Genetic algorithms (GA) are among the widely used in various areas of computer science, including optimization problems. Genetic algorithms (GA) are based on the biological process of natural selection. Many simulations have demonstrated the efficiency of GAs on different optimization problems, among them, bin-packing, qaudratic assignment problem, graph partitioning, job-shop scheduling problem, set covering problem, traveling salesman problem, vehicle routing. The quadratic assignment problem (QAP) belong to the class of NP-hard combinatorial optimization problems. One of the main operators in GA is a crossover (i.e. solution recombination). This operator plays a very important role by constructing competitive genetic algorithms (GAs). In this work, we investigate several crossover operators for the QAP, among them, ULX (uniform like crossover), SPX (swap path crossover), OPX (one point crossover), COHX (cohesive crossover), MPX (multiple parent crossover) and others. Comparison of these crossover operators was performed. The results show high efficiency of the cohesive crossover.