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Meta-ticket: Audit/fix all uses of MixedIntegerLinearProgram #32191

@mkoeppe

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@mkoeppe

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One class of bugs comes from using the raw solution values for integer or binary variables from numerical solvers. Using #32197, they can be converted to integers/booleans with integrality tolerance checking. The tolerance parameter depends on the model and the solver, but a rough guideline is that it should be greater than solvers' default integrality tolerances: 1e-5 (CPLEX: https://www.ibm.com/docs/en/icos/12.8.0.0?topic=parameters-integrality-tolerance, Gurobi: https://www.gurobi.com/documentation/9.1/refman/grb_tolerances_and_the_lim.html), 1e-6 (GLPK), ...

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CC: @dcoudert @tscrim @seblabbe @dimpase @DaveWitteMorris

Component: graph theory

Issue created by migration from https://trac.sagemath.org/ticket/32191

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