Integer programming computer codes

Except for the fact that the numerical code may choose pseudo-components (i.e., ways of discretizing the relevant integrals), which have no direct physical meaning. For instance, if x is taken to be (proportional to) the number of carbon atoms in, say, a mixture of hydrocaibons, the computer code, if cleverly programmed, may well choose to discretize x in such a way that the corresponding number of actual carbon atoms is not an integer (see, e.g., Shibata et al, 1987). 

The most widely used method for solving both integer and MIP problems is the branch-and-bound algorithm. Most commercial computer codes for solving integer programming problems use this approach. The method performs an efficient enumeration of a small fraction of the possible feasible integer solutions to locate the optimum. 

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