It is known that some of the algorithms in optimization field have originated from inspiration from animal behaviors in nature. Natural phenomena such as searching behavior of ants for food in a collective way, movements of birds and fish groups as swarms provided the inspiration for solutions of optimization problems. Traveling Salesman Problem (TSP), a classical problem of combinatorial optimization, has implementations in planning, scheduling and various scientific and engineering fields. Ant colony optimization (ACO) and Particle swarm optimization (PSO) techniques have been commonly used for TSP solutions. The aim of this paper is to propose a new hierarchical ACO- and PSO-based method for TSP solutions. Enhancing neighboring operators were used to achieve better results by hierarchical method. The performance of the proposed system was tested in experiments for selected TSPLIB benchmarks. It was shown that usage of ACO and PSO methods in hierarchical structure with neighboring operators resulted in better results than standard algorithms of ACO and PSO and hierarchical methods in literature.

中文翻译：

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邻域运营商基于 ACO 和 PSO 的分层方法用于 TSP 解决方案

众所周知，优化领域的一些算法的灵感来源于自然界中的动物行为。蚂蚁的集体觅食行为、鸟群和鱼群的运动等自然现象为优化问题的解决提供了灵感。旅行商问题 (TSP) 是组合优化的经典问题，在计划、调度和各种科​​学和工程领域都有实现。蚁群优化 (ACO) 和粒子群优化 (PSO) 技术已普遍用于 TSP 解决方案。本文的目的是为 TSP 解决方案提出一种新的基于分层 ACO 和 PSO 的方法。通过分层方法增强相邻算子以获得更好的结果。在选定的 TSPLIB 基准的实验中测试了所提出系统的性能。结果表明，在具有相邻算子的分层结构中使用 ACO 和 PSO 方法比文献中的 ACO 和 PSO 标准算法和分层方法产生更好的结果。