My first question, please excuse me if its too basic.
I have a matrix of evenly spaced geographical points; say
10 x 10, which I will call seed points. Each seed point has a lat/long and the spacing can vary.
Then I place $n$ random points on the same matrix. I call these demand points.
What algorithm can I use to calculate a variable $n$ seed points which will minimize the distance to all the demand points in the matrix?
The user will decide if he/she needs a single seed or multiple seeds to satisfy all the demand points. If a single seed is selected its similar to an average of the demand points, a centroid. But what if multiple seed points need to be selected, say 2. So the problem becomes, which two seed points if selected would give the minimum distance to all the demand points. Each demand point will connect to a single seed and not both.
What I would ideally like is this problem identified as a MIP / LP problem, its name given (i.e. "Travelling Salesman"). Then I can go and research how to solve it using a solver. But that is only if it is possible with a solver.