MAPCLUS uses an alternating least squares method combined with a mathematical programming optimization procedure based on penalty function approach, to impose discrete constraints on parameters defining cluster membership. This procedure is supplemented by several other numerical techniques (notably a heuristically based combinatorial optimization procedure) to provide an efficient general-purpose computer-implemented algorithm for obtaining ADCLUS representations. MAPCLUS is illustrated with an application to one of the examples given by Shepard and Arabie using the older ADCLUS procedure. The MAPCLUS solution uses half as many clusters to achieve nearly the same level of goodness-of-fit. Finally, the paper considers an extension of the present approach to fitting a three-way generalization of the ADCLUS model, called INDCLUS (INdividual Differences CLUStering). Equations, figures, 7 reference notes, and about 40 references are supplied. (Author abstract modified)