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Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications
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Optimizing the multi-objective traveling salesman problem with a deep reinforcement learning algorithm using cross

Xiaoyu Fu1, Shenshen Gu1, Chee-Meng Chew2

  • 1School of Mechatronic Engineering and Automation, Shanghai University, 99 Shangda Road, Shanghai, 200444, China.

Neural Networks : the Official Journal of the International Neural Network Society
|July 31, 2025
PubMed
Summary

This study introduces a novel deep reinforcement learning algorithm, the Cross Fusion Attention Network (CFAN), to solve complex multi-objective traveling salesman problems efficiently. CFAN demonstrates superior performance and generalization across diverse problem instances.

Keywords:
Attention mechanismCombinatorial optimization problemDeep reinforcement learningMulti-objective traveling salesman problem

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Area of Science:

  • Artificial Intelligence
  • Operations Research
  • Computer Science

Background:

  • The multi-objective traveling salesman problem (MOTSP) is a critical combinatorial optimization challenge with broad applications.
  • Traditional algorithms struggle with MOTSP due to large search spaces and conflicting objectives.

Purpose of the Study:

  • To develop an efficient deep reinforcement learning (DRL) algorithm for solving MOTSP.
  • To enhance the ability of DRL models to handle varying weight preferences and explore boundary solutions.

Main Methods:

  • A novel Cross Fusion Attention Network (CFAN) architecture was developed.
  • The CFAN's cross fusion attention encoder captures instance-problem relationships and weight preferences for unified context features.
  • Weight distribution adjustments were used to improve exploration of boundary solutions.

Main Results:

  • CFAN demonstrated superior performance compared to classical evolutionary and advanced DRL algorithms.
  • Significant improvements were observed in hypervolume (HV) metrics: 1.43% on KroAB, 3.12% on tri-objective, and 2.17% on large-scale instances.
  • The CFAN model showed strong generalization capabilities across diverse MOTSP instances.

Conclusions:

  • The proposed CFAN algorithm effectively addresses the challenges of MOTSP.
  • CFAN offers a powerful and versatile approach for multi-objective combinatorial optimization problems.