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PROJECT
Use Simulated Annealing for the Traveling Salesman Problem
In this project, we will use simulated annealing to approximate an optimal solution to the Traveling Salesman Problem. We will implement the simulated annealing algorithm from scratch and apply it to a given instance of the Traveling Salesman Problem.
You will learn to:
Implement the simulated annealing algorithm.
Apply a global optimization algorithm to a combinatorial optimization problem.
Observe the performance of a global search algorithm over a solution space.
Plot data using Python libraries.
Skills
Data Plotting
Probabilistic Metaheuristics
Combinatorial Optimization
Prerequisites
Basic understanding of optimization theory
Basic understanding of graph theory
Experience with Python
Technologies
NumPy
Python
Matplotlib
Project Description
The Traveling Salesman Problem (TSP) is one of the most famous problems in combinatorial optimization, in which the target is to find the shortest route for the salesman through various cities. In every known algorithm that solves this problem exactly, increasing the number of cities increases the running time of the problem exponentially.
Simulated annealing is a probabilistic technique to approximate the global optimum. Inspired by metallic annealing, where metal is first heated and then cooled to increase its ductility, the step size of simulated annealing is initially kept high to traverse the entire solution space and is gradually decreased to improve the accuracy of the solution.
In this project, we will implement the simulated annealing algorithm and apply it to find an approximate solution to TSP.
Project Tasks
1
Implement TSP
Task 0: Introduction
Task 1: Import Libraries
Task 2: Visualize the TSP Data
Task 3: Construct the Adjacency Matrix
Task 4: Create a Function to Evaluate Distance
2
Implement the Simulated Annealing Algorithm
Task 5: Set the Initial State of the System
Task 6: Find a Candidate State
Task 7: Update the State of the System
Task 8: Implement the Metropolis Acceptance Criterion
Task 9: Save Temperature and Cost Data in Arrays
Task 10: Print the Optimization Results at Different Iterations
3
Use Simulated Annealing to Solve TSP
Task 11: Run the simulated_annealing() Function
Task 12: Plot the Shortest Route on a Graph
Task 13: Plot the Cost Value
Task 14: Plot the Evolution of Temperature
Congratulations!
Relevant Course
Use the following content to review prerequisites or explore specific concepts in detail.