Implicit enumeration

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Applied to integer programming, this is a systematic evaluation of all possible solutions without explicitly evaluating all of them. For example, suppose a feasible solution is at hand with objective value 100. Now suppose we solve a relaxation, such as fixing some of the variables and solving the resulting linear program, and we obtain a value of only 90. If we seek a maximum, we can ignore all possible solutions having the fixed values in the relaxation since they must all have an objective value of at most 90. This is often said to be equivalent to branch and bound; however, the early versions of these methods were related, but different. The early branch and bound was a best-first (even breadth-first) heuristic search   strategy. Early implicit enumeration schemes were depth-first.


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