Slightly improve a tolerance issue in KirlikSayin (#198)

From a previous solve, z_k may be a value like z+eps where z in Z and eps is the
feasibility tolerance. However, if scalars[k] is integer valued, then presolve
may (somewhat reasonably) deduce that this problem is infeasible. Instead of
rounding z_k, changing EqualTo to LessThan seemed to work on the instances I
have. I don't know why. There is also a weird situation in which Gurobi declared
a problem unbounded. I can't reproduce without running the entire thing, but I
think it is a mix of presolve proving that there is no finite solution (because
its infeasible) and yet there being a "feasible" MIP solution in memory from the
previous solve. It comes down to the weird mix of tolerances in MIP starts,
presolve, simplex, and this equality constraint. This is most probably a bug in
Gurobi, in that it should either report optimal or infeasible. But not
unbounded. I've seem something similar in SDDP.jl.

Author: odow

src/algorithms/KirlikSayin.jl

@@ -170,7 +170,7 @@ function minimize_multiobjective!(
         zₖ_constraint = MOI.Utilities.normalize_and_add_constraint(
             inner,
             scalars[k],
-            MOI.EqualTo(zₖ),
+            MOI.LessThan(zₖ),
         )
         optimize_inner!(model)
         if !_is_scalar_status_optimal(model)

test/test_model.jl

@@ -258,12 +258,12 @@ function test_printing()
         return
     end
     contents = read(joinpath(dir, "log.txt"), String)
-    for line in [
+    for line in Any[
         "Algorithm: KirlikSayin",
         "1    0.00000e+00  0.00000e+00",
         "----------------------------------------------",
         "termination_status: OPTIMAL",
-        "result_count: 10",
+        r"result_count: [0-9]+",
         "Time spent in subproblems: ",
     ]
         @test occursin(line, contents)