This tutorial presents a novel search system—the Attractor-Based Search System (ABSS)—that can solve the Traveling Salesman Problem very efficiently with optimality guarantee. From the perspective of dynamical systems, a heuristic local search algorithm for an NP-complete combinatorial problem is a discrete dynamical system. In a local search system, an attractor drives the search trajectories into the vicinity of a globally optimal point in the solution space, and the convergence of local search trajectories makes the search system become a global and deterministic system. The attractor contains a small set of the most promising solutions to the problem. The attractor can reduce the problem size exponentially, and thus make the exhaustive search feasible. Therefore, this new search paradigm is called optimizing with attractor. The ABSS consists of two search phases: local search phase and exhaustive search phase. The local search process is used to quickly construct the attractor in the solution space, and the exhaustive search process is used to completely search the attractor to identify the optimal solution. Therefore, the exact optimal solution can be found quickly by combining local search and exhaustive search. This tutorial introduces the concept of an attractor in a local search system, and describes the process of optimizing with the attractor, using the Traveling Salesman Problem as the study platform.

本教程提出了一种新颖的搜索系统——基于吸引子的搜索系统（ABSS）——它可以非常有效地解决旅行商问题并保证最优性。从动力系统的角度来看，NP完全组合问题的启发式局部搜索算法是一个离散动力系统。在局部搜索系统中，吸引子将搜索轨迹驱动到解空间中的全局最优点附近，并且局部搜索轨迹的收敛使搜索系统成为全局的确定性系统。吸引子包含一小组最有希望解决该问题的解决方案。吸引子可以指数级减小问题规模，从而使穷举搜索变得可行。因此，这种新的搜索范式被称为吸引子优化。 ABSS由两个搜索阶段组成：局部搜索阶段和穷举搜索阶段。局部搜索过程用于在解空间中快速构造吸引子，穷举搜索过程用于完全搜索吸引子以确定最优解。因此，结合局部搜索和穷举搜索可以快速找到准确的最优解。本教程以旅行商问题为研究平台，介绍了本地搜索系统中吸引子的概念，并描述了利用吸引子进行优化的过程。