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13 votes
Accepted

Branch and Price algorithm is exact?

To answer your question, it is good to have in mind the following concepts: Dantzig-Wolfe decomposition : in essence, this is a change of variables. The initial variables are expressed as a convex ...
Kuifje's user avatar
  • 13.5k
11 votes

How to implement branch and price?

Before starting implementation, I would make sure I am comfortable with all the theoretical aspects, which are somewhat tricky as well. This is quite an advanced topic in OR and requires some ...
Kuifje's user avatar
  • 13.5k
11 votes
Accepted

Integer column generation without branch & price

This approach is sometimes referred to as price-and-branch (vs branch-and-price), or solving the restricted master, and it does not guarantee optimality. It is equivalent to the following question: is ...
Kuifje's user avatar
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9 votes

Odd behavior in the branch bound and price algorithm with column generation

There can be many reasons why a branch-cut-and-price algorithm fails to solve an instance to optimality in a reasonable time. A large primal-dual gap because a heuristic solution is absent or of a ...
Ruslan Sadykov's user avatar
9 votes

Branch and Price Algorithm

Being a good or bad approach will depend on several factors, for example: the size of the instances time available to find a solution (this tends to be an important matter in vehicle routing ...
dhasson's user avatar
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7 votes
Accepted

A Question on A tutorial on column generation and branch-and-price for vehicle routing problems by Dominique Feillet

Note that (as is asserted in the cited tutorial): The cost of a route is the addition of the arcs that compose it: $c_k = \sum_{(v_i, v_j) \in A} b_{ijk}c_{ij}$ Relate $a_{ik}$ ($r_k$ visits customer ...
dhasson's user avatar
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5 votes

How to implement branch and price?

Using a framework like SCIP may be a good idea for starting. By doing so, you can quickly implement your formulation. It has interfaces on both C++ and Python. The documentation contains examples of ...
bugra's user avatar
  • 61
5 votes

Branch and Price Algorithm

VRPy (v0.3.0) now supports this option : all you have to do is set the minimize_global_span option to True when instantiating ...
Kuifje's user avatar
  • 13.5k
5 votes

Puzzles of branch and price algorithm

At each node, you need to ensure that the initial LP is feasible. For example, for the Bin Packing problem, you can add a column for each item or group of items that must be in the same bin ...
fontanf's user avatar
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5 votes

How to implement branch and price?

Nah. Building an ASL interface is hard, BnP is OK. Assuming you are familiar with its building blocks (just like with any other algorithm), the challenge lies in the implementation details. There are ...
Nikos Kazazakis's user avatar
5 votes

How to implement branch and price?

If you want to look at C++ source code, there are some COIN-OR projects that provide frameworks for "branch price and cut" or "branch cut and price" as it's sometimes known. Two ...
prubin's user avatar
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4 votes
Accepted

Branch and price with two sets of exponential variables

A common case where you would see 2 or more exponentially large sets of variables, is in: VRPs with heterogeneous vehicles: some vehicles have special equipment or larger capacity and can serve ...
Joris Kinable's user avatar
4 votes

Puzzles of branch and price algorithm

The columns of the child can be initialized by the subset of columns of the parent that also satisfy the branching conditions. For each child node, you would perform column generation to solve the ...
RobPratt's user avatar
  • 32.7k
4 votes

C++ code for branch and price

Out of the multiple options, the open-source option is Coin-OR's BCP (Branch-Cut-Price) [github]. SCIP also offers branch-and-price via its GCG (generic branch-cut-and-price) solver [link].
Divyam Aggarwal's user avatar
4 votes
Accepted

Branch-and-Price: return gap using SCIP

Accepted answer from the cross-post: Stop Branch-and-Price tree and return gap You can easily compute this yourself: SCIPgetDualbound will return you the best (...
4 votes
Accepted

When using column generation, can I delete a node with negative reduced cost from my subproblem?

If your sub-problem is a shortest path problem on a complete graph, without resource constraints, you can delete vertices which don't decrease the reduced cost. Indeed, for any path containing such a ...
Alberto Santini's user avatar
3 votes
Accepted

How to evaluate the quality of a solution obtained using the price-and-branch method for an IP problem?

Assuming your problem is minimization, the step of solving the master LP yields a global lower bound, from which you can compute an optimality gap for your integer feasible solution.
RobPratt's user avatar
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3 votes

Puzzles of branch and price algorithm

After branching, where do the columns of child node come from before new column being added by sub-problem? It is very common to use previously generated columns because they could both be of high ...
Alberto Santini's user avatar
3 votes

Tools to implement branch-and-price algorithms

You can check out the MINOTAUR codebase, it's pretty well written and designed for people to create their own algorithms. Last time I checked (a few years ago), it wasn't very well documented, but the ...
Nikos Kazazakis's user avatar
2 votes

How do we branch a Cutting Stock problem using Branch and Price?

At this stage you have the following options : you could solve the restricted master problem with integer variables (this is also called price-and-branch). In this case you are using classical branch-...
Kuifje's user avatar
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2 votes
Accepted

Name of graph algorithm arising while using the Ryan Foster Branching

Let $U$ be the universe (e.g. total set of elements). Then, if I understand your post correctly, you are looking for a function which given two elements $e_1,e_2\in U, e_1\neq e_2$, tells you if they ...
rolfvdhulst's user avatar
2 votes

How to implement branch and price?

One of the main ideas behind our decomposition solver GCG (gcg.or.rwth-aachen.de/dev) is to save you the time experimenting with your own B&P code only to find out that B&P is not the right ...
Marco Lübbecke's user avatar
2 votes

Dual of a model to obtain reduced costs

It's a bit tricky to sort out what is going on here. Given a dual solution ($\lambda,\gamma,\theta$) to the LP relaxation of the master problem, your subproblem will need to solve for $a_{ir}$ and $\...
prubin's user avatar
  • 39.6k
1 vote

Branch-and-Price for VRPs: Enforcing branching on arcs

Removing arcs in the graph is effective only for one branch (arc <= 0). You can certainly impose this constraint in the master and also remove the arc from the graph. Although removing an arc can ...
Ruslan Sadykov's user avatar

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