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This paper proposes an effective multiobjective estimation of distribution algorithm (MoEDA) which solves the bi-criteria stochastic job-shop scheduling problem with the uncertainty of processing time. The MoEDA proposal minimizes the expected average makespan and the expected total tardiness within a reasonable amount of computational time. With the framework of proposed MoEDA, the probability model of the operation sequence is estimated firstly. For sampling the processing time of each operation with the Monte Carlo methods, allocation method is used to decide the operation sequence, and then the expected makespan and total tardiness of each sampling are evaluated. Subsequently, updating mechanism of the probability models is proposed according to the best solutions to obtain. Finally, for comparing with some existing algorithms by numerical experiments on the benchmark problems …