一个贪婪的旅行推销员的扩散行为
Diffusive behavior of a greedy traveling salesman
摘要：
使用蒙特卡罗模拟，我们研究了扩散性质的贪婪算法在d维旅行商问题。我们的结果表明，对于d=3和4，到原点的平均平方距离<r^2>与步数t成正比。在d=2的情况下，这种缩放通过一些对数修正进行修改，这可能表明d=2是问题的关键维度。长度分布在d=2和d>2的版本之间也显示出显著的差异。推销员采用的简单策略可能类似于一些觅食和狩猎动物选择的策略，最近有报道称，这些动物的异常扩散行为可以用利维飞行来解释。我们的研究结果表明，广泛的Levy分布在这样的系统中可能会出现由于搜索空间的维数依赖性。
英文摘要：
Using Monte Carlo simulations we examine the diffusive properties of the greedy algorithm in the d-dimensional traveling salesman problem. Our results show that for d=3 and 4 the average squared distance from the origin <r^2> is proportional to the number of steps t. In the d=2 case such a scaling is modified with some logarithmic corrections, which might suggest that d=2 is the critical dimension of the problem. The distribution of lengths also shows marked differences between d=2 and d>2 versions. A simple strategy adopted by the salesman might resemble strategies chosen by some foraging and hunting animals, for which anomalous diffusive behavior has recently been reported and interpreted in terms of Levy flights. Our results suggest that broad and Levy-like distributions in such systems might appear due to dimension-dependent properties of a search space.
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