Bug: Optimal solution with binary variable constraints is infeasible about highs

[jajhall]

HiGHS (like any practical software) solves problems to within tolerances. For x50=0 and x168=1, the activity of constraint c397 is 1e-08. Although the bound is <=0, the activity satisfies the bound to within the (default) mip_feasibility_tolerance of 1e-06. Hence the solution returned by HiGHS is feasible

If mip_feasibility_tolerance is set to 0.99e-08, then HiGHS yields the solution

• x50 0
• x168 0
• c397 0

The same solution is obtained using mip_feasibility_tolerance=1e-06, if the coefficient of x168, in constraint c397 is changed to 1.01e-06.

Since CBC and GLPK will solve using a similar tolerance, it' probably just chance that they find a solution with x168=0 before the solution with x168=1 obtained by HiGHS.

I note that the optimal objective values of both Gurobi (1.249985942024e+06) and HiGHS (1.249985942207e+06) are equal to within normal tolerances.