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.
47
questions
1
vote
1
answer
77
views
How to Set Up an Optimization Problem Like the 0/1 Knapsack
I'd like some help in understanding and setting up (what may be) an optimization problem that has some similarities to the 0/1 knapsack problem. In this problem the items are a given number of words (...
- 113
2
votes
0
answers
63
views
Branching the product of binary and continuous variable in Gurobi
I have a binary variable (X) multiplying a continuous variable (Y). I know I can linearize by adding an auxiliary variable (I have that model working), but I now want to do my own branching in the ...
- 507
3
votes
1
answer
145
views
Reoptimization with GLPK in Julia/JuMP
I've been looking everywhere, and I can't seem to find any information on whether GLPK can do successive optimizations on the same model, on which we add a constraint at each iteration.
More ...
- 33
4
votes
1
answer
269
views
How do we branch a Cutting Stock problem using Branch and Price?
I'm sure this is a straightforward question, but since I started learning integer programming recently this isn't clear to me.
Consider solving a 1 dimensional cutting stock problem using delayed ...
- 41
7
votes
1
answer
164
views
Name of graph algorithm arising while using the Ryan Foster Branching
I'm using the Ryan-Foster branching in my Branch and Price algorithm for a pickup and delivery problem, but I'm having trouble keeping track of all the pairs as I go down the search tree.
Let's say ...
- 173
4
votes
1
answer
157
views
Bounding function for branch-and-bound in game tree search
The scenario is a game where each round you can buy or sell farms that make a set profit each round. I thought about applying branch-and-bound to a game tree, where each node represents the game state ...
- 141
4
votes
1
answer
204
views
Reduce optimality gap and get a solution faster
I have a maximization problem that I know that the maximum value of the objective function should be 6000. When solving the problem using Xpress, I end up on something like the following:
...
2
votes
1
answer
45
views
Objective value estimate for branches I create in Cplex
I' implementing custom branching heuristics for Cplex in python. I have a way to choose a (binary) variable to branch on, so use the following code to create two branches from BranchCallback (...
- 251
2
votes
2
answers
157
views
A branch-and-bound algorithm for number partitioning
I am working on a branch-and-bound algorithm for number partitioning, similar to Complete greedy algorithm. The input is a list of positive integers and an integer $k$; the output is a partitioning of ...
4
votes
0
answers
72
views
Changing a parameter while branching in SCIP
I use pyscipopt. I know how to add constraints while branching using handlers (kind of), but now I want also to change some parameters. I imagine is similar, but couldn’t found an example.
What I want ...
- 507
3
votes
1
answer
658
views
Solving a MIP by Relaxation
I have tried to understand the method of relaxing an integer program. I am in the process of implementing and solving a MIP for the FJSSP. For this I use the python-MIP package to solve it. From my ...
- 43
4
votes
0
answers
307
views
CPLEX Python: Current subproblem model in branch and bound
I have an MILP problem and use CPLEX (Python interface). I am working on user heuristics for branching in the branch-and-bound procedure. With HSCallback I managed to get the information about the ...
- 251
7
votes
1
answer
167
views
What insights/info can be gathered from visualizing the Branch & Bound tree
What insights/info can be gathered from visualizing the Branch & Bound tree. Some commercial solvers (FICO Xpress) don't seem to provide any API to readily visualize the tree. It has to be ...
- 305
6
votes
1
answer
139
views
Strong branching scores when objective function is constant
I have a MILP feasibility problem, so the objective function is constant (0). I have read that strong branching scores measure changes in the objective value. So my question is, what would be the ...
- 251
2
votes
3
answers
148
views
Warm starting ideas for iteratively solving a model with a few additional constraints
I'm trying to solve a MILP model iteratively, and at each iteration a few constraints are added to the problem that cut off the previous optimal solution. I'm trying to figure out ways to implement a ...
- 29
2
votes
1
answer
302
views
Strong branching
Within B&B when it comes to select variables to branch on, I can use the concept of "strong branching". The optimizer, in my case CPLEX, then performs branching on variables it selects.
...
- 2,170
9
votes
1
answer
262
views
Odd behavior in the branch bound and price algorithm with column generation
I have two questions on branch-bound-and-price.
Why does it sometimes fail? For instance, the paper by Dabia et al shows results where the proposed algorithm fails for some cases. The paper does not ...
7
votes
1
answer
381
views
Data structures for branch and bound: Efficiently finding the branch node vs. efficiently fathoming
I am implementing a branch and bound algorithm for the knapsack program that is essentially identical to the one described here. I am trying to decide on the optimal data structure to store the set of ...
- 524
1
vote
1
answer
94
views
Can branch and bound be defined as a method to search a non-convex solution space which uses linear programming models to guide the search?
Can branch and bound be defined as a method to search a non-convex solution space which uses linear programming models(and solving them) to guide the search?
- 557
7
votes
1
answer
909
views
Is "Branch and Bound" better than Evolutionary Algorithms?
I have been trying to find examples of major research studies examining the properties and performance of the "Branch and Bound" Algorithm compared to "Evolutionary Algorithms".
...
- 1,821
5
votes
1
answer
734
views
CPLEX gives different solutions of MILP every run
I am solving a mixed-integer (binary) linear problem using CPLEX as a solver (branch-and-bound method). But I encountered the following issue. Each run I get a different solution at a different node ...
3
votes
1
answer
714
views
B&B hot and warm starting
In a branch and bound algorithm, what is the difference between hot and warm starting and what kind of information does each of them require to store in memory? Otherwise, for the hot starting, what ...
- 65
1
vote
2
answers
229
views
Branch and bound method for solving non-convex integer non-linear multi-objective optimization problem?
Following are the characteristics of my problem:
Objective function: two non-linear functions and one linear function
Decision variable: two integer variables ($X_1$ and $X_2$)
Constraint: three (two ...
- 169
2
votes
1
answer
124
views
Suggestions how to get access to MINTO MILP solver?
I came across the MINTO MILP solver today. A solver i wasn't aware of or at least had not paid attention too. While development seem to have stopped two decades ago however i still wouldn't mind ...
- 3,965
2
votes
0
answers
79
views
What if anything do linear relaxations of "nearby" MILP nodes tell us about other MILP nodes
Assume we are given MILP where $y \in (\mathbb{R}^+)^n$, $x_1, x_2 \in \{0, 1\}$ are the integer variables. It is obvious that this problem when solved via branch and bound has a 2 deep b&b-tree.
...
- 3,965
9
votes
2
answers
200
views
MINLP involving integrals, sparse matrices and CDF of random variables. Best environment?
INTRODUCTION
My research often involves solving MINLP problems with few constraints (usually two) and not many variables (say between one and three integer ones, and between one and five real-valued ...
- 191
4
votes
2
answers
269
views
When solving many MILPs how to assign CPU cores to solver instances?
Let's say I have an 16 core machine and many roughly equally hard MILP problems and enough RAM. The latency of solving doesn't matter. With how many cores should I start solvers on to maximize ...
- 3,965
5
votes
1
answer
132
views
Breadth First Search vs. Best First Search
What is the main difference between Breadth First Search and Best First Search? What is meant by saying Breadth First Search requires previous knowledge?
- 45
2
votes
0
answers
96
views
How to implement CPLEX user cuts using CPXaddusercuts in C API?
I am trying to use CPXaddusercuts to add cutting planes, which have not been violated yet but are likely to be violated as we go down the branch & bound tree, to the list (pool) of constraints. As ...
7
votes
3
answers
1k
views
How do Quadratic Programming solvers handle variables without bounds?
Solvers for non-convex QPs generally do the McCormick relaxation of the term $xy=z$ and then do spatial branch and bound.
This requires that $x$ and $y$ have given bounds, how do they handle the case ...
- 3,635
4
votes
4
answers
474
views
What expresses the efficiency of an algorithm when solving MILPs
What is the appropriate measure to indicate the efficiency of an algorithm\model that solves a MILP through B&B?
Is it
the number of nodes examined to reach the optimum?
the number of iterations ...
- 2,170
13
votes
1
answer
762
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 ...
- 233
2
votes
2
answers
701
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
3
answers
2k
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 ...
- 81
11
votes
3
answers
3k
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 (...
1
vote
1
answer
262
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
1
answer
208
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 ...
- 2,047
8
votes
1
answer
677
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 ...
- 183
5
votes
2
answers
159
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 ...
- 83
16
votes
4
answers
5k
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 ...
- 2,140
17
votes
2
answers
3k
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 ...
- 1,113
10
votes
3
answers
973
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 ...
- 596
11
votes
4
answers
337
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 ...
- 579
9
votes
1
answer
296
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, ...
- 2,089
12
votes
3
answers
5k
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 ...
- 8,187
14
votes
1
answer
721
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 ...
- 8,592
8
votes
2
answers
142
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?
- 366