The point I was making was I think that only the LP & brute force methods generate optimal results consistently. Maybe the MC & LS methods might be faster or maybe even take less key strokes but that is irrelevant if they don't generate optimal results all the time.

If I am reading the thread correctly, Richard has shown that the brute force method generates at least one solution more "optimal" than the Gold Standard. If this is so,it is proof that this strategey doesn't consistently generate optimal results.

Also, what exactly do you mean by Monte-Carlo? Is this just a simple random selection process or is it something more complicated?

PS: I not sure that I understand your reference to seeding in LP solution. If you wanted to minimize key strokes, I suggest you could seed the first iteration with x(1)=x(2)=..=X(n)=0 but if your playlist were always small you could seed it with the first m elements whose sum fits below the threshold. This would converge very fast in the examples given. Maybe with less than 10 iterations in the cases shown.

[ 12. March 2003, 20:41: Message edited by: Jack Lothian ]
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Jack