We present a Monte Carlo optimization algorithm to search for the boun
dary points of the orbit space which is important in determining the s
ymmetry breaking directions in the Higgs potential and the Landau pote
ntial. Our algorithm is robust and generally applicable. For large pro
blems we have also developed a parallel version. We apply the method t
o the Landau potential of the d-wave abnormal superconductor, He-3, an
d a SU(5) Higgs potential. (C) 1998 Elsevier Science B.V.