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Graph partitioning is a NP-hard problem with multiple conflicting objectives. The graph partitioning should minimize the inter-partition relationship while maximizing the intra-partition relationship. Furthermore, the partition load should be evenly distributed over the respective partitions. Therefore this is a multi-objective optimization problem (MOO). There are two approaches to MOO using genetic algorithms: weighted cost functions and finding the Pareto front. We have combined Pareto front method and cellular learning automata to exploit the potentiality of both in the hybridized algorithm. The proposed methods of this paper used to improve the performance addition to hybridization, are using an optimized method in generating reinforcement signal vector and considering the solutions of each non-dominated set as neighbours. These improvements make the search more efficient and increase the probability of finding more optimal solutions, also changing neighbour set at each generation, prevent the neighbours from getting stuck in the neighbourhood local optima. Finally, a simulation research is carried out to investigate the effectiveness of the proposed hybrid algorithm. The simulation results confirm the effectiveness of the proposed method.