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POAlgorithm for cleaning some spots on a floor using automatic vacuum cleaners?
 

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  1. POAlgorithm for cleaning some spots on a floor using automatic vacuum cleaners?
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    <p>Please feel free to rename the question...</p> <p>Here's the problem:</p> <p>I have a certain number 'n' of automatic vacuum cleaners on a floor with a number 'k' of dirty spots on it. What's the optimal way to assign the vacuum cleaner to the dirty spots in order to clean the floor in the most efficient way?</p> <p>Details:</p> <ul> <li>The floor is represented by a not weighted graph with n/k randomly placed on it</li> <li>At most one vacuum cleaner can be assigned to a dirty spot</li> <li>Ignore the possibility that two vacuum cleaners might hit each other</li> <li>The time for cleaning a spot is not relevant. Only the distance between them it is</li> <li>Keep in mind that k might be greater than n</li> </ul> <p>What "kind" of problem is this?</p> <p>How would you implement a solution for it?</p> <p>I thought about calculating the distance between all the possible pairs ('n' * 'k'), ordering them in ascending order, and matching vacuum cleaners and dirty spots making sure not to send two cleaners to the same spot. This might not be efficient and it probably doesn't find the best solution at all times..</p> <p>Thanks!</p>
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    1. USGevorg
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      1. POAlgorithm for cleaning some spots on a floor using automatic vacuum cleaners?
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      1. POAlgorithm for cleaning some spots on a floor using automatic vacuum cleaners?
      1. USStuart Golodetz
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    1. CODefine 'efficient'. That is, what's your _fitness function_? For example: is it minimum total travel distance for all cleaners?
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      1. USAlistair A. Israel
    2. COYes, performances can be calculated considering the travel distance of the cleaners (they all have same speed). `The floor has to be clean and the task is over`. As you said -minimum total travel distance for all cleaners- should be a correct and more formal description of what I'm looking for.
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      1. USGevorg
 

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