In integer linear programming, what is the role of cutting planes in improving the solution quality?
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In integer linear programming, cutting planes are used to improve solution quality by adding additional constraints that help eliminate parts of the solution space that don't contain optimal integer solutions. These constraints "cut away" non-integer solutions, making it easier to find the best integer solution without having to search through all possible options. By doing this, cutting planes help narrow down the feasible solutions, leading to faster and more efficient problem-solving.
In Integer Linear Programming, cutting planes improve solution quality by eliminating fractional solutions from the relaxed linear program, tightening the feasible region, and pushing the solution towards integer values without excluding any valid integer solutions.