This paper presents an efficient graph-based evolutionary optimization tech
nique called Evolutionary Graph Generation (EGG), and its application to th
e design of fast constant-coefficient multipliers using parallel counter-tr
ee architecture. An important feature of EGG is its capability to handle th
e general graph structure: directly in evolution process instead of encodin
g the graph structures into indirect representations, such as bit strings a
nd trees. This paper also addresses the major problem of EGG regarding the
significant computation time required fur verifying the function of generat
ed circuits. To solve this problem, a new functional verification technique
for arithmetic circuits is proposed. It is demonstrated that the EGG syste
m can create efficient multiplier structures which are comparable or superi
or to the known conventional designs.