Questions tagged [branch-and-bound]

For questions related to the branch-and-bound method for integer programming problems, which recursively divides the solution space and identifies upper and lower bounds on the optimal objective function value.

Filter by
Sorted by
Tagged with
10
votes
1answer
102 views

Branch and Price algorithm is exact?

I know that the Column Generation algorithm delivers an exact solution when you are solving a linear programming optimization problem. I want to know that, does this column generation approach deliver ...
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 ...
4
votes
3answers
302 views

Branch and bound algorithm programming code

I want to solve an integer programming problem using the branch and bound method, but I'm having trouble finding the programming code. From what I saw, almost all algorithms use it for traveling ...
10
votes
3answers
435 views

Settings for a faster solution of a MILP (GUROBI, python)

Using GUROBI with python. When solving a MILP, I notice that the incumbent is very early (25sec) at the optimal point but the best bound is so slow to fall (maximization problem) that it takes ages (...
2
votes
0answers
65 views

Branch-and-Price: return gap using SCIP

I implemented a branch-and-price tree in python. I would like to stop the process after 5 hours and return the gap in % between the best integer solution found so far and the optimal solution. How ...
7
votes
1answer
68 views

Gurobi: can you retrieve the dual solution from each node of the B&B tree using callbacks

When solving a MIP with Gurobi, one can use the cbGetNodeRel() function to extract the primal solution to the LP relaxation at each node in the branch and bound ...
7
votes
1answer
148 views

Diving heuristics in branch and bound

I am reading about extensions on plain vanilla B&B and heuristics for smaller trees/better branching. I have come across diving heuristics, which on the SCIP site is defined as: A diving ...
5
votes
2answers
98 views

What is the technique of branch-and-bound used in Knitro to solve MINLP?

I am using Knitro to solve an MINLP using branch-and-bound and I want to know about the reference or technique they are adopting to code their algorithm. I know that there are many applications of ...
16
votes
4answers
2k views

Branch and Bound Implementation

Branch and Bound (B&B) is a general solution approach to solve combinatorial optimisation problems. I was wondering how B&B is implemented in practice. Although it may be relevant, but I am ...
12
votes
2answers
237 views

Dual bounds of integer programming problems

I often read in papers when branch-and-X algorithms are used to solve mixed integer programming problems, that the lower bound (in the minimization case) obtained from solving a linear programming ...
10
votes
3answers
732 views

Do solvers use GUB/SOS1 branching?

GUB/SOS1 branching is an old and well-known idea (see for example page 9 of Jeff Linderoth's notes). Is this implemented in commercial solvers these days? The Gurobi documentation mentions SOS1 ...
10
votes
3answers
134 views

Theoretical results on performance of branch-and-bound

Are there any theoretical results on the performance of branch-and-bound, even for a subset of instances of a particular discrete optimization problem? As an example, does there exist a result of ...
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 ...
14
votes
1answer
521 views

Estimation of the size of Branch-and-Bound trees using ML

A short background: A paper [1] published in 2006 intends to show that the time needed to solve mixed-integer programming problems by branch and bound can be roughly predicted early in the solution ...
8
votes
2answers
116 views

How to change the search strategy in a B&B framework, i.e., start with depth first and then continue with best node?

Is there any implementation, code or software, which can switch between search strategies in a B&B framework?