Allow subproblem failures in DominguezRios

[odow]

x-ref #120

[odow]

Q: in what situations can this model not be OPTIMAL? And if it isn't, what should we do with the box?

[odow]

the other option is

@@ -207,7 +208,11 @@ function minimize_multiobjective!(algorithm::DominguezRios, model::Optimizer)
         new_f = t_max + ϵ * sum(w[i] * (scalars[i] - yI[i]) for i in 1:n)
         MOI.set(model.inner, MOI.ObjectiveFunction{typeof(new_f)}(), new_f)
         MOI.optimize!(model.inner)
-        @assert _is_scalar_status_optimal(model)
+        if !_is_scalar_status_optimal(model)
+            deleteat!(L[k], i)
+            MOI.delete.(model.inner, constraints)
+            continue
+        end
         X, Y = _compute_point(model, variables, model.f)
         obj = MOI.get(model.inner, MOI.ObjectiveValue())
         # We need to undo the scaling of the scalar objective. There's no

The tolerance issue with HiGHS means that we discard some points, so we find 36 solutions instead of 43:

Test Failed at /Users/oscar/.julia/dev/MultiObjectiveAlgorithms/test/vOptLib.jl:41
  Expression: MOI.get(model, MOI.ResultCount()) >= length(solutions)
   Evaluated: 36 >= 43

[odow]

The paper says

but this is true in theory but not always numerically.

[kofgokhan]

I think the model should always be feasible (in theory) as long as the feasible set of the original problem is nonempty. The result is used to figure out the location of the nondominated point (whether it is in the box that we are currently looking into to find nondominated points). So it can be infeasible at the very beginning and can return an empty nondominated set.

[odow]

If the whole problem is infeasible, then we'll catch that in the ideal point computation.

Problem still remains: what if the problem is feasible but our solver fails for some boxes. Perhaps the right behavior is to just skip some? If we error completely, we ignore the fact that this is a nice anytime algorithm with a bunch of good solutions already.

[kofgokhan]

If the whole problem is infeasible, then we'll catch that in the ideal point computation.

Yes, that is true.

Problem still remains: what if the problem is feasible but our solver fails for some boxes. Perhaps the right behavior is to just skip some? If we error completely, we ignore the fact that this is a nice anytime algorithm with a bunch of good solutions already.

Maybe the fact that we are not applying the reduction rule of the algorithm and deleting the only problematic box is fine. Should we mention somewhere that this is an anytime algorithm and best suited for use with SolutionLimitor TimeLimit? If someone wants to get all the nondominated solutions, they should use something else. That is actually one of the things I want to explain in the talk.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.85%. Comparing base (08f7799) to head (6304ce3).
Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #121   +/-   ##
=======================================
  Coverage   98.85%   98.85%           
=======================================
  Files           9        9           
  Lines         959      960    +1     
=======================================
+ Hits          948      949    +1     
  Misses         11       11           

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