# Questions tagged [column-generation]

Questions on algorithms that solve mathematical models by generating columns (variables) in the pricing step during solution on demand.

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### General question regarding column generation

Assume one have an integer problem. Is the master problem in the column generation algorithm the original integer problem, or its linear relaxation? Thank you in advance.
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### Problem related to machine's performance while solving an LP-relaxation of a set-covering problem using the Column Generation

PS: I am familiar with performance variability encountered while solving large-scale MIPs. My question may not be explicitly related to it but maybe to the inefficiency of python packages. I have ...
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### When using column generation, can I delete a node with negative reduced cost from my subproblem?

I am solving a minimization problem with a column generation procedure. The master problem is of the form $$\min \sum_{i\in \Omega}c_i \lambda_i$$ subject to  \sum_{i\in \Omega \mid v \in i } \...
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### When using column generation, can a sub-problem be ignored once and for all once it fails to generate a new column?

Suppose you are solving a minimization problem with a column generation procedure, and that you have $2$ sub-problems. At some point, one of the $2$ sub-problems is no longer able to generate a column ...
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### Column generation for TSP

For teaching purposes, I would like to solve the Travelling Salesman Problem with a column generation approach. In the academic literature, an approach is proposed (for example here), where columns ...
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I am solving a scheduling problem-to find shifts and task schedules- using column generation. In essence, it is a set covering problem with additional constraints. The problem seems to be that the ...
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### Tools to implement branch-and-price algorithms

As far as I know, implementing a branch-and-price algorithm is a task far from trivial. However, there are tools such as SCIP or the BCP framework of COIN-OR that help implement such algorithms. I ...
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769 views

### Obtaining optimality gaps when using hybrid exact-heuristic approaches to vehicle routing problems

I'm starting to read about column generation-based approaches to vehicle routing problems (VRP). Let's say that I want to solve very large instances of an intricate VRP, I'm not looking to always ...
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### Stabilization techniques in column generation when subproblems are not solved optimally

Which stabilization techniques in column generation, like penalty function approaches and dual price smoothing, can be used when subproblems are not solved optimally? (I am particularly interested in ...
585 views

### Online Education for OR and Developing Decision Support Systems

I am looking for educational programmes which can be conducted online, such as full MSc., degree certificates, postgraduate courses/modules, MOOCs. Topics I am looking for are on advanced ...
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When using DOCplex to implement column generation, is it possible to add columns as an object, as opposed to creating a variable and then modifying the coefficients in the constraints? Edit: In ...
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### Optimality in a simultaneous column and row generation procedure

What is the optimality argument in a simultaneous column and row generation procedure? By column and row generation procedure I mean a procedure in which every time a column in generated, several ...
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### Solving pricing problem heuristically in column generation algorithm for VRP

In the set covering/column generation approach for the VRP (Balinski and Quandt (1964), or e.g. this tutorial), the basic idea is: Generate some routes. Solve the set covering problem using those ...
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### Variable bounds in column generation

Consider the set covering problem \begin{align} \min&\ \sum_{j=1}^nc_jx_j\\ s.t.:&\ \sum_{j=1}^na_{ij}x_j\geq 1,\quad \forall i=1,\dots,m\\ &\ 0\leq x_j \leq 1 \end{align} ...
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### Automating the column generation decomposition process

When trying a decomposition technique such as column generation, most of the times my approach is to look at the problem and then: Decide what a column should represent Write the Master Problem Write ...
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### Reference for column generation applications

When talking about column generation algorithms, the main example is the cutting stock problem. I'm aware that variations of vehicle routing problem (VRP) can be solved using a column generation ...
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