This paper applies genetic simulated annealing algorithm (SAGA) to solving the geometric constraint problems. Genetic simulated annealing algorithm itself has many merits

such as implicit parallelism

stability of numerical computation and the global searching ability together with the local fast converging ability

etc. This paper takes the special characters of constraint solving into consideration and integrates the SAGA well with it. After the geometry constraint problem is transformed into the optimal one

it is solved by SAGA that making full use of the advantages of SAGA. This approach can deal with the over-/under-constraint problems because of this conversion. It also has advantages due to its not being sensitive to the initial values over the Newton-Raphson method

and its yielding of multiple solutions is an advantage over BFGS(Broyder|Fletcher|Goldfard|Shanno) for multi-solution constraint system. Our experiments have proved the robustn.