A method for obtaining solutions to combinatorial problems by way of a discrete state-based search approach utilizes a node evaluation function based both on solution quality and distance in search steps to a goal. The method considers the problem as finding the shortest path between an initial state and a goal state in a large graph and performs solution evaluation utilizing computation time balanced against solution quality. Rather than solely using a lower bound on the solution cost achievable below a search node, an estimate of the distance (in search steps) to the nearest solution below a search node is also utilized. These are combined using the user's stated utility function (represented as a function of time and cost) to evaluate candidate search nodes.