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Questions tagged [subtour-elimination]

For questions related to constraints intended to eliminate subtours (disconnected tours) in routing problems.

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What reasons would cause lazy constraints to degrade the performances when reoptimizing with a different objective?

We are currently solving a hard MILP problem on optimality. Once it has been solved, several times (from 5 to 10 times), we change one coefficient of the objective function and reoptimize. Thus the ...
JKHA's user avatar
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0 votes
2 answers
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"GLPK: No Primal Feasible Solution" for Travelling Salesman Problem (Dantzig–Fulkerson–Johnson formulation)

I have a problem with implementing the Dantzig–Fulkerson–Johnson formulation to solve the following Travelling Salesman Problem: \begin{bmatrix} M & 21 & 17 & 19 & 21 & 22\\ 26 &...
satk0's user avatar
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3 votes
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Number of Subtour Elimination Constraints for ATSP (DFJ Formulation)

In the DFJ formulation of the symmetric TSP, the subtour elimination constraints are typically written as: $$\sum_{\{i,j\} \in E: \ i \in S, j \notin S} x_{ij} \geq 2, \qquad \forall S \subset V, \; 3 ...
user11589's user avatar
5 votes
1 answer
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Flow problem with side constraints: how to eliminate subtours?

I am working on a flow problem with side constraints. More specifically, I have a usual flow problem, with constraints that require some arcs to have exactly one unit of flow on them. This makes the ...
Kuifje's user avatar
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7 votes
4 answers
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Interpretation of a subtour elimination constraint in the TSP

I have a problem with understanding the following mathematical model of the TSP. Given that the TSP is: $$\min \sum_{i,j\in N} d_{i,j} \cdot x_{i,j}$$ subjected to: $$\begin{array}{rrrr}\sum_{j\in N}...
Snowflake's user avatar
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4 votes
1 answer
410 views

The difference between subtour-elimination constraints in the symmetric and asymmetric TSP

We know that there are lots of formulations for traveling salesman problem. Some of them are based on the directed graph (asymmetric) and others are based on the undirected graph (symmetric). Also, ...
A.Omidi's user avatar
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10 votes
1 answer
2k views

How to remove or replace sub tour elimination constraints in the VRP variant models?

In many of vehicle routing problems variant (VRP), which can be formulated using MIPs, to avoid creating sub tour, we need to use sub tour elimination constraints (SEC). One of the known SEC is (I ...
A.Omidi's user avatar
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14 votes
2 answers
397 views

Subtour elimination constraints - enumeration vs dynamically adding

The classical constraints to prevent subtours in routing problems (i.e., to make sure every route is connected to a depot), are of the following form, $$ \sum_{(i,j) \in \delta(S)} x_{ij} \leq |S| - 1 ...
Albert Schrotenboer's user avatar