# 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.

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### 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 (...
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 ...
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 ...
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 ...
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 ...
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 ...
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: ...
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 (...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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 ...
1 vote
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?
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". ...
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 ...
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 ...
1 vote
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 ...
124 views

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 ...
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. ...
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 ...
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 ...
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?
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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, ...
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 ...