Comparison of shortest sailing distance through random and regular sampling points

摘要

The shortest sailing distance through n sampling points is calculated for simple theoretical sampling domains (square and circle) as well as for a rather irregular and concavely shaped real sampling domain in the Barents Sea. The sampling sites are either located at the nodes of a square grid (regular sampling) or they are randomly distributed. For n less than ten, the exact shortest sailing distance is derived. For larger n, a traveling salesman algorithm (simulated annealing) was applied, and its bias (distance from true minimum) was estimated based on a case where the true minimum distance was known. In general, the average minimum sailing distance based on random sampling was considerably shorter than for regular sampling, and the difference increased with sample size until an asymptotic value was reached at about n = 60 for a square domain. For the sampling domain in the Barents Sea used for shrimp (Pandalus borealis) abundance surveys (n = 118 stations), the cruise-track lengths based on random sampling were approximately normally distributed. The mean sailing distance was 18% shorter than the cruise track for regular sampling and the standard deviation equalled 2.6%.