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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In column generation is it possible that a new column from sub problem doesn't enter master's base?

In some iterations, when a new column is added to the master, it does not enter the base and a stop condition occurs, or a new column with a better objective function is found. is it correct?
1 vote
62 views

Partially modify LHS of a constraint set?

I have implemented a column generation algorithm in Gurobi in Python. The most computationally expensive aspect of this algorithm is the reconstruction of the master problem when a column is added (or ...
56 views

Is there existing code for the set partitioning formulation of routing problems?

The set partitioning formulation of routing problems is pretty well-accepted as perhaps the best exact method to solve routing problems. However, these methods are difficult to implement as many ...
188 views

Column generation: set partitioning vs set covering

I am working with a column generation algorithm and have noticed that convergence is much faster when my master is a set covering problem ($Ax\ge 1$) compared to when it is a set partitioning problem (...
1 vote
64 views

366 views

Integer column generation without branch & price

Consider the following situation. I have an integer program which I want to solve using column generation. After a suitable decomposition, the master problem has decision variables that select the ...
406 views

Metaheuristics vs Column generation for VRP

I am solving a vrp and its variants (pick up drop off, milk-run problem) using genetic algorithms. The issue that I am getting with the genetic algorithm is the randomness associated with the ...
267 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 ...
103 views

Dual instability, degeneracy, tailing off effect - Which are the causes and which are the effects?

Dual instability, degeneracy, and the tailing off effect are often mentioned together in papers. However, I cannot seem to find a clear explanation on which of these cause the other and vice versa? ...
75 views

Linear programming approach to dynamic programming - an initial pair of state-decisions

I aim to solve the following Bellman equation: v(\vec{s}) = \min_{\vec{x} \in \Xi_{\vec{s}}} \big\{c(\vec{s}, \vec{x}) + \lambda \times \sum_{\vec{s}^{'}\in S} p(\vec{s}^{'} | \...
489 views

What kind of data structure should be used to store labels when implementing a labeling algorithm?

The shortest path problem with resource constraints is a common subproblem when doing column generation. It is often solved with a labeling algorithm. The procedure is very well explained here and ...
186 views

How do you know if Column Generation is any faster than standard MIP formulations?

I'm currently in the process of learning about column generation, so I apologize in advance if I show a gross lack of understanding about it. Anyways, what I've gathered so far is that Column ...
597 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 ...
395 views

Dual of a model to obtain reduced costs

I have the following model which I am going to solve with column generation. \begin{align} \max & \sum_{b \in B} \sum_{s \in S} \sum_{r \in \Omega_s}\beta_{bs}p_r y_{br}\label{objective-set1}\\ ...
264 views

Heuristic solution to the graph partitioning problem

I am working on a graph partitioning problem. A static column generation based solution was proposed in How to partition a graph with optimal number of groups? But I need some MILP solver to solve ...
1 vote
292 views

Set Covering and Column Generation

I need some set covering and column generation examples in OR-Tools python. If anyone can provide or direct me to some resources that would be great..!
80 views

Branch and price with two sets of exponential variables

There are classes of problems which allow for "natural" extended formulations using multiple exponential-size sets of variables. For example, 2-echelon routing problems can be modelled ...
931 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 ...
1k 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 ...
91 views

Materials or sample code for column generation book (GERAD 25th Anniversary Series)

As far as I know, one of the interesting resource to learn the basic concept of the decomposition methods is column generation book (GERAD 25th Anniversary Series), which has been mentioned in some ...
587 views

Column generation for a linear optimization problem

I have an LP that has exponentially many constraints, and just linearly many variables. The dual of the problem, therefore, has exponentially many variables, while just linearly many constraints. My ...
560 views

Branch and Price Algorithm

Can branch and price be a good solution approach for a routing problem with min-max objective function? For example, minimizing the max length of any vehicle route in a VRP. In the literature, I haven'...
833 views

Does pyomo support column generation?

I want to use column generation technique to solve cutting stock problem. Is there any other python modeling library that supports column generation?
489 views

Column Generation algorithm for vehicle routing problem

I want to solve a VRP with a column generation algorithm. The objective of the problem is makespan minimization. In more detail, I want to minimize the arrival time of the last vehicle in the depot. I ...
255 views

Column Generation algorithm

I want to solve a VRP with a column generation algorithm. The objective of the problem is makespan minimization. but there is a point in calculating the arrival time of the vehicle in each node. the ...
399 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 ...
259 views

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

I am reading A tutorial on column generation and branch-and-price for vehicle routing problems by Dominique Feillet to learn the column generation approach, but I have a problem. in section 3.3 ...
795 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 ...