Linear programming relaxation: Difference between revisions

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Branch and bound for exact solutions: more explicit about subproblem variables
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# If the current subproblem's relaxed solution is worse than the best integer solution found so far, backtrack from this branch of the recursive search.
# If the relaxed solution has all variables set to 0 or 1, test it against the best integer solution found so far and keep whichever of the two solutions is best.
# Otherwise, let ''x<sub>j</sub>'' be any variable that is set to a fractional value in the relaxed solution. Form two subproblems, one in which ''x<sub>j</sub>'' is set to 0 and the other in which ''x<sub>j</sub>'' is set to 1; in both subproblems, andthe existing assignments of values to some of the variables are still used, so the set of remaining variables becomes ''V<sub>i</sub>''&nbsp;\&nbsp;{''x<sub>j</sub>''}. recursivelyRecursively search both subproblems.
 
Although it is difficult to prove theoretical bounds on the performance of algorithms of this type, they can be very effective in practice.