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In this paper, we develop a decision making system in order to assist a transport client to do his travel in the optimum way. Our approach is based on the implementation of a distributed system. The objective of our system is to help the users as well as possible to facilitate their displacement in the dynamic graph. A displacement between two nodes in the normal mode can be transformed into displacement between two uncertain and dynamic nodes in a disturbed network. In this purpose, we present a multi-objective method including an optimal search routes, based on hybridization between Dijkstra algorithm and genetic algorithm. To assure the diversification of solutions, we have to manage the population by controlling the crossover and mutation operators. This management of the "population" allows the system to find a solution in case of disturbance by exploiting the final population. The advantage of this method is to give more choices to the users to assure continuity in their multimodal displacement.