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I am trying to determine the optimal search strategy for the problem stated below.

I have to search a raster in order to localize an object with unknown position.

I assume that the optimal route to search for this object can be solved using TSP, if there is no further information about the objects location. In this case the probability of the object beeing in a certain grid is 1/#numberOfGrids (Figure 1) Uniform location distribution

In contrast to this "simple" setting I now assume that we have knowledge about the probability of the object beeing in a certain grid (Figure 2). New location distribution

Starting at any point on this raster, the search process stops as soon as the object is found or after all grids have been searched. Does anyone know an algorithm to solve such problems?

Niko
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1 Answers1

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This is not a traveling salesman problem.

I assume you can randomly go from any raster point to any other, at constant cost.

In that case, go first to the most likely raster point, then the second, and so on. That will minimize the expected time.

Mike Dunlavey
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  • Thanks for your reply. If I can go to any raster point at constant cost your approach will work. But the cost (time) from raster to raster is not constant. In fact, it is direct proportional in the distance. We have to search the area shown in the figure for an object. So walking from the lower left edge to the upper right edge without checking any raster in between will not be the optimal way even if this two rasters have the highest probability. – Niko Jun 02 '16 at 16:18
  • @Niko: Then it becomes more like a traveling salesman problem, and I would look for some kind of heuristic approach. For example, if the probability function has a single peak, it is obvious to start there, and proceed outward in layers of descending probability. If there is more than one peak, I would consider descending from one until getting to the vicinity of another, then doing the same thing from that peak, and so on. – Mike Dunlavey Jun 02 '16 at 17:48
  • Thanks again Mike. I was talking about this problem with a colleague working on graph theory and he was proposing a similar approach. Hence, I will follow your advise and try an heuristic approach. I was thinking that "optimal search path" is some kind of standard problem with existing algorithms I just don't know about. But obviously it is not as easy as that :) – Niko Jun 02 '16 at 19:30