In an apparatus and method of solving a combinatorial exchange, a plurality of candidate allocations of input bids is determined from input bids and a set of bid vectors is formed from the input bids. A probability value, representing how likely the bids of a bid vector will comprise the bids from which a final allocation is determined, is associated with each bid vector. A mapping is then determined between each bid vector and at least one of the candidate allocations based on a set of objectives and a set of constraints. A candidate allocation is selected as a final allocation based on a comparison of another set of bids that define an exchange event bid vector with at least one of the bid vectors.