A method and apparatus: (1) select and apply a transition from a set of first objective enhancing transitions to an initial information integration flow graph based upon how application of each transition impacts a length of a chain of nodes to produce a first set of modified information integration flow graphs that satisfy a first objective; (2) select and apply a second transition from the set of first objective transitions and a set of second objective enhancing transitions to the first set of modified information integration flow graphs to produce a second set of modified information integration flow graphs that satisfy the first objective and the second objective; and (3) identify an information integration flow graph from the first set and the second set having a lowest cost.