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This paper presents a detailed treatment of genetic algorithms with decomposition procedures as developed for large scale multidimensional 0-1 knapsack problems with block angular structures. Through the introduction of a triple string representation and the corresponding decoding algorithm, it is shown that a potential solution satisfying not only block constraints but also coupling constraints can be obtained for each individual. Then genetic algorithms with decomposition procedures are presented as an approximate solution method for multidimensional 0-1 knapsack problems with block angular structures. Many computational experiments on numerical examples with 30, 50, 70, 100, 150, 200, 300, 500, and 1000 variables demonstrate the feasibility and efficiency of the proposed method.