Best Fit Logic

[tim2...@gmail.com]

I am trying to determine where I might find the logic behind determing
the best fit solution for a problem.

I am trying to produce programmically the logic to split a set of data
to fit with a set of parameters.

The parameters are thus:
Maximum number of members to a group M.
Maximum weight allowed in group W.
Maximum number of groups G.
Each member of the group has a weight w.
Each member is unique and can only belong to 1 group.

So what I want to do is develop the logic in which I can distribute
the weight as evenly as possible up to the maximum with in the
different groups. I also want to use (if possible) the maximum number
of groups.

So as an example I have a maximum number of groups is 3 : G1, G2, G3
My members and weight (m,w) are: (a,200)(b,50)(c,100)(d,50)(e,150)(f,
300)(g,100)(h,50)(i,250)(j,100)(k,50)
The maximum weight is 450.
So one possible solution would be:
G1:(a,200)(b,50)(c,100)(h,50)(k,50)
G2:(d,50)(e,150)(j,250)
G3:(f,300)(g,100)

This is a solution without the maximum members...what if the maximum
members was set to M=4.
What is the logic to find the best fit solution. Not for this
specific case but just in general.

Can anyone point me in the right direction?

Regards
Tim

[OP]

tim2...@gmail.com wrote:
> I am trying to determine where I might find the logic behind determing
> the best fit solution for a problem.

I'm not fluent enough to give you a quick top-of-the-head example,
but have you looked into logic programming with any of the Prolog
variants, or constraint logic programming with ECLiPSe? They're
made for this sort of thing.

http://www.eclipse-clp.org/

Hope this is what you were asking.

[unixops]

Tim

> Maximum number of members to a group M.
>Maximum weight allowed in group W.
>Maximum number of groups G.

WGM in M

WG in M, G=3, W=450=[0,1) G>1 else W=[0,1]
Remove G, such that G<=M

So one possible solution would be:
G1:(a,200)(b,50)(c,100)(h,50)(k,50)

V=W(1),W(2), e.g. f(a,b,c)

>members and weight (m,w)

m~g(x), w~f(x)

g(x,f(x,y,z)) <=M

-Doug

[unixops]

Hello Tim,

Thought more on your topic, the idea is to run g(f()) for each set in
M
Keep it simple, kernel functions as weight densities.

I run them fast and think few careful observations, to much thinking,
small time for computation.

-Doug