https://github.com/e-candeloro/modified-tsp-optimization
A modified Traveling Salesman Problem (TSP) optimization where a directed graph tour starting and ending at the first node is chosen so to maximize a custom objective function (net profit)
https://github.com/e-candeloro/modified-tsp-optimization
data-visualization graph-algorithms gurobi gurobipy maximization operational-research optimization-algorithms pandas python traveling-salesman-problem
Last synced: 2 months ago
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A modified Traveling Salesman Problem (TSP) optimization where a directed graph tour starting and ending at the first node is chosen so to maximize a custom objective function (net profit)
- Host: GitHub
- URL: https://github.com/e-candeloro/modified-tsp-optimization
- Owner: e-candeloro
- Created: 2022-04-28T14:00:08.000Z (over 3 years ago)
- Default Branch: master
- Last Pushed: 2022-04-28T15:55:24.000Z (over 3 years ago)
- Last Synced: 2025-05-16T05:37:00.410Z (5 months ago)
- Topics: data-visualization, graph-algorithms, gurobi, gurobipy, maximization, operational-research, optimization-algorithms, pandas, python, traveling-salesman-problem
- Language: Jupyter Notebook
- Homepage:
- Size: 1.67 MB
- Stars: 2
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Modified-TSP-Optimization
This is the first homework done for the course of Automated Decision Making (2021-2022) at the University of Modena and Reggio Emilia.
It consists of a Python script (and also a notebook used for debugging purposes) that executes modified TSP optimization algorithm, using Gurobi and other common scientific libraries such as Pandas.
### Setup
Consider a directed asymmetric graph **G = (V, A)** with vertex set **V = {0, 1, . . . , n − 1}**.
- Vertex 0 is a depot
- Let **c : A → Z** denote the cost of the arcs
- Let **p : V → Z** denote the profit of the vertices
### Example of a directed asymmetric graph
NB: Vertex profits are represented by the blue dot dimension while the arches costs were not printed due to the high number of them. The arrows show the direction of each arch.
### Objective of the homework
**The problem asks to find a tour that starts and terminates in
the depot, visist a (sub)set S ⊆ V of the vertices and
maximizes the difference between the prizes of the vertices
visited and the costs of the arcs used.**
## ALGORITHM DESCRIPTION
**NOTE**: the main script has comments explaining thealgorithm, also in this document all the
support functions used in the script for loading data, visualizing it, etc... are not described.
### 1)Data Loading and Visualization
Inside the main() function of the script, the data for a directed graph is generated in three
possible ways: loading the data from two CSV files, loading the data from one CSV file
(comparison data) or generating a random directed graph.
After the data generation, the graph is visualized using Matplotlib (the script will continue
closing the graph).
The three main data are: the points dict, the points profits dict and the arches dict with the
cost associated.
### 2)Model Creation
The Gurobi model is created and then the model variable, constraint and objective function
are initialized.
Variables:
- Y_vertices = vector for selecting some or all of the given n vertices
- X_archs = matrix for selecting the arches for a vertex i to a vertex j
### 3)Constraints:
- Depot constraint = always selects the vertex 0
- Degree-2 constraint = every selected vertex (with the Y_vertices vector) needs to have
one arch entering it and one arch leaving it, so a degree of two
### 4)Objective function:
The problem requires maximizing the total net profit: that is the difference between the total
gains minus the total costs, where:
- total gains = sum of all the selected vertex profits
- total costs = sum of all the selected arches costs
### 5)Model Optimization using lazy constraints
Using the lazy constraints functionalities of Gurobi, the model is optimized applying a
sub-tour elimination for each step. The sub-tour elimination is considered only on the
selected vertices of that step, and it is necessary to avoid sub-tours that don’t consider the
vertex 0 (because we can find solutions where the vertex 0 is selected, but it is inside
another cycle!). The toy dataset shown in the default script, shows that the sub-tour
elimination discard multiple independent cycles as a solution.
After the optimization, the results are shown printing the optimal path (as a list of selected
vertices), the total maximum net profit obtained, the computation time and finally the graph
tour is shown.
## RESULTS
### Test Graph
### Test Graph Solution
**The solution of this graph is the selection of nodes 0,1,3 with a total gain of 50 + 50 + 1 = 101 minus the arch cost 1 + 1 +1 = 3
The total profit is 101 - 3 = 98**
### SCRIPT SOLUTION:
Optimal tour: **(0, 1, 3)**
Optimal cost: **98**
## ADDITIONAL INFO
All the additional info can be found in the repository pdf files, as well as the notebook (.ipynb) and Python (.py) script plus the csv files for some of the graph data used.