Kandarim wrote:that doesn't take into account overflow though, e.g. your system very well may study an aphid if only 200 s&c is required and a brain would suffice

It's called the knapsack problem, and there are no efficient optimal solvers: it's an NP-hard problem. Genetic algorithms

are probably the way to go, but that doesn't mean I have to like it.

Praise be to JC for such an interesting system!

This is not true in this case. For this to be a Knapsack problem, the amount of inspiration you are willing to spend would have to be limited. However, there is no limit on inspiration; the only restriction is that you want it to be small. Explicitly, you are not saying it has to be smaller than an arbitrary limit L. It is still NP hard (though in practice, given the very limited set of input variables, it may very well still be tractable).

The problem really DOES stem from overspill. While overspill can easily be compensated for, its very existence precludes a guaranteed optimal solution based on a greedy algorithm. First, about compensating: when you have got the bound for a given proficiency, then if an inspirational would go beyond the desired value, the new efficiency ratio would still be (useful amount / total amount), with the correction that part of "useful" goes to "waste" instead. Say you're at 4000 / 6000, something would add 2500 at cost 5000, then the actual ratio in this case would be 2000 / 5000 = 0.4 instead of 0.5. Now, the problem why this may not result in an optimal solution is simple: assume you want to reach 5000. If you study the aphid first, you've got 500 remaining. According to the calculation above, the best thing to study may be a wicker man. But if you had studied a mayapple first, you might have been able to study a more efficient second inspirational.

For the single proficiency case, the scheme above is still asymptotically optimal (if the desired proficiency goes toward infinity, the described overspill problems vanish

. In other words, the error gets smaller the higher the proficiency you're aiming for. It would need testing, but I believe that this already holds true for all practical purposes once your desired proficiency is noticeably higher than your inspirational values.

About genetic algorithms, I'm not getting into that debate

sometimes they do work better than alternatives, sometimes they don't. They are definitely very hard to judge mathematically in terms of any guarantees.