We propose an efficient algorithm for the purpose of satisfying a wide rang
e of design constraints represented with equality and inequality equations
as well as production rules. The algorithm employs simulated-annealing and
a production rule inference engine and works on design constraints represen
ted with networks. The algorithm fulfills equality constraints through cons
traint satisfaction processes like variable elimination while taking into a
ccount inequality constraints and inferring production rules. It can also r
educe the load of the optimization procedure if necessary. We demonstrate t
he implementation of the algorithm with the result on machine tool design.