# 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.

57 questions
Filter by
Sorted by
Tagged with
60 views

### How is a branch-and-bound tree's size estimated in solvers that display it?

I was pleasantly surprised that HiGHS is able to display what I believe is an estimation of the Branch & Bound tree size and what fraction of the nodes are explored. See the following for such ...
• 801
200 views

### Is the Network Simplex Algorithm Efficient for Mixed Binary and Linear Flows in Network Flow Problems?

I'm working on a network flow problem where the flow on all edges originating from the source node must be binary. Beyond this initial stage, the flows can be linear, and given the capacities are ...
28 views

### What are the "cutoff values" in Hybrid Branching?

In "Hybrid Branching" by Achterberg and Berthold, we have this line: the number of subproblems that could be pruned due to branching on this variable, called the cutoff values Can you ...
• 920
212 views

### Unable to find good solution for CVRP with Time Window

I am trying to solve Capacitated VRP with Time Window for 50 demand points. I was trying to optimize this in Gurobi Solver but it doesn't give good answer like optimality gap is 30% or more. Any idea ...
25 views

### Defining augmenting path for Traveling salesman problem

I am currently looking into solving TSP using Branch and Bound method. In the book by Wayne and Winston, they have solved each subproblem (i.e. tree nodes) using Hungarian algorithm. Using the lecture ...
• 109
154 views

### Branch & bound: why does the lower bound increase?

For a minimization problem, when running a branch & bound algorithm, I understand that: Every integer feasible solution provides an upper bound on the optimal objective value of the original ...
127 views

### In which circumstances is it sufficient to branch on the flow on edges to ensure integrality in VRPs?

I know that it is common to branch on the flow on arcs to ensure intergrality when solving VRPs, but in which circumstances is valid to branch on the flow on edges instead of arcs? References to ...
• 668
1 vote
69 views

### Connections between Bounds in MIPs

we are currently learning about MIP/MILP minimization at university and have become familiar with the branch-and-bound algorithm. Unfortunately, the relationship between upper bound, lower bound and ...
• 19
52 views

### Local Branching in Branch-And-Price

Is it somehow possible to apply local branching in branch-and-price? In branch-and-bound it is easy to add a constraint that allows at most k decision variables to change compared to a given solution. ...
153 views

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

I understand how exploring the Branch-and-cut tree would help improve the best bound known and the incumbent of a MILP, however, on some instances that I deal with, my solver (Gurobi) seems to keep ...
• 801
1 vote
87 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
93 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 ...
• 517
242 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
421 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
175 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
206 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
261 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: ...
50 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
207 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 ...
• 1,015
166 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 couldnāt found an example. What I want ...
• 517
1k 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 ...
388 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
222 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
153 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
204 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
344 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. ...
• 2,252
316 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 ...
466 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 ...
• 564
1 vote
124 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?
• 668
1k 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". ...
• 1,841
972 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 ...
742 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
328 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 ...
• 179
138 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 ...
• 4,037
82 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. ...
• 4,037
212 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
385 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 ...
• 4,037
787 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
119 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 ...
• 3,655
480 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 ...
• 2,252
1k 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
961 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 ...
• 81
4k 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
343 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 ...
257 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 ...
• 2,117
783 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