Julia JuMP returns Binary variable at 0.99

Question

I cannot put the whole code here, and was not able to reproduce the problem with a small code, but here is the beginning of the code:

using JuMP, Cbc, StatsBase

n = 3;
V = 1:(2n+1);

model = Model(with_optimizer(Cbc.Optimizer, seconds=120));

@variable(model, x[V], Bin);

...

@objective(model, Min, total_blah);

JuMP.optimize!(model)
result = termination_status(model)

JuMP.objective_value(model)

xsol = JuMP.value.(x);

The problem I have is that the solver returns a solution where some of the xsol have values like 0.99995, where I am expecting Binary, ie either 0 or 1.

Can someone explain this behavior?

Maybe the solver is not able to find a feasible solution within the 120 second time limit that you set? Instead of using a time limit, you could try setting maxSolutions=1 or set ratioGap to something large enough that the solver terminates in a reasonable time. — Cameron Bieganek
Solvers have an Integer feasibility tolerance. I believe CBC uses a default of 1e-6 for this. — Erwin Kalvelagen

Erwin Kalvelagen Erwin Kalvelagen · Accepted Answer · 2019-07-31T18:27:25

I looked this up and CBC has an option called integerTolerance (or integerT) that helps CBC to decide whether a variable is integer valued. Using CBC.exe, I see:

Coin:integerTolerance
integerTolerance has value 1e-006

Indeed the default is 1e-6. You cannot set it to zero but you can make it smaller (valid range is 1e-020 to 0.5). (The only solver I know of that allows this tolerance to be set to zero is Cplex; usually doing that leads to longer solution times).

In general I would advice to keep it as it is. If small deviations from integer values irritate you, I would round integer variables in the solution before printing. This gives better looking solutions (but this rounding step may make the solution slightly infeasible).

Julia JuMP returns Binary variable at 0.99

1 Answers