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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8
votes
0answers
49 views

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 ...
8
votes
0answers
61 views

Adjusting duals heuristically

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 ...
11
votes
0answers
123 views

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 ...
14
votes
2answers
603 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 ...
10
votes
1answer
76 views

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 ...
14
votes
4answers
492 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 ...
10
votes
1answer
117 views

DOCplex adding columns

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 ...
18
votes
1answer
112 views

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 ...
21
votes
5answers
868 views

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 ...
18
votes
3answers
204 views

Variable bounds in column generation

Consider the set covering problem \[ \begin{align} \min&\ \sum_{j=1}^nc_jx_j\\ s.t.:&\ \sum_{j=1}^na_{ij}x_j\geq 1,\quad \forall i=1,\dots,m\\ &\ 0\leq x_j \leq 1 \end{align} \] ...
16
votes
2answers
138 views

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 ...
19
votes
8answers
307 views

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 ...
19
votes
3answers
454 views

Column generation stabilisation

Has anyone performed a benchmark of the various stabilisation techniques in column generation? Which ones perform better for set pack/partition/cover problems like VRP? And are there theoretical ...