The Traveling Salesman Problem (TSP) is a standard combinatorial optimization problem. The goal is to find the best route that visits all cities, where best route usually means shortest distance.

Simulated Annealing is a very simple heuristic for solving combinatorial optimization problems. Briefly:

make an initial guess route loop generate a new route if new route is better, accept route if new route is worse, accept route anyway with a small probability decrease accept_probability slightly end-loop return best route found

The devil is in the details: defining how to generate a new route and modifying the small acceptance probability of accepting a worse route.

I implemented simulated annealing for TSP using the Python language for an article in Visual Studio Magazine. Here is a C# implementation of the VSM article program.

*The C# program results (top) are slightly different than the Python program results (bottom) because simulated annealing is probabilistic and the C# and Python random number generation functions are a bit different.*

Because Python and C# are both C-family languages, it was relatively easy to refactor the original Python code to C# code. I did have to implement a Shuffle() function in C# to replace the built-in Python shuffle() function, but I’ve done that many times (using the Fisher-Yates mini-algorithm).

Good fun.

*When I was just out of college, I worked on a cruise ship for a couple of years. I got to visit dozens of interesting countries — but all of them bordered the ocean. I know next to nothing about land-locked places such as these three adjacent Central Asian countries. Left: Kazakhstan (population 19 million). Center: Uzbekistan (population 34 million). Right: Kyrgyzstan (population 7 million). I wonder how similar their spoken and written languages are.*

Demo C# code. Replace “lt” and “gt” with symbols — my blogging editor chokes on these symbols.

using System; namespace TSP_Annealing { class TSP_Annealing_Program { static void Main(string[] args) { Console.WriteLine("\nBegin TSP simulated annealing C# "); int nCities = 20; Console.WriteLine("\nSetting num_cities = " + nCities); Console.WriteLine("\nOptimal solution is 0, 1, 2, . . " + (nCities - 1)); Console.WriteLine("Optimal soln has total distance = " + (nCities - 1)); Random rnd = new Random(2); int maxIter = 25000; double startTemperature = 10000.0; double alpha = 0.98; Console.WriteLine("\nSettings: "); Console.WriteLine("max_iter = " + maxIter); Console.WriteLine("start_temperature = " + startTemperature.ToString("F1")); Console.WriteLine("alpha = " + alpha); Console.WriteLine("\nStarting solve() "); int[] soln = Solve(nCities, rnd, maxIter, startTemperature, alpha); Console.WriteLine("Finished solve() "); Console.WriteLine("\nBest solution found: "); ShowArray(soln); double dist = TotalDist(soln); Console.WriteLine("\nTotal distance = " + dist.ToString("F1")); Console.WriteLine("\nEnd demo "); Console.ReadLine(); } // Main() static double TotalDist(int[] route) { double d = 0.0; // total distance between cities int n = route.Length; for (int i = 0; i "lt" n - 1; ++i) { if (route[i] "lt" route[i + 1]) d += (route[i + 1] - route[i]) * 1.0; else d += (route[i] - route[i + 1]) * 1.5; } return d; } static double Error(int[] route) { int n = route.Length; double d = TotalDist(route); double minDist = n - 1; return d - minDist; } static int[] Adjacent(int[] route, Random rnd) { int n = route.Length; int[] result = (int[])route.Clone(); // shallow is OK int i = rnd.Next(0, n); int j = rnd.Next(0, n); int tmp = result[i]; result[i] = result[j]; result[j] = tmp; return result; } static void Shuffle(int[] route, Random rnd) { // Fisher-Yates algorithm int n = route.Length; for (int i = 0; i "lt" n; ++i) { int rIndx = rnd.Next(i, n); int tmp = route[rIndx]; route[rIndx] = route[i]; route[i] = tmp; } } static void ShowArray(int[] arr) { int n = arr.Length; Console.Write("[ "); for (int i = 0; i "lt" n; ++i) Console.Write(arr[i].ToString().PadLeft(2) + " "); Console.WriteLine(" ]"); } static int[] Solve(int nCities, Random rnd, int maxIter, double startTemperature, double alpha) { double currTemperature = startTemperature; int[] soln = new int[nCities]; for (int i = 0; i "lt" nCities; ++i) { soln[i] = i; } Shuffle(soln, rnd); Console.WriteLine("Initial guess: "); ShowArray(soln); double err = Error(soln); int iteration = 0; while (iteration "lt" maxIter && err "gt" 0.0) { int[] adjRoute = Adjacent(soln, rnd); double adjErr = Error(adjRoute); if (adjErr "lt" err) // better route { soln = adjRoute; err = adjErr; } else { double acceptProb = Math.Exp((err - adjErr) / currTemperature); double p = rnd.Next(); if (p "lt" acceptProb) // accept anyway { soln = adjRoute; err = adjErr; } } if (currTemperature "lt" 0.00001) currTemperature = 0.00001; else currTemperature *= alpha; ++iteration; } // while return soln; } // Solve() } // Program class } // ns

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