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I'm trying to implement a recursive algorithm that I came up with that first solves the knapsack for a given objective and then cuts off the solution and then finds the next best solution. However, I have some dependencies among the items in the knapsack which basically group certain items into one big item. I can either choose all or them, or none of them. Is there a way to model this without using additional variables apart from the n indicator ones representing the ones in the knapsack?

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What do you mean by "cuts off the solution"? –  Ricky Demer Aug 1 '11 at 22:35
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Why not aggregating and have just one variable per "big item"? –  Thomas Kalinowski Aug 1 '11 at 23:08
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