Questions tagged [branch-and-cut]

Questions on algorithms that combine branch-and-bound search and the generation of cutting planes.

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2
votes
2answers
134 views

How to use tight upper and lower bounds to get to the optimal value via branch and bound?

I have algorithms that get me a tight upper (UB) and lower (LB) bound to a maximization binary integer program (a routing problem). My formulation is non-compact and requires the addition of sub-tour ...
1
vote
0answers
78 views

Branch and Cut algorithm

Could someone please explain what is the point of this added cut? Also how was it deduced? Could someone please give some examples of this sort? As I've been searching for such examples but did not ...
8
votes
1answer
134 views

Why isn't $x_2+x_3+x_4\le 2$ a cutting plane?

In my textbook, to generate cutting planes, they tell you to proceed as follows: A procedure for generating cutting planes: Select a ($\le$) constraint that has only nonnegative coefficients. ...
15
votes
1answer
213 views

Was there something specific that caused graph cuts to lose popularity in the last 5 years?

Almost every graph-cut paper I look at seems to have exactly the same pattern of monotonic growth in citations and then monotonic decline starting around 5 years ago: For privacy I've cut the all ...
7
votes
1answer
135 views

Program can't stop when using callback of usercut in CPLEX to solve a branch-and-cut problem

When I tried to use Java to call CPLEX and use callback functions to solve a VRP problem with branch-and-cut, some problems emerged. I took out the subtour elimination constraint from the original ...
9
votes
1answer
133 views

Rules of thumb for using classic methods (e.g. branch and bound) vs. meta-heuristics (G.A, S.A, etc..) for non-convex problems?

Are there any rules of thumb for when to use classical methods like branch and bound, branch and cut, etc...for non-convex problems, vs using meta-heuristic methods like genetic algorithms, ...
11
votes
3answers
1k views

Performance of a branch and bound algorithm VS branch-cut-heuristics

I was trying to solve a moderate scheduling model using an open-source solver. I did two different ways. A) using pure branch and bound algorithm (disable all options). B) using the default setting ...
16
votes
1answer
179 views

Family of hard instances for Gomory's cutting plane algorithm

Is there a variant of integer programs for which Gomory's cutting plane algorithm demonstrably takes a superpolynomial number of iterations?
16
votes
2answers
238 views

Branching rules in commercial MIP solvers

I am working on a branch-and-cut algorithm, and I have spent quite some effort into improving the branching decisions that are made by commercial solvers, such as CPLEX and Gurobi. However, it was ...
12
votes
2answers
283 views

When does Gurobi add cuts from callback

A while ago I used Gurobi and I added user cuts from within a callback. However, I got the feeling that my user cuts were not directly added to the model. Is it right that Gurobi can decide to ...