In this project, the travelling salesman problem, its complexity, variations and its applications in various domains was studied. Here, we proposed GACO to solve the complex problem and compare the result with the nearest Neighbour method, metaheuristics such as Simulated Annealing, Tabu Search and Evolutionary Algorithms like Genetic Algorithm and Ant Colony Optimization. The experimental results demonstrated that the HYBRID GACO approach of finding the solution gives the best result in terms of the optimal route travelled by the salesman as compared to other heuristics used in this project. The minimum distance travelled by the salesman is the least for GACO.

1. Shruti Gandhi
(06913502809)
Sonal Doomra
(06513502809)
Indira Gandhi Institute of Technology
Department of Electronics and
Communication Engineering

2. Definition:
Given a set of cities and the
distance between each possible
pair, the Travelling Salesman
Problem is to find the best
possible way of ‘visiting all the
cities exactly once and returning
to the starting point’
TRAVELLING SALESMAN
PROBLEM
An Introduction

3. •.
TSP: An NP Hard
Problem
TSP is an NP-
hard problem
in
combinatorial
optimization
studied in
theoretical
computer
science.
In many
applications,
additional
constraints
such as limited
resources or
time windows
make the
problem
considerably
harder.
Removing
the
constraint of
visiting each
city exactly
one time
also doesn't
reduce
complexity
of the
problem
In spite of the
computational
difficulty of the
problem, a
large number of
heuristics and
exact methods
are known,
which can
solve
instances with

4. • In these applications, the concept city represents, for
example, customers, soldering
In these applications, the concept city represents, for
example, customers, soldering points, or DNA
fragments
• The concept distance represents travelling times or
cost, or a similarity measure between DNA fragments.
Even in its purest form
the TSP, has several
applications such as
planning, logistics,
DNA sequencing
and the
manufacture of
microchips.
Applications of TSP
• When a mechanical arm is used to fasten the nuts for
assembling parts, it moves through each nut in proper
order and returns to the initial position.
• The most economical travelling route will enable the
mechanical arm to finish its work within the shortest
time.
Mechanical
arm
• Inserting electrical elements in the manufacturing of
integrated circuits consumes certain energy when
moving from one electrical element to the other
during manufacturing.
• We need to arrange the manufacturing order to
minimize the energy consumption.
Integrated
circuit

5. Brief Summary of the
Project
Solving the TSP was an interesting problem during recent decades.
Almost every new approach for solving engineering and optimization
problems has been tested on the TSP as a general test bench. First
steps in solving the TSP were classical methods. These methods
consist of heuristic and exact methods. These classical methods for
solving the TSP usually result in exponential computational
complexities. Hence, new methods are required to overcome this
shortcoming. These methods include different kinds of optimization
techniques, nature based optimization algorithms i.e. Genetic
Algorithm, Ant Colony Optimization ,etc.
Metaheuristics , which represent a family of approximate optimization
techniques that have gained a lot of popularity in the past two decades,
are the tools we have used for solving TSP. They provide “acceptable”
solutions in a reasonable time for solving hard and complex problems
in science and engineering. In this project, the population based
metaheuristics i.e Genetic Algorithm and Ant Colony Optimization are
explained and then modified to solve TSP. The results are then
compared with the classical techniques of Nearest Neighbour, Tabu
Search and Simulated Annealing to find out the most optimum solution.
The highlighting feature of our work is the development of a new hybrid
algorithm GACO , that merges two most popular Evolutionary
Algorithms , Ant Colony Optimization and Genetic Algorithm, to solve
the most complex combinatorial optimization problem, the TSP.

6. olving the Problem

7. Here we propose a hybrid metaheuristic (GACO), a hybrid of
genetic algorithm and ant colony optimization to solve the
generalized TSP, and the result obtained is compared with
the stand alone heuristics, to prove the efficiency of our
algorithm. All the codes were written and implemented in
MATLAB 8.

8. The proposed GACO algorithm is to enhance the
performance of genetic algorithm (GA) by
incorporating local search, ant colony optimization
(ACO), for TRAVELLING SALESMAN PROBLEM. In the
proposed GACO algorithm, genetic algorithm is
conducted to provide the DIVERSITY OF
ALIGNMENTs. Thereafter, ant colony optimization is
performed to MOVE OUT OF LOCAL OPTIMA.
From simulation results, it is shown that the proposed
GA-ACO algorithm has superior performance when
compared to other existing algorithms.
TSP using GACO
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1

9. Other heuristics used for TSP
Nearest Neighbor Algorithm For TSP
The NN method compares the distribution
of distances that occur from a data point to
its nearest neighbour in a given data set
with a randomly distributed data set
Best tour =
19 1 26 14 31 38 36 22 30 5 4 2 15 21 27
24 18 16 3 9 34 13 10 29 12 23 7 40 32 37
6 39 25 28 11 8 33 20 35 17
Minimum Distance =
5.1689
Time taken = 280.388999
TSP using GACO
9

11. SIMULATED ANNEALING
Simulated annealing is a single solution based
metaheuristic. The SA algorithm simulates the energy
changes in a system subjected to a cooling process until it
converges to an equilibrium state.
The graph for simulated annealing escaping from local minima. The higher the
temperature, the more significant the probability of accepting a worst move. At a
given temperature, the lower the increase of the objective function, the more
significant the probability of accepting the move. A better move is always
accepted.

12. The basic principle of tabu search is to pursue local search
whenever it encounters a local optimum by allowing non-
improving moves, cycling back to previously visited
solutions is prevented by the use of memories, called tabu
lists (short-term memory), that record the recent history of
the search.
TABU SEARCH

13. GENETIC ALGORITHMS
Population
size
Number of
generation
s
Crossover
rate
Mutation
rate
Factors affecting GA perform

14. ACO was developed by Dorigo , based on the fact that ants are
able to find the shortest route between their nest and a source of
food.This is done using pheromone trails, which ants deposit
whenever they travel, as a form of indirect communication.
ANT COLONY
OPTIMIZATION
Algorithm: ACO For TSP
Set parameters, initialize pheromone
trails
While (termination condition not
met) do
{ ConstructSolutions
UpdateTrails }

15. Simulation
Results•Using Nearest Neighbour
•Using Tabu Search
•Using Simulated Annealing
•Using Genetic Algorithm
•Using Ant Colony Optimization
•Using Hybrid GA and ACO ( GACO)

16. TSP using Nearest Neighbour
Best tour =
30 26 19 38 9 37 1 28 32 40 12 10 34
17 5 25 16 22 27 3
23 18 4 6 24 8 2 35 31 15 7 20 11
21 14 39 13 33 36 29
Minimum distance = 59.3578
Time taken =0.082592
-4 -2 0 2 4 6 8 10 12 14
-2
0
2
4
6
8
10
12
Path length = 59.3578

17. TSP using Tabu Search
Best tour =
20 40 13 26 28 29 30 14 8 36 22 5 38
34 2 17 10 4 18 24 31 37 9 23 27 16
32 39 11 25 35 19 12 21 33 6 15 7 3 1
Minimum distance =
6.1218
Time taken = 1.528810 seconds
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1

18. TSP using Simulated Annealing
Best tour =
22 36 40 38 16 2 9 21 39 8 10 17 15 14 12
11 30
19 33 26 28 29 4 25 24 20 13 32 7 34 27 6
37 3 18 5 35 23 31 1
Minimum distance= 5.8825
Time taken = 49.951520
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1

19. TSP using Genetic
Algorithm
Best tour =
38 20 39 34 29 9 12 4 3 22 8 5 31 11 28 15 35
30 7 32 33 23 18 14 6 26 13 16 24 19 2 25 10
21
17 37 40 27 1 36
Minimum distance =
5.3990
Time taken = 5.406894
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Total Distance = 5.3990, Iteration = 479

20. TSP using ACO
Best tour =
36 19 25 15 16 27 32 22 39 29 21 37 7
28 4 23 17 30 3 34 38 2 10 13 1 14 35
5 33 9 8 20 12 40 26 31 6 18 11 24 36
Minimum distance= 16.6220 Time taken =777.869303
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1

21. Algorithm
used
Min
Distance
Time taken
(sec)
Nearest
neighbour
245.9496 0.067407
Tabu Search 80.7395 20.623332
Simulated
Annealing
76.7459 60.715589
Genetic
Algorithm
55.4096 13.039126
ACO 21.2349 25.050779
GACO 20.6386 10.746399
Result
Comparison

22. Conclusion
In this project, the travelling salesman problem, its
complexity, variations and its applications in various
domains was studied. Here, we proposed GACO to solve
the complex problem and compare the result with the
nearest Neighbour method, metaheuristics such as
Simulated Annealing, Tabu Search and Evolutionary
Algorithms like Genetic Algorithm and Ant Colony
Optimization. The experimental results demonstrated that
the HYBRID GACO approach of finding the solution gives
the best result in terms of the optimal route travelled by the
salesman as compared to other heuristics used in this
project. The minimum distance travelled by the salesman is
the least for GACO.
Future ScopeThe work can be further extended to solve the travelling
salesman problem using the other hybrid metaheuristics
such as Genetic Algorithm with Particle Swarm
Optimization, or Simulated Annealing. Presently we are
working on hybridizing three metaheuristics (GA-ACO-SA)
to obtain a more optimal tour for the travelling salesman
and to improve the convergence behavior.