Questions tagged [column-generation]
Questions on algorithms that solve mathematical models by generating columns (variables) in the pricing step during solution on demand.
14
questions with no upvoted or accepted answers
9
votes
0
answers
93
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 ...
6
votes
0
answers
207
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) ...
- 109
6
votes
0
answers
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? ...
- 622
5
votes
0
answers
75
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}^{'} | \...
- 575
4
votes
0
answers
85
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 ...
- 668
4
votes
1
answer
120
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+...
3
votes
0
answers
360
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 ...
- 668
2
votes
0
answers
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 ...
- 8,382
2
votes
0
answers
111
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}+...
- 21
1
vote
0
answers
64
views
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?
- 11
1
vote
0
answers
95
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 ...
- 409
1
vote
0
answers
293
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..!
- 137
0
votes
0
answers
96
views
How should one proceed with column generation when the subproblem generates only columns with positive reduced costs?
I try to solve a MILP with Column generation. The Master Problem is a minimization problem with " $\le$ " constraint which lead to non-positive dual values. The problem is that the ...
- 409
0
votes
0
answers
38
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 ...
