Random-centroid optimization was modified by introducing a penalty fun
ction to accommodate constraints in formula optimization. Quality para
meters not significantly different (p > 0.05) from those obtained by t
he Complex (constrained simplex) modified for formulation (Forplex) we
re computed by this new program and yielded similar ingredient composi
tions to those computed by Forplex. The new program was similar or mor
e efficient in optimization than Forplex which occasionally stalled du
ring searching for the optimum. It has been found that the new, multif
actor program written to accommodate up to 20 factors is appropriate f
or use in research and development, especially for formulations with c
onstraints, while Forplex is recommended for routine formulation.