This article describes the development of a new intelligent heuristic search algorithm (IHSA*) which guarantees an optimal solution for flow-shop problems with an arbitrary number of jobs and machinesprovided the job sequence is constrained to be the same on each machine. The development is described in terms of 3 modifications made to the initial version of IHSA*. The first modification concerns thechoice of an admissible heuristic function. The second concerns the calculation of heuristic estimates as the search for an optimal solution progresses, and the third determines multiple optimal solutions whenthey exist. The first 2 modifications improve performance characteristics of the algorithm and experimental evidence of these improvements is presented as well as instructive examples which illustrate the use of initial and final versions of IHSA*.