### Proposed combinatorial algorithms for solving Quadratic Assignment problem

#### Abstract

This research includes construction of combinatorial algorithms for solving the Problem, used Harmony Search algorithm in this research but added the improvement Procedures to increase the Performance of algorithm and speed up access to the optimal solution of the problem, The algorithm consists of two phases, the first phase will improve all the existing solutions in the Harmony Memory use some improvement measures is the property of Crossover existing solutions in the Harmony. Memory use some improvement measures is the property of Crossover used in genetic algorithm and also guided search to reduce the objective function, the second phase will depend on the Procedures of the Harmony search algorithm (HS) but using a new Improvise, The algorithm has proven its efficiency in solving the problem is resolved (15) standard problem from the special library of Quadratic Assignment Problem (QAPLIB), and compare the results with the local search algorithm (LS), Tabu search (TS), Simulated annealing (SA) after solving each problem (25) times and record the results of the algorithm shown open her with total access to the optimal solution (282) of the total (375) repetition of the test as the total reached the local search algorithm (2) Simulated annealing algorithm (117) and Tabu search algorithm is (174).

#### Keywords

Quadratic Assignment Problem, Harmony search algorithm, combinatorial optimization problem, Local search#### Metrics