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A new heuristic for solving the multichoice multidimensional knapsack problem (MMKP) is presented in this paper. The MMKP is first reduced to a multidimensional knapsack problem (MKP). A linear programming relaxation of the resulting MKP is solved, and a series of new values for the variables is computed. These values, pseudo-utility values, and resource value coefficients computed as well, are used in order to obtain a feasible solution for the original MMKP. Finally, the quality of the feasible solution is improved using the pseudo-utility values and the coefficient values of the objective function. Numerical results show that the performance of this approach is superior to that of previous techniques.