The problem of finding a subset of points in a pattern that best match to a subset of points in another pattern through a transformation in an optimal sense is considered. An exhaustive search to find the best assignment mapping one set of points to another set is, if the number of points that are to be matched is large, computationally expensive. A genetic algorithm that searches for the best ('almost the best') assignment efficiently is described. To map the point pattern matching into the framework of a genetic algorithm, a fitness function that is inversely proportional to the match error and a scheme for encoding an assignment between two sets of points into a string are used, along with a genetic operator known as the mixed-type partial matching crossover. Experimental results have demonstrated the robustness and the fast convergence of the algorithm. The algorithm can be applied to n-dimensional point patterns and any transformation. Results are presented for two-dimensional point patterns and a similarity transformation.