Trouble finding shortest possible distance between all points

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Isabelle Davies
Isabelle Davies on 9 Jun 2022
Edited: Mathieu NOE on 9 Jun 2022
Hi,
I'm trying to find the shortest possible distance between these points, with the red dot being the start and finishing point.
I have two 14x1 arrays with each point's x and y position, and I already have a function to tell me how long a path of the points ordered in a certain way is, but I'm wondering if there's any way to automatically find the shortest possible distance?
Here's my code for context:
[location_data, location_names] = xlsread('exposure_sites.xlsx') ;
latitude_dms = location_data(:, 1:3);
longitude_dms = location_data(:, 4:6);
latitude_degrees = dms2degrees(latitude_dms) ;
longitude_degrees = dms2degrees(longitude_dms) ;
exposure_origin = [mean(latitude_degrees), mean(longitude_degrees)] ;
origin_x = exposure_origin(1,2) ;
origin_y = exposure_origin(1,1) ;
km_per_degree_latitude = 2 .* pi .* 6373.6 / 360 ;
km_per_degree_longitude = km_per_degree_latitude * cos((-27.4743) .* (pi/180)) ;
exposure_x = longitude_degrees * km_per_degree_longitude ;
exposure_y = latitude_degrees * km_per_degree_latitude ;
figure
plot(exposure_x, exposure_y, '.', MarkerSize = 15)
grid on
axis equal
xlabel('x-coordinates'), ylabel('y-coordinates'), title('Coronavirus Variant Exposure Sites')
text(exposure_x, exposure_y, location_names, 'VerticalAlignment', 'bottom')
box off
c = convhull(exposure_x, exposure_y)' ;
first_trip = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 1] ;
computeTripDistance([exposure_x exposure_y], first_trip) ;
axis([1.5095*10^4, 1.512*10^4, -3066, -3045])
trip_3 = ([1 4 8 10 5 3 7 2 13 11 9 14 12 6 1]) ;
computeTripDistance([exposure_x exposure_y], trip_3) ;
axis([1.5095*10^4, 1.512*10^4, -3066, -3045])
As you can see, I've gotten one that works pretty well but I'm wondering if anyone can get it lower? Sorry if this turned out to be more of a maths thing than a coding thing, I just wanted to give as much context as possible.
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