Given two polygons P and Q in a plane and a translation vector

t∈R2 the area-of-overlap function of P and Q is defined as Ar(t) =Area(P∩(t+Q))

where t+ Q) denotes the new polygon formed by translating Q with t. In order to rapidly compute the maximum value of the area-of-overlap function

an optimal computing strategy is developed in this paper

which includes both combining genetic algorithm with gradient algorithm for rapidly global searching the maximum value of the function and using modified scan-line algorithm for computing the value of the function efficiently in local range.