In this paper the problem of obtaining the Voronoi diagram which approximates a given tessellation of the plane is formulated as the optimization problem, where the objective function is the discrepancy of the Voronoi diagram and the given tessellation. The objective function is generally non-convex and nondifferentiable, so we adopt the primitive descent algorithm and its variants as a solution algorithm. Of course, we have to be content with the locally minimum solutions. However the results of the computational examples suggest that satisfactory good solutions can be obtained by our algorithm. This problem includes the problem to restore the generators from a given Voronoi diagram (i.e., the inverse problem of constructing a Voronoi diagram from the given points) when the given diagram is itself a Voronoi diagram. We can get the approximate position of the generators from a given Voronoi diagram in practical time; it takes about 10s to restore the generators from a Voronoi diagram generated from thirty-two points on a computer of speed about 17 MIPS. Two other practical examples are presented where our algorithm is efficient, one being a problem in ecology and the other being one in urban planning. We can get the Voronoi diagrams which approximate the given tessellations (which have 32 regions and are defined by 172 points in the former example, 11 regions and 192 points in the latter example) within 10s in these two examples on the same computer.