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Some local search methods (LSMs) for solving the Quadratic Assignment Problem (QAP), which is considered an NP-hard problem, are proposed in this paper. The aim of the problem is to minimize the sum of the distances multiplied by the corresponding flows by assigning the same number of facilities to the same number of different locations. Tabu search (TS) and Bees Algorithm (BA) are two suggested LSMs for solving QAP. We compared the results of LSMs with the complete enumeration method (CEM) and some strong heuristic methods in the first part of this paper. The results studied the existence of TS and BA in resolving our problem. The second part is split into two sections. As a practical application, we solve the QAP represented by civil engineering for Al-Zahra hospital in Kut/Iraq in the second part. The discussed methods are used to find the optimal and approximation solutions for this problem. [ABSTRACT FROM AUTHOR]