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A decomposition and optimization algorithm is presented for large-scale job shop scheduling problems in which the total weighted tardiness must be minimized. In each iteration, a new subproblem is first defined by a heuristic approach and then solved using a genetic algorithm. We construct a fuzzy controller to calculate the characteristic values which describe the the bottleneck jobs in different optimization stages. Then, these characteristic values are used to guide the process of subproblem-solving in an immune mechanism. Numerical computational results show that the proposed algorithm is effective for solving large-scale scheduling problems.