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<p>This article discusses a constrained Travelling Salesman Problem (TSP), in which the traveler determines the shortest route to take in order to place a limit on the total journey time and costs. In actual life, the length of a tour and its total cost might be scheduled. The goal of the proposed TSP is the expense of travel. It is a cost optimization based TSP. The overall cost of travel cannot be more than the proposed TSP’s total travel allowance and time ceiling. The expenses and duration of travel are regarded as type-2 fuzzy (T2F) variables. Using a defuzzification technique, we came across the crisp equivalency of fuzzy objective or fuzzy cost. An approach motivated by ant colony optimization (ACO) has been employed to solve the hypothesized TSP. To solve the suggested TSP, two features–"probabilistic selection" and "neighborhood path search"-have been added to the fundamental ACO. Furthermore, we have adopted a 2-optimal strategy for the ACO technique to obtain a better path quickly. A few common benchmark problem examples or datasets have been explored in order to illustrate the utility of the depicted approach. In addition, this paper computes a few benchmark cases that have been redefined in a random T2F circumstance.</p>

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Solving a cost- and time-limited travelling salesman problem by an ant colony-based algorithm in a random type-2 fuzzy environment

  • 期刊论文

  • 发表日期：

    2026年5月4日

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  • Chiranjit Changdar,
  • Pravash Kumar Giri,
  • Utpal Nandi,
  • Sudip Kumar Sahana

摘要

This article discusses a constrained Travelling Salesman Problem (TSP), in which the traveler determines the shortest route to take in order to place a limit on the total journey time and costs. In actual life, the length of a tour and its total cost might be scheduled. The goal of the proposed TSP is the expense of travel. It is a cost optimization based TSP. The overall cost of travel cannot be more than the proposed TSP’s total travel allowance and time ceiling. The expenses and duration of travel are regarded as type-2 fuzzy (T2F) variables. Using a defuzzification technique, we came across the crisp equivalency of fuzzy objective or fuzzy cost. An approach motivated by ant colony optimization (ACO) has been employed to solve the hypothesized TSP. To solve the suggested TSP, two features–"probabilistic selection" and "neighborhood path search"-have been added to the fundamental ACO. Furthermore, we have adopted a 2-optimal strategy for the ACO technique to obtain a better path quickly. A few common benchmark problem examples or datasets have been explored in order to illustrate the utility of the depicted approach. In addition, this paper computes a few benchmark cases that have been redefined in a random T2F circumstance.