What is the difference between Manhattan distance and Hermann Minkowski distance as the less computational time fitness function?
I used one of them as the best fitness function for the lowest evolving time in my paper titled:
Using Genetic Algorithm to Improve Information Retrieval Systems, but I do not know the difference between them.
Could you please explain:
1) What is "less computational time fitness function"?
2) Why do you use these distances - measuring the distance/similarity of what? Your algorithm makes the decision based on the distance as "weight" parameter? (Manhattan is, of course, the simplest by means of mathematical operations, while calculating Minkowski for p>1 (p=1 equals the Manhattan) involves at least some more complex operations - exponention and calculating root if necessary) If you refer to "less computational time" at algorithm performance level, Manhattan calculation is less complex and therefore it should be faster... but, if you refer to finding some minimum/optimum based on distance calculation, than of course selection of the distance type may depend on the use-case.
I believe the importance and difference of solutions may depend on the use-case. The obtained results and their validation on smaller cases may lead to conclusion which distance gives "better" results. (In case of finding the lowest evolving time in your paper, for example - what are the results if you use different distance calculation? How do you decide than one of the distances performed as the best fitness function? Have you tried another one, does is influence the solution?)
When Minimizing the subtraction between query and document vectors is less complex than maximizing the distance between query and document vectors and consequently it will have the lowest evolving time. This is if both were used as objective function on the same metaheuristic algorithm.
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