The quadratic assignment problem (QAP) is a classical NP-hard combinatorial optimization problem. It has many real life applications such as airport gate assignment, and facility location problems. This paper proposes an algorithm using a Multi-Agent based Algorithm (MAA), Bayesian reasoning, and a stochastic resetting algorithm. The MAA enhances the relevance of the cognitive process inside a population-based search algorithm, where each agent is connected to others employing a static scale-free network. Experimental results show that our multi-agent approach can produce high-quality and efficient solutions for 12 well-known data instances of the QAP problem.