In this book, we consider the benchmark quadratic assignment problem which is very difficult NP-hard problem that has several practical applications. Several exact and heuristic algorithms are developed for solving the problem. In general, large sized instances cannot easily be solved optimally by an exact algorithm, but there are some situations where only exact optimal solution is required. Hence, we first present a reformulation of the problem, and then we apply simple and data-guided lexisearch algorithm to obtain exact optimal solutions to the problem. We also develop simple and improved genetic algorithms using sequential constructive crossover operator to find heuristic solution to the problem. Finally, a hybrid algorithm that combines lexisearch and genetic algorithms is developed. The proposed algorithm uses lexisearch algorithm to generate initial population, self-adaptive three crossover operators, and randomly one of four mutation operators, restricted combined mutation operator as local search, and multi-parent sequential constructive crossover as immigration method. Experimental results on benchmark QAPLIB instances show the effectiveness of the developed algorithms.