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Solving the Min-Max Clustered Traveling Salesmen Problem Based on Genetic Algorithm.

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  • 1College of Information Technology, Shanghai Ocean University, Shanghai 201306, China.

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Summary
This summary is machine-generated.

This study introduces a novel two-stage genetic algorithm to solve the min-max clustered traveling salesmen problem (MMCTSP). The method efficiently determines optimal routes for visiting clustered vertices, minimizing the maximum tour weight.

Keywords:
clustered traveling salesman problemgenetic algorithmmin-maxmultiple traveling salesmen problemtraveling salesman problem

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Area of Science:

  • Operations Research
  • Computer Science
  • Combinatorial Optimization

Background:

  • The min-max clustered traveling salesmen problem (MMCTSP) is a complex variant of the classic Traveling Salesmen Problem (TSP).
  • It involves partitioning graph vertices into clusters and finding tours that visit all vertices consecutively within their assigned clusters.
  • The objective is to minimize the maximum tour weight among all salesmen.

Purpose of the Study:

  • To develop an efficient algorithm for solving the MMCTSP.
  • To minimize the maximum tour weight in a clustered TSP scenario.
  • To provide a robust solution method for complex routing problems.

Main Methods:

  • A two-stage solution approach utilizing genetic algorithms.
  • Stage 1: Solves a TSP for each cluster to determine intra-cluster visiting order.
  • Stage 2: Models clusters as nodes, constructs an MTSP, and applies a grouping-based genetic algorithm for inter-cluster assignment and ordering.

Main Results:

  • The proposed two-stage genetic algorithm effectively addresses the MMCTSP.
  • The algorithm demonstrates superior solution quality across various instance scales.
  • It exhibits good computational performance and solution efficiency.

Conclusions:

  • The developed algorithm provides an effective method for solving the MMCTSP.
  • It offers improved solutions compared to existing methods for complex routing problems.
  • The approach shows promise for practical applications in logistics and operations research.