Heuristic search is used to efficiently solve the single-node
shortest path problem in weighted graphs. In practice, however,
one is not only interested in finding a short path, but
an optimal path, according to a certain cost notion. We propose
an algebraic formalism that captures many cost notions,
like typical Quality of Service attributes. We thus generalize
A*, the popular heuristic search algorithm, for solving
optimal-path problem. The paper provides an answer to a
fundamental question for AI search, namely to which general
notion of cost, heuristic search algorithms can be applied. We
proof correctness of the algorithms and provide experimental
results that validate the feasibility of the approach.