The dynamic traveling salesman problem (DTSP) falls under the category of combinatorial dynamic optimization problems. The DTSP is composed of a primary TSP sub-problem and a series of TSP iterations; each iteration is created by changing the previous iteration. In this article, a novel hybrid metaheuristic algorithm is proposed for the DTSP. This algorithm combines two metaheuristic principles, specifically ant colony optimization (ACO) and simulated annealing (SA). Moreover, the algorithm exploits knowledge about the dynamic changes by transferring the information gathered in previous iterations in the form of a pheromone matrix. The significance of the hybridization, as well as the use of knowledge about the dynamic environment, is examined and validated on benchmark instances including small, medium, and large DTSP problems. The results are compared to the four other state-of-the-art metaheuristic approaches with the conclusion that they are significantly outperformed by the proposed algorithm. Furthermore, the behavior of the algorithm is analyzed from various points of view (including, for example, convergence speed to local optimum, progress of population diversity during optimization, and time dependence and computational complexity).

中文翻译：

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基于蚁群优化和模拟退火的混合算法在动态旅行商问题中的应用

动态旅行商问题 (DTSP) 属于组合动态优化问题的范畴。DTSP 由一个主 TSP 子问题和一系列 TSP 迭代组成；每次迭代都是通过更改前一次迭代来创建的。在本文中，针对 DTSP 提出了一种新颖的混合元启发式算法。该算法结合了两个元启发式原理，特别是蚁群优化 (ACO) 和模拟退火 (SA)。此外，该算法通过以信息素矩阵的形式传输在先前迭代中收集的信息来利用有关动态变化的知识。在包括小型、中型和大型 DTSP 问题在内的基准实例上检查和验证了混合的重要性以及动态环境知识的使用。将结果与其他四种最先进的元启发式方法进行比较，得出的结论是所提出的算法明显优于它们。此外，还从多个角度分析了算法的行为（包括，例如，收敛到局部最优的速度、优化过程中种群多样性的进展，以及时间依赖性和计算复杂度）。