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Search graph structure and its implications for multi-graph constrained routing and scheduling problems.

Michal Weiszer1, Edmund K Burke2, Jun Chen3

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This study analyzes how multi-graph structures impact routing algorithm solutions for optimization problems. More parallel edges can improve solution quality and efficiency, especially with time window constraints.

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Area of Science:

  • Operations Research
  • Computer Science
  • Graph Theory

Background:

  • Multi-graphs, featuring multiple edges between nodes, are crucial for modeling real-world optimization problems based on infrastructure.
  • Understanding the influence of multi-graph properties on algorithmic solutions is essential for improving efficiency and solution quality.

Purpose of the Study:

  • To investigate the impact of parallel edges and their costs in multi-graphs on routing and scheduling problem solutions.
  • To develop an indicator for determining when increased parallel edges benefit multi-graph models.
  • To explore the effect of including dominated cost edges in multi-graphs with time window constraints.

Main Methods:

  • Case studies using the airport ground movement problem.
  • Analysis of routing algorithms applied to multi-graph structures.
  • Evaluation of solution quality, computational complexity, and trade-off solutions.

Main Results:

  • The number of parallel edges significantly affects computational complexity, the number of trade-off solutions, and overall solution quality.
  • A proposed indicator can predict when a higher number of parallel edges is advantageous.
  • Including edges with dominated costs can enhance results, particularly under time window constraints.

Conclusions:

  • Multi-graph structure, specifically the number and cost of parallel edges, critically influences the performance of routing algorithms.
  • Informed multi-graph creation, considering edge properties and constraints, can lead to better optimization outcomes.
  • The findings offer a methodological basis for designing multi-graph representations in similar optimization challenges.