用收缩块计算旅行商问题
Computation of the Travelling Salesman Problem by a Shrinking Blob
摘要：
旅行商问题（TSP）是一个著名的和具有挑战性的组合优化问题。它的计算难度吸引了一些启发式方法来产生令人满意的，如果不是最佳的，候选解决方案。在本文中，我们展示了一个简单的非常规计算方法来近似欧几里德TSP使用虚拟材料的方法。材料的形态适应行为来自扩散晶格内移动的粒子群体的低水平相互作用。这种材料的“斑点”被放置在一组投影到网格中的数据点上，代表TSP城市位置，斑点的大小随着时间的推移而减小。随着斑点的缩小，它在形态上适应了城市的结构。当斑点不再完全覆盖所有城市时，收缩过程自动停止。通过手动跟踪斑点的周边，引出对应于TSP之旅的城市之间的路径。在20个城市的20个随机生成的数据集上运行6次以上，这种简单且无指导的方法发现，当表示为由精确TSP求解器计算的最小行程的一部分时，平均最佳行程长度为1.04，平均平均行程长度为1.07，平均最差行程长度为1.09。我们研究的插入机制，其中的斑点构建一个旅游，注意到一些属性和其性能的限制，并讨论了斑点TSP和邻近图的组点在平面上的关系。该方法以其简单性和其操作的空间表示机械模式而闻名。我们讨论了这种方法和以前提出的模型的TSP上的人类表现之间的相似之处，并提出进一步改进的可能性。
英文摘要：
The Travelling Salesman Problem (TSP) is a well known and challenging combinatorial optimisation problem. Its computational intractability has attracted a number of heuristic approaches to generate satisfactory, if not optimal, candidate solutions. In this paper we demonstrate a simple unconventional computation method to approximate the Euclidean TSP using a virtual material approach. The morphological adaptation behaviour of the material emerges from the low-level interactions of a population of particles moving within a diffusive lattice. A `blob' of this material is placed over a set of data points projected into the lattice, representing TSP city locations, and the blob is reduced in size over time. As the blob shrinks it morphologically adapts to the configuration of the cities. The shrinkage process automatically stops when the blob no longer completely covers all cities. By manually tracing the perimeter of the blob a path between cities is elicited corresponding to a TSP tour. Over 6 runs on 20 randomly generated datasets of 20 cities this simple and unguided method found tours with a mean best tour length of 1.04, mean average tour length of 1.07 and mean worst tour length of 1.09 when expressed as a fraction of the minimal tour computed by an exact TSP solver. We examine the insertion mechanism by which the blob constructs a tour, note some properties and limitations of its performance, and discuss the relationship between the blob TSP and proximity graphs which group points on the plane. The method is notable for its simplicity and the spatially represented mechanical mode of its operation. We discuss similarities between this method and previously suggested models of human performance on the TSP and suggest possibilities for further improvement.
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