforming standalone B&B in challenging scenarios.

Abstract

Autonomous mobile robots enable increased flexibility of manufacturing systems. The design and operating strategy of such a fleet of robots requires careful consideration of both fixed and operational costs. In this paper, a Monte-Carlo Tree Search (MCTS)-based metaheuristic is developed that guides a Branch & Bound (B&B) algorithm to find the globally optimal solution to the Fleet Size and Mix Vehicle Routing Problem with Time Windows (FSMVRPTW).The metaheuristic and exact algorithms are implemented in a parallel hybrid optimization algorithm where the metaheuristic rapidly finds feasible solutions that provide candidate upper bounds for the B&B algorithm. The MCTS additionally provides a candidate fleet composition to initiate the B&B search. Experiments show that the proposed approach results in significant improvements in computation time and convergence to the optimal solution.

A Parallel Monte-Carlo Tree Search-Based Metaheuristic For Optimal Fleet Composition Considering Vehicle Routing Using Branch & Bound

TL;DR

The paper tackles FSMVRPTW by jointly optimizing heterogeneous fleet composition and routing under time windows, a problem that combines fixed and operational costs. It introduces a parallel hybrid optimizer that couples a Monte-Carlo Tree Search-based metaheuristic (UCT-MH) with an incremental Branch & Bound (B&B) framework, where MCTS guides fleet sizing and provides upper bounds to accelerate the exact search. Key contributions include an exact incremental B&B for the RAP with a nested TSPTW, the UCT-MH metaheuristic for fleet design, and a hybrid schema that warm-starts and tightens the global search, dramatically reducing computation time. Empirical results show substantial speedups (up to 86.5%) and feasibility improvements on real-life case studies, enabling larger FSMVRPTW instances and outperforming standalone B&B in challenging scenarios.

Abstract

Autonomous mobile robots enable increased flexibility of manufacturing systems. The design and operating strategy of such a fleet of robots requires careful consideration of both fixed and operational costs. In this paper, a Monte-Carlo Tree Search (MCTS)-based metaheuristic is developed that guides a Branch & Bound (B&B) algorithm to find the globally optimal solution to the Fleet Size and Mix Vehicle Routing Problem with Time Windows (FSMVRPTW).The metaheuristic and exact algorithms are implemented in a parallel hybrid optimization algorithm where the metaheuristic rapidly finds feasible solutions that provide candidate upper bounds for the B&B algorithm. The MCTS additionally provides a candidate fleet composition to initiate the B&B search. Experiments show that the proposed approach results in significant improvements in computation time and convergence to the optimal solution.
Paper Structure (12 sections, 6 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 12 sections, 6 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation & Methodology
  3. Exact Algorithm: Incremental Branch & Bound
  4. Metaheuristic: Monte-Carlo Tree Search
  5. Hybrid Optimization: Guiding B&B with the UCT-MH
  6. Results
  7. Computational Experiments
  8. Case Studies
  9. $n=10$ and $m_{max} = 6$
  10. $n=20$ and $m_{max} = 21$
  11. Discussion
  12. Conclusions

Figures (3)

  • Figure 1: Parallel implementation of the RAP B&B algorithm for the Resource Allocation Problem formulation.
  • Figure 2: Overview of the multi-stage design problem, with the FSMVRPTW (red) and the nested VRPTW (blue), and the proposed UCT-MH Algorithm.
  • Figure 3: Case Study 1: The UCT-MH and B&B algorithm, number of tasks $n=10$, maximum number of AMRs: $m_{max} = 6$, $\mathbf{k}_{max}^\top = [2,2,2]$.