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Consider a situation where you have a 'm' number of robots and 'n' number of tasks. Each task is at a different location. What optimization algorithm should I use in order to assign a set of tasks to the robot. The constraints I am taking are battery percentage and distance. How should I assign the tasks to the robots taking into account the constraints.

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Try looking to Linear Integer Programming LIP where you are doing optimization by maximizing task allocation or Utility function at the same time minimizing distance and energy constraints. You will have to formulate the set of equations and use available LIP solvers.

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This seems like a mTSP (multi traveling salesman problem).

Summary: The Multiple Traveling Salesman Problem (mTSP) is a generalization of the Traveling Salesman Problem (TSP) in which more than one salesman is allowed. Given a set of cities, one depot where m salesmen are located, and a cost metric, the objective of the mTSP is to determine a tour for each salesman such that the total tour cost is minimized and that each city is visited exactly once by only one salesman.

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