A NEW APPROACH TO DISCRETE MATHEMATICAL PROGRAMMING
CALIFORNIA UNIV LOS ANGELES WESTERN MANAGEMENT SCIENCE INST
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The paper presents an algorithm for solving the zero-one integer programming problem. In contrast to the usual approach, which reduces the problem to finding the optimal values for variables restricted to values of zero and one, we view the problem as finding an optimal map among a class of mappings of one finite set into another. The basic approach is to characterize the statistical structure of the finite class of maps. Our technique consists of trying to identify the optimal feasible map in a class of maps, by introducing random variables as functionals on the class of maps. We derive explicitly the statistical properties of the class of maps associated with the zero-one integer programming problem. Using the mean and variance-covariance matrix the idea of confidence level enumeration is developed.
- Statistics and Probability