Fixed Endpoints Open Traveling Salesman Problem - Genetic Algorithm

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

Description

TSPOF_GA Fixed 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 a FIXED END while visiting the other cities exactly once)

Summary:
1. A single salesman starts at the first point, ends at the last point, and travels to each of the remaining cities in between, 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, and the Fixed End is taken to be the last XY point

Input:
XY (float) is an Nx2 (or Nx3) matrix of cities
DMAT (float) is an NxN matrix of point to point distances/costs
POP_SIZE (scalar integer) is the size of the population (should be divisible by 4)
NUM_ITER (scalar integer) is the number of desired iterations for the algorithm to run
SHOW_PROG (scalar logical) shows the GA progress if true
SHOW_RES (scalar logical) shows the GA results if true

Output:
OPT_RTE (integer array) is the best route found by the algorithm
MIN_DIST (scalar float) is the cost of the best route

Example:
n = 50;
xy = 10*rand(n,2);
a = meshgrid(1:n);
dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),n,n);
pop_size = 60;
num_iter = 1e4;
show_prog = 1;
show_res = 1;
[opt_rte,min_dist] = tspof_ga(xy,dmat,pop_size,num_iter,show_prog,show_res);

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Traveling Salesman Problem - Genetic Algorithm

• MATLAB release: MATLAB 7.6 (R2008a)
• Other Files: license.txt, ; tspof_ga.m