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A Clustering-Enhanced Memetic Algorithm for the Quadratic Minimum Spanning Tree Problem.

Shufan Zhang1, Jianlin Mao1, Niya Wang1

  • 1Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China.

Entropy (Basel, Switzerland)
|January 21, 2023
PubMed
Summary
This summary is machine-generated.

A new clustering-enhanced memetic algorithm (CMA) tackles the NP-hard quadratic minimum spanning tree problem (QMSTP). This approach improves solutions for challenging instances, demonstrating its competitiveness against state-of-the-art methods.

Keywords:
agglomerative clusteringcombinatorial optimizationmemetic algorithmquadratic minimum spanning tree problem

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Area of Science:

  • Operations Research
  • Computer Science
  • Combinatorial Optimization

Background:

  • The quadratic minimum spanning tree problem (QMSTP) is an NP-hard optimization challenge.
  • Existing methods struggle to find optimal solutions efficiently due to problem complexity.

Purpose of the Study:

  • To introduce a novel clustering-enhanced memetic algorithm (CMA) for solving the QMSTP.
  • To provide a computationally efficient method for finding near-optimal QMSTP solutions.

Main Methods:

  • Developed a CMA integrating clustering-based initialization, tabu-search exploration, a three-parent combination operator, and Lévy mutation.
  • Tested the CMA on 36 benchmark instances from standard datasets.

Main Results:

  • The CMA achieved competitive performance against state-of-the-art algorithms.
  • Improved upper bounds were reported for 25 challenging QMSTP instances.
  • The algorithm matched best-known results for most other instances.

Conclusions:

  • The proposed CMA is effective and efficient for the QMSTP.
  • The clustering mechanism and combination operator significantly contribute to the algorithm's performance.
  • CMA offers a promising approach for complex spanning tree optimization problems.