MTSPO_GA Open Multiple Traveling Salesmen Problem (MTSP) Genetic Algorithm (GA)
Finds a (near) optimal solution to a variation of the MTSP by setting
up a GA to search for the shortest route (least distance needed for the
salesmen to travel to each city exactly once without returning to their
starting location)
Summary:
1. Each salesman travels to a unique set of cities (although none of
them close their loops by returning to their starting points)
2. Each city is visited by exactly one salesman
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 citytocity distances or costs
 NSALESMEN (scalar integer) is the number of salesmen to visit the cities
 MINTOUR (scalar integer) is the minimum tour length for any of the salesmen
 POPSIZE (scalar integer) is the size of the population (should be divisible by 8)
 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
 OPTBREAK (integer array) is the list of route break points (these specify the indices
into the route used to obtain the individual salesman routes)
 MINDIST (scalar float) is the total distance traveled by the salesmen
Route/Breakpoint Details:
If there are 10 cities and 3 salesmen, a possible route/break
combination might be: rte = [5 6 9 1 4 2 8 10 3 7], brks = [3 7]
Taken together, these represent the solution [5 6 9][1 4 2 8][10 3 7],
which designates the routes for the 3 salesmen as follows:
. Salesman 1 travels from city 5 to 6 to 9
. Salesman 2 travels from city 1 to 4 to 2 to 8
. Salesman 3 travels from city 10 to 3 to 7
Usage:
mtspo_ga
or
mtspo_ga(userConfig)
or
resultStruct = mtspo_ga;
or
resultStruct = mtspo_ga(userConfig);
or
[...] = mtspo_ga('Param1',Value1,'Param2',Value2, ...);
Example:
% Let the function create an example problem to solve
mtspo_ga;
Example:
% Request the output structure from the solver
resultStruct = mtspo_ga;
Example:
% Pass a random set of userdefined XY points to the solver
userConfig = struct('xy',10*rand(35,2));
resultStruct = mtspo_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:n1);
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 = mtspo_ga(userConfig);
Example:
% Pass a random set of 3D (XYZ) points to the solver
xyz = 10*rand(35,3);
userConfig = struct('xy',xyz);
resultStruct = mtspo_ga(userConfig);
Example:
% Change the defaults for GA population size and number of iterations
userConfig = struct('popSize',200,'numIter',1e4);
resultStruct = mtspo_ga(userConfig);
Example:
% Turn off the plots but show a waitbar
userConfig = struct('showProg',false,'showResult',false,'showWaitbar',true);
resultStruct = mtspo_ga(userConfig);
1.3.0.0  Major overhaul of input/output interface. 

1.2.0.0  Minor cosmetic updates. 

1.1.0.0  Added 3D capability. 

1.0.0.0  Removed the SINGLES parameter and replaced it with a more generalized MIN_TOUR 
Inspired by: Multiple Traveling Salesmen Problem  Genetic Algorithm
Create scripts with code, output, and formatted text in a single executable document.
Update: The SINGLES parameter has been replaced with a more generalized MIN_TOUR.