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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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9 votes
0 answers
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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 ...
German Velasquez Diaz's user avatar
6 votes
0 answers
212 views

Benders decomposition for a dense MILP

I am trying to solve a large MILP, but it seems like dense problems can be very difficult for moderns solvers. I tried to solve the problem described below considering only constraints (1) and (2) ...
Enthusiast's user avatar
6 votes
0 answers
110 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? ...
gmn's user avatar
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5 votes
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77 views

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

I aim to solve the following Bellman equation: \begin{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}^{'} | \...
mdslt's user avatar
  • 615
5 votes
0 answers
117 views

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

As far as I know, one of the interesting resources to learn the basic concept of the decomposition methods is column generation book (GERAD 25th Anniversary Series), which has been mentioned in some ...
A.Omidi's user avatar
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4 votes
0 answers
87 views

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 ...
Divyam Aggarwal's user avatar
4 votes
1 answer
131 views

How to find the vectors to be added as the columns in the master problem of Dantzig-Wolfe Decomposition?

I have a Dantzig-Wolfe decomposition question with the following questions \begin{align} &Maximize: 2x_1 +3x_2+4x_3+2x_4 \\ s.t. \quad & x_1 +x_2+2x_3+x_4 \le 15\\ & x_1 +x_2+2x_3+...
Romio Rodriguez's user avatar
3 votes
0 answers
436 views

On solving the Restricted Master Problem in Column Generation technique

I am working on developing a column generation (CG) based optimization framework for a large-scale airline crew pairing problem (a set-covering problem). First, I generate an initial feasible solution ...
Divyam Aggarwal's user avatar
2 votes
0 answers
151 views

Why the column generation algorithm remains stuck at the same solution?

I was trying to solve a MILP by a column generation algorithm, and I noticed that the algorithm was stuck at the same solution, I tried to diversify the pool of initial columns, but the problem I ...
Nada.S's user avatar
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2 votes
0 answers
125 views

Dantzig decomposition and Column Generation for equality constraints

I was trying to apply Dantzig Decomposition followed by Column Generation. The following is how I was taught. \begin{array}{l} \text { Minimize }-10 x_1-2 x_{2}-4 x_{3} \\ \text { subject to: } x_{1}+...
Shadab Ahmed's user avatar
1 vote
0 answers
317 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..!
user3237357's user avatar
0 votes
1 answer
28 views

Adding additional coordinating constraint to a decomposed model

As suggested by @RobPratt, here is the new opened question. I have these decomposed master and subproblems: \begin{align} &\text{minimize} &\sum_t \sum_s \text{slack}_{ts} \\ &\text{...
nflgreaternba's user avatar
0 votes
2 answers
52 views

Modification of subproblem objective function

I have the following decomposed compact model with the following master problem: \begin{align} &\text{minimize} &\sum_t \sum_s \text{slack}_{ts} \\ &\text{subject to} &\sum_i \sum_r \...
nflgreaternba's user avatar
0 votes
0 answers
61 views

Dual stabilization doesnt work properly

I am currently trying to speed up my column generation approach to reduce the tailing-off effect. I have modified my master problem as follows. For this I have introduced $\phi_{ts}^+,\phi_{ts}^-,\...
nflgreaternba's user avatar
0 votes
1 answer
75 views

Gurobi - Problem with adding a non-linear constraint to a column object

I have implemented the following Column Generation model in Gurobi. Unfortunately, I currently have the problem that the constraint in the master problem is not linear and therefore I cannot add the ...
nflgreaternba's user avatar
0 votes
1 answer
88 views

How can I add columns from the subproblem to the master problem in my column generation model?

I have one last question about my column generation model. I am currently trying to implement it in code, and I am successfully solving the subproblem. So I can solve the dual values of the master ...
nflgreaternba's user avatar
0 votes
0 answers
42 views

Dual prices remain stable but negative in column generation

I arrive at an objective function value that I know to be optimal. However, dual prices remain negative (which leads me to believe another pattern can be added, but when I do, the dual prices don't ...
user11638's user avatar