The purpose of the article is to explore the application of Ordered Fuzzy Numbers (OFN) in solving the Traveling Salesman Problem (TSP) using Ant Colony Optimization (ACO). Incorporating OFN into the ant algorithm represents a fresh approach to optimizing this particular problem. The authors introduce the antOFN method as a solution to this optimization problem. In the following steps, we discuss the TSP itself and possible solutions. The authors then present solutions to the problem using ACO. The main goal of the article is a discussion of the solution based on directed fuzzy numbers OFN, where we explain the interpretation of pheromone and describe the operations performed. In the concluding section, the authors concentrate on the experiment in which they present results for solutions from the ACO group and those dedicated to the Traveling Salesman Problem. Ultimately, the experiment’s outcomes demonstrate that methods rooted in Ant Colony Optimization excel in achieving solutions, with the proposed antOFN solution falling within the realm of optimal solutions.

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Application of Fuzzy Ant Colony in Solving Traveling Salesman Problems

  • Wojciech T. Dobrosielski,
  • Leonid Rusanov,
  • Grzegorz Czeczot,
  • Rafał Lizut,
  • Jacek Zalewski

摘要

The purpose of the article is to explore the application of Ordered Fuzzy Numbers (OFN) in solving the Traveling Salesman Problem (TSP) using Ant Colony Optimization (ACO). Incorporating OFN into the ant algorithm represents a fresh approach to optimizing this particular problem. The authors introduce the antOFN method as a solution to this optimization problem. In the following steps, we discuss the TSP itself and possible solutions. The authors then present solutions to the problem using ACO. The main goal of the article is a discussion of the solution based on directed fuzzy numbers OFN, where we explain the interpretation of pheromone and describe the operations performed. In the concluding section, the authors concentrate on the experiment in which they present results for solutions from the ACO group and those dedicated to the Traveling Salesman Problem. Ultimately, the experiment’s outcomes demonstrate that methods rooted in Ant Colony Optimization excel in achieving solutions, with the proposed antOFN solution falling within the realm of optimal solutions.