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How should I solve this problem? Linear Programming? And if, so, any ideas how? I don't know very much about LP.

I have 1200 items. Each item has 8 properties. Each property is scaled from -5 to 5. -5 is worse. 5 is best. I want to select 10 items that will yield the "best" combined group. By best, I value having the sum of each property in the group being more evenly distributed over having the sum of one property really high with the sum of another property being really low.

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Do you mean maximising the minimum value over your 8 properties? What will you want to do if there is a hypothetical feature of property 8 which means it is always -5 whenever any of the other seven properties is positive? How are you measuring "evenly distributed" against "total value" i.e. how do you measure the relative importance of your two competing criteria? At the moment the problem needs to be pinned down to a proper formalisation, which would also clarify concepts like "even distribution". –  Mark Bennet Jan 9 '12 at 5:45
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second Mark. You need to specify at least one precisely defined constraint. If you talk of even distribution, then in the light of information given by you, one can as well take the value of each property as 5: in that case, even distribution will be achieved. If this thing can somehow be formulated as nonlinear problem, maybe one can look at unconstrained optimization techniques-but there also many c onditions need to be satified by the objective function. –  Nikhil Bellarykar Jan 9 '12 at 6:35

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