Just cos it’s fun…
From the second edition of The Dictionary of Human Geography, written by Prof. Peter Gould:
A step-by-step procedure, usually supported by a formal mathematical proof, that leads to a desire solution. An example is the Simplex Algorithm in Linear Programming. Heuristic algorithms are not supported by formal proofs, but are highly likely to lead to the optimal solutions. Examples include finding multiple locations within, and the shortest paths through, a network. The word derives from the name Al-Ghorizmeh, a distinguished Arab geographer-mathematician of the sixth century A.D. (See also Districting Algorithm.) PG
Slightly different from the two-sentence version by Prof. Ron Johnston in the 5th edition (2009).