Stack Overflow
Stack Overflow

Questions tagged [branch-and-bound]

Branch and bound is a general technique for finding optimal solutions of various combinatorial and integer programming problems. It entails examining candidates (“branches”), while utilizing knowledge of upper and lower limits (“bounds”) to eliminate sub-trees, to find the optimal solution quicker.

Branch and bound is a general technique for finding optimal solutions of various combinatorial and integer programming problems. It involves partial enumeration, by examining candidates (“branches”), while also utilizing knowledge of upper and lower limits (“bounds”) to eliminate sub-trees.

The B&B technique is widely used in discrete optimization problems where the solution falls in the integer space (Traveling salesman, cutting stock etc.) This method was introduced in 1960.

For further reference: The Wikipedia page on Branch-and-bound (B&B)

114 questions
0
votes
1 answer

Modified TSP with Branch-and-Bound algorithm

I've been struggling to solve it using branch-and-bound to find the optimal path for the next task: There's a list of cities, that are all connected with each other, basically, a complete graph, each city has a interest index ( city 'A' has 8…
unfavourite
  • 7
  • 3
0
votes
0 answers

Create custom branches for cplex

Below i have a simplified code example of what i want to achieve. Basically i want to select a starting time for two different items (each chosen from a list of possible starting times). The goal is to find equal starting times for the two items. To…
Luuk van Nes
  • 41
  • 2
0
votes
1 answer

Branch and bound method for rcpsp

How do I construct a tree in branch and bound method to solve rcpsp? Suppose, I have: 4 tasks that have durations d=[2,3,1,4] These tasks need resource_amount = [3,2,5,4] of resource that has capacity 6. And task 3 should be completed before start…
ellana_d
  • 1
0
votes
1 answer

GRBCallback for nodes count and LP relaxation of a MILP

I am solving a MILP using Gurobi called from a C++ program. I want to retrieve the number of generated nodes and the value of the objective function of the LP relaxation. For the nodes count, I used this class: class NodeCounter : public…
Farah Mind
  • 143
  • 5
0
votes
1 answer

Can Cplex prioritize a variable over the others when branching?

Using C++, I have two sets of binary decision variables, y[i] and x[i][j]: IloNumVarArray y = CreateNumVarArray(env, int1, "y", 0, 1, ILOINT); NumVarMatrix x(env, int1); for (IloInt i = 0; i < int1; ++s) { x[i] =…
Ozan Aksu
  • 17
  • 2
0
votes
0 answers

Duals of a cubic program get stuck at some numeric value in SCIP

I am trying to solve a cubic program using SCIP. All variables are bounded between 0 and 1 with the exception of the objective function, which is bounded between -1 and 1. Giving the nature of branch and bound algorithms, I thought the problem would…
DunhoClark
  • 61
  • 1
  • 4
0
votes
0 answers

Branch and Bound algorithm for Max Clique returns empty set

Hello I am trying to find the max clique of a graph using the algorithm 1 from p.2 of that paper so far the algorithm returns just an empty set and I can't seem to find the mistake in my code. Any suggestions would be appreciated. Cheers! my…
C96
  • 477
  • 8
  • 33
0
votes
1 answer

Getting the reason why a node in SCIP was pruned

I've implemented a Branch-and-Cut algorithm using SCIP in C++. My optimization problem has a minimization objective function and currently my code have a bug that I'm struggling to fix it. My problem has an optimal value of 100, but the program…
user1346085
  • 15
  • 4
0
votes
1 answer

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 also want to change some parameters. I imagine that is similar, but couldn’t found an example. What I want is as follows: -Every time a feasible node…
orpanter
  • 115
  • 6
0
votes
1 answer

Why does my memoization code not save the correct keys with the values?

I'm currently learning dynamic programming with Python to write a rather simple Branch & Bound algorithm. I found this video on Youtube with kind of good explanations in the first place. The examples there are written in JavaScript. Only few changes…
Luca Graebenteich
  • 1
  • 1
  • 1
0
votes
1 answer

How to disable all branch & bound improvements in Cplex?

I want to solve a MIP in Cplex (with IloCplex for C++) using only the branch & bound feature (i.e. without all the enhancements that speed up the solving like probing, running heuristics at each node, adding cuts etc.). The idea is to be able to…
Mep M
  • 17
  • 5
0
votes
0 answers

Why branch-and-bound is approximate and not exact?

I have read that branch-and-bound paradigm is approximate. Can someone explain why this method is approximate and not exact? what it means that it's approximation? I implemented it for knapsack problem and always when I run this algorithm, it gives…
Fibonacci
  • 5
  • 2
0
votes
1 answer

ORTools CP-Sat Solver Channeling Constraint dependant of x

I try to add the following constraints to my model. my problem: the function g() expects x as a binary numpy array. So the result arr_a depends on the current value of x in every step of the optimization! Afterwards, I want the max of this array…
Branko Mo
  • 11
  • 2
0
votes
1 answer

Selecting items with highest value in a list with the right order

I am solving a knapsack problem by using branch and bound algorithm I am working on right now. In the algorithm, I wanted to start selecting the items with the highest density(value/weight). I created a list named "density" and made necessary…
diabolik
  • 55
  • 6
0
votes
0 answers

Complexity of Spatial Branch and Bound

What is the time complexity of Spatial Branch and Bound? I'm interested in how does the complexity depends on the number of variables and their dimensions. Thank you!
Seda
  • 1
1 2 3 4
5
6 7 8