Questions tagged [subtour-elimination]
For questions related to constraints intended to eliminate subtours (disconnected tours) in routing problems.
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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 &...
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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:
$$\sum_{\{i,j\} \in E: \ i \in S, j \notin S} x_{ij} \geq 2, \qquad \forall S \subset V, \; 3 ...
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Flow problem with side constraints: how to eliminate subtours?
I am working on a flow problem with side constraints. More specifically, I have a usual flow problem, with constraints that require some arcs to have exactly one unit of flow on them. This makes the ...
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Interpretation of a subtour elimination constraint in the TSP
I have a problem with understanding the following mathematical model of the TSP.
Given that the TSP is:
$$\min \sum_{i,j\in N} d_{i,j} \cdot x_{i,j}$$
subjected to:
$$\begin{array}{rrrr}\sum_{j\in N}...
- 517
4
votes
1
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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, ...
- 8,382
10
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1
answer
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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 ...
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14
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2
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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 ...
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