File Exchange

## Fixed Start Open Traveling Salesman Problem - Genetic Algorithm

version 1.3.0.0 (10.1 KB) by Joseph Kirk

### Joseph Kirk (view profile)

Finds a near-optimal solution to a "open" variation of the TSP with fixed start points using a GA

Updated 06 May 2014

TSPOFS_GA Fixed Start Open Traveling Salesman Problem (TSP) Genetic Algorithm (GA)
Finds a (near) optimal solution to a variation of the TSP by setting up
a GA to search for the shortest route (least distance for the salesman
to travel from a FIXED START to the other cities exactly once without
returning to the starting city)
Summary:
1. A single salesman starts at the first point and travels to each of
the remaining cities but does not close the loop by returning to
the city he started from
2. Each city is visited by the salesman exactly once

Note: The Fixed Start is taken to be the first XY point

Input:
USERCONFIG (structure) with zero or more of the following fields:
- XY (float) is an Nx2 matrix of city locations, where N is the number of cities
- DMAT (float) is an NxN matrix of point to point distances/costs
- POPSIZE (scalar integer) is the size of the population (should be divisible by 4)
- NUMITER (scalar integer) is the number of desired iterations for the algorithm to run
- SHOWPROG (scalar logical) shows the GA progress if true
- SHOWRESULT (scalar logical) shows the GA results if true
- SHOWWAITBAR (scalar logical) shows a waitbar if true

Input Notes:
1. Rather than passing in a structure containing these fields, any/all of
these inputs can be passed in as parameter/value pairs in any order instead.
2. Field/parameter names are case insensitive but must match exactly otherwise.

Output:
RESULTSTRUCT (structure) with the following fields:
(in addition to a record of the algorithm configuration)
- OPTROUTE (integer array) is the best route found by the algorithm
- MINDIST (scalar float) is the cost of the best route

Usage:
tspofs_ga
-or-
tspofs_ga(userConfig)
-or-
resultStruct = tspofs_ga;
-or-
resultStruct = tspofs_ga(userConfig);
-or-
[...] = tspofs_ga('Param1',Value1,'Param2',Value2, ...);

Example:
% Let the function create an example problem to solve
tspofs_ga;

Example:
% Request the output structure from the solver
resultStruct = tspofs_ga;

Example:
% Pass a random set of user-defined XY points to the solver
userConfig = struct('xy',10*rand(50,2));
resultStruct = tspofs_ga(userConfig);

Example:
% Pass a more interesting set of XY points to the solver
n = 50;
phi = (sqrt(5)-1)/2;
theta = 2*pi*phi*(0:n-1);
rho = (1:n).^phi;
[x,y] = pol2cart(theta(:),rho(:));
xy = 10*([x y]-min([x;y]))/(max([x;y])-min([x;y]));
userConfig = struct('xy',xy);
resultStruct = tspofs_ga(userConfig);

Example:
% Pass a random set of 3D (XYZ) points to the solver
xyz = 10*rand(50,3);
userConfig = struct('xy',xyz);
resultStruct = tspofs_ga(userConfig);

Example:
% Change the defaults for GA population size and number of iterations
userConfig = struct('popSize',200,'numIter',1e4);
resultStruct = tspofs_ga(userConfig);

Example:
% Turn off the plots but show a waitbar
userConfig = struct('showProg',false,'showResult',false,'showWaitbar',true);
resultStruct = tspofs_ga(userConfig);

### Cite As

Joseph Kirk (2020). Fixed Start Open Traveling Salesman Problem - Genetic Algorithm (https://www.mathworks.com/matlabcentral/fileexchange/21198-fixed-start-open-traveling-salesman-problem-genetic-algorithm), MATLAB Central File Exchange. Retrieved .

Nabeel N

### Nabeel N (view profile)

What is the type of mutation, selection, and crossover used in this code

Venky Suriyanarayanan

### Venky Suriyanarayanan (view profile)

Thanks a lot for sharing this..!! Where do I make the change in the code if I want to find the Longest path instead of Shortest path?

Dennis Ehlers

Joseph Kirk

### Joseph Kirk (view profile)

@junjiao, in your case, you do not need to make any modifications to the code. Just reorder the final solution output:

>> optRoute = resultStruct.optRoute
>> route = circshift(optRoute,1-find(optRoute == startPoint,1))

junjiao ma

### junjiao ma (view profile)

how should I change the code if the problem is like this: travel from a fixed start point but return to this point at last ?

Min Zheng

Lusia Rakhmawati

SL B

### SL B (view profile)

User friendly. Used in batch processing type program and only slight modifications were necessary. Saved me a lot of time.