Is it possible to find a solution for TSP that avoids crossing over the object?

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No, it is not possible to find a solution for TSP that avoids crossing over the object. The nature of the problem requires visiting all of the vertices in the graph exactly once, and the most direct route between two points may sometimes require crossing over the object. While it may be possible to find a route that minimizes the number of crossings, it is not possible to completely avoid them in all cases.