5 votes
Accepted

Can we add a certain binary row to a matrix which preserves total unimodularity?

Your conjecture is wrong as the following counterexample demonstrates. Consider $$ A = \begin{pmatrix} 1 & 0 & -1 \\ 1 & 1 & 0 \end{pmatrix} $$ and $$ b^\top = \begin{pmatrix} -1 & ...
joni's user avatar
  • 1,562
4 votes

How to turn off tree search in fico xpress ? Couldn't see relevant documentation

Use MAXNODE option to limit the tree search. You might also try setting HEURSEARCHROOTCUTFREQ to 1 to run heuristics between each cutting plane round.
fontanf's user avatar
  • 2,623
3 votes
Accepted

Why would a solver stay on node 0 and still improve the gap?

The solver generates and applies cuts at the root node. The cuts are designed to tighten the LP relaxation, which results (hopefully) in the best bound tightening. The solver also applies heuristics ...
prubin's user avatar
  • 38.8k
3 votes
Accepted

What does a solver do with a MIP warmstart solution?

Besides getting the initial primal bound provided by the (feasible) starting solution, one possible use for a warm start is to seed a heuristic that looks for an even better feasible solution. Given a ...
prubin's user avatar
  • 38.8k
3 votes
Accepted

How to modify master problem and individual sub problems in column generation?

Your problem is: \begin{align} &\text{minimize} &\sum_t \sum_s \text{slack}_{ts} \\ &\text{subject to} &\sum_i \text{motivation}_{its} + \text{slack}_{ts} &= \text{demand}_{ts} &...
RobPratt's user avatar
  • 31.5k
3 votes
Accepted

How to model the following Constraint

As in How to enforce logical implication $\sum_j a_j x_j \le b \implies \sum_j c_j x_j \le d$, (temporarily) introduce constant $\epsilon>0$ and binary variable $Z$, and impose linear big-M ...
RobPratt's user avatar
  • 31.5k
2 votes
Accepted

Equivalent constraints in MILP give different answers

The primal bound of one problem should not be less than dual bound of the other problem. This suggests a bug somewhere. In a comment, @Hubcity wrote "For the x[0] >= 100 it reports a primal ...
Mark L. Stone's user avatar
1 vote
Accepted

Temporal changing model parameters/constraints/variables in MILPs

Some solvers will allow you to add constraints on the fly, possibly with some restrictions. I don't think any would allow you to add variables mid-solve. Column generation techniques allow you to add ...
prubin's user avatar
  • 38.8k
1 vote

Exploiting identical subproblems in column generation

With individual nurses, you generate columns specific to each nurse, use binary variables to indicate which column is used for each nurse, and constraints on the binary variables saying that exactly (...
prubin's user avatar
  • 38.8k
1 vote

Convex approximation of a constraint

The first absolute value appears in a convex manner, so can be left as is in CVX or other convex optimization modeling tool. The second absolute value appears in a non-convex manner. It can be handled ...
Mark L. Stone's user avatar
1 vote

How to formulate case distinctions in AMPLs objective function?

You can express this objective using AMPL's builtin if-then-else expression. I think the following corresponds to what you want to write: ...
4er's user avatar
  • 628

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