In this paper we present a method of applying the GPGPU technology to compute the approximate optimal solution to the Heilbronn problem for nine points in the unit square, namely, points $$P_1,P_2,\ldots ,P_9$$ P 1 , P 2 , … , P 9 in $$[0,1]\times [0,1]$$ [ 0 , 1 ] × [ 0 , 1 ] so that the minimal area of triangles $$P_iP_jP_k\,(1\le i<j<k\le 9)$$ P i P j P k ( 1 ≤ i < j < k ≤ 9 ) gets the maximal value $$h_9(\Box )$$ h 9 ( □ ) . We construct nine rectangles with edge length 1 / 80 in the unit square which contain all optimal Heilbronn configurations up to possible rotation and reflection, and prove that $$\frac{9\sqrt{65}-55}{320}=0.054875999\cdots<h_9(\Box )<0.054878314$$ 9 65 - 55 320 = 0.054875999 ⋯ < h 9 ( □ ) < 0.054878314 , the lower bound here comes from Comellas and Yebra’s paper.