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I have constructed this problem myself and wanted to solve this problem myself as well, however cannot come across and efficient solution to this problem.

A group of soldiers are injured in a difficult mountainous terrain. Each soldier has a device which has GPS tracker to locate him upon any emergency and a functionality to send a distress signal at times of emergency. Upon reciept of a distress signal, the command center dispatches another soldier who comes across one of the injured soldiers. Upon recovering the injured soldier, the two uninjured soldiers decide to help other (injured) soldiers so that they can similarly help in recovering the remaining injured soldiers. The mountains are guarded by miltia and need to be avoided, and their bases are expressed as polygons.

Given: Coordinates of every injured soldier, Coordinates of polygon representing the base of moutains.

Required: Optimal solution to find optimized path until all injured soldiers are recovered.

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    It is not clear what is being optimized here. Since this is "difficult terrain", minimizing straight-line distances of path segments may not be a good idea. Otherwise, it seems like essentially a Travelling Salesman problem once you determine optimal routes between each pair of injured soldiers. – 2017-02-20
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    Why don't you first attempt a simplified version of the problem. Say the mountain is a cone for example. Then you can try to generalize your solution. – 2017-02-20
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    @RobertIsrael This definitely is not a Travelling Salesman Problem as we are not finding a Hamiltonian Circuit, when each soldier 'revives' he will be able to help another soldier, and so would the soldier who has arrived previously to wake him up. – 2017-02-20
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    You should have made that more clear in the statement of the problem. Apparently you want a binary tree, not a path. You still haven't said what you want to optimize. – 2017-02-21
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    I expect there should be an integer (or maybe mixed integer) linear programming formulation with binary variables $x_{ij}$ for each pair of locations of injured soldiers, where $x_{ij} = 1$ if a soldier goes from location $i$ to location $j$. – 2017-02-21
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    Sorry for not making that more clear sir, we are trying to find the optimal set of paths for each soldier, which minimises the time spent on reviving the soldiers is what we are going to call Move-and-Tag Problem (MAT). The described challenge is a combination of a well-known Robot Motion Planning problem (RMP) and less well-known Freeze-Tag problem (FT). In RMP, one should find an optimal way for a soldier from a point A to a point B in the presence of multiple obstacles. In FT, a swarm of soldiers must wake up in the shortest possible time, starting from one specified soldier. – 2017-02-21
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    How should I go about the Linear Programming formulation you are describing? Can you elaborate more clearly in steps, I am not demanding an exhaustive explanation but a little more elaborate. Thank you so much. – 2017-02-21

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