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# Frequency Model Based Crossover Operators for

The quadrati c assignment problem aims to find an optimal assignment of a set of facilities to a set of locations that
minimizes an objective function depending on the flow between facilities and the distance between locations. In this paper we
investigate Genetic Algo rithm (GA) using new crossover operators to guide the search towards unexplored regions of the
search space. First , we define a frequency model which keeps in memory a frequency value for each pair of facility and
location. Then, relying on the frequency m odel we propose three new crossover operators to enhance g enetic algorithm for the
quadratic assignment problem. The first and second ones, called Highest Frequency crossover (HFX) and Greedy HFX
(GHFX), are based only on the frequency values, while the third one, called Highest Frequency Minimum Cost crossover
(HFMCX), combines the frequency values with the cost induced by assigning facilities to locations. The experimental results
comparing the proposed crossover operators to three efficient crossover ope rators, namely, One Point crossover ( OPX ), Swap
Path crossover (SP X) and Sequential Constructive crossover (SCX ), show effectiveness of our proposed operators both in
terms of solution quality and computational time.

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[ 28] V zquez M. and Whitley L. D., A Hybrid Genetic Algorithm for th e Quadratic Assignment Problem , in Proceedings of the 2nd Annual Conference on Genetic and Evolutionary Computation, Las Vegas, pp. 135- 142, 2000. Hachemi Bennaceur is Full Professor in Computer cience Department of Al Imam Mohammad bin Saud Islamic University. He worked for over twenty years in various academic institutions in France. He was promoted to full professor in 2007 at Artois University (Lille -Nord academy, France). During the same period he was successively researcher at the Computer Science Lab of Paris -Nord University (LIPN), and then at the Research Center of Computer Science of Lens (CRIL). His main research topics involve Constraint Programming and Reasoning with Propositional Logic (SAT). More recently, he is interested in Robot Path Planning and Multi -Robots Task Allocation applications. Zakir Hussain Ahmed is an Associate Professor in the Department of Computer Science at Al Imam Mohammad Ibn Saud Islamic University, Saudi A rabia. He obtained MSc in Mathematics (Gold Medalist), MTech in Information Technology and PhD in Mathematical Sc iences from Tezpur University (Central), Assam, India. He served in various institutions in India. His research interests include artificial intelligence, discrete optimization, digital image processing and pattern recognition. He has publications in the f ields of artificial intelligence, discrete optimization and image processing.