In a computer-implemented method for finding a high quality allocation of one or more bids in a combinatorial auction, a number of bids is electronically received. Each bid includes a number of sub bids and a Boolean operator logically connecting each pair of sub bids. Each sub bid is either (1) a good and an associated price or (2) one of the Boolean operators associated with a price and at least two other sub bids. From a number of allocations of goods to sub bids, wherein each allocation of the goods is to a different set of sub bids, an allocation is output that has the greatest value. The value of each allocation includes of a sum of prices of bids that have at least one satisfied sub bid. The price of each bid includes a sum of the prices associated with each satisfied sub bid of the bid.