Please follow the step-by-step instructions below:
S1: Consider Travelling Salesman Problem. Problem parameters are randomly generated from the uniform distribution between 10 and 100.
S2: Solve the problem with the mathematical model.
S3: Solve the problem with heuristic algorithm.
S4: Compare results of mathematical model and algorithm.
S5: Your report should have something like the following outline:
A. Introduction (probably 1-2 paragraphs, information about your algorithm)
B. Your problem (information about TSP and mathematical model)
C. Implementation (the steps for your algorithm and their codes in the software package)
D. Numerical Results and Discussion (The solutions of your algorithms in a table, discussion about the results)
2) Simulated Annealing
Consider different sizes of given TSP:
a) small with 5 cities,
b) medium with 15 cities,
c) large with 50 cities.
An example of medium-sized TSP is given in below:
I/J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 69 97 27 21 68 45 27 15 42 23 92 15 81 36
2 - 66 62 84 89 94 53 17 71 39 25 93 63 38
3 - - 58 61 22 19 60 92 35 65 62 51 52 52
4 - - - 28 63 66 56 51 96 78 79 72 67 58
5 - - - - 51 24 77 97 19 47 15 88 15 40
6 - - - - - 66 87 72 20 41 68 44 23 86
7 - - - - - - 17 24 27 44 83 25 65 42
8 - - - - - - - 96 27 33 34 49 49 89
9 - - - - - - - - 34 69 34 77 86 25
10 - - - - - - - - - 52 36 64 45 43
11 - - - - - - - - - - 46 51 74 35
12 - - - - - - - - - - - 32 90 39
13 - - - - - - - - - - - - 80 21
14 - - - - - - - - - - - - - 55
15 - - - - - - - - - - - - - -
Temperature 1:
$T_1 = 0.4 Z_c$, $Z_c$ objective function value for initial solution
$T_{k+1} = 0.7T_k$, $k > 1$
Temperature 2:
$T_1 = 0.6 Z_c$, $Z_c$ objective function value for initial solution
$T_{k+1} = 0.5T_k$, $k > 1$
Temperature 3:
$T_1 = 0.1 Z_c$, $Z_c$ objective function value for initial solution
$T_{k+1} = 0.9T_k$, $k > 1$
Run time=3
Apply inversion, insertion and exchange parameter. Choose two of them.
Iteration number depends on problem size: 50 for small size, 150 for medium size, 300 for large size.