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In this paper we introduce our asynchronous parallel genetic algorithm ASPARAGOS. The two major extensions compared to genetic algorithms are the following. First, individuals live on a 2-D grid and selection is done locally in the neighborhood. Second, each individual does local hill climbing. The rationale for these extensions is discussed within the framework of population genetics. We have applied ASPARAGOS to an important combinatorial optimization problem, the quadratic assignment problem. ASPARAGOS found a new optimum for the largest published problem. It is able to solve much larger problems. The algorithm uses a polysexual voting recombination operator.