1. Ant colonies for traveling salesman problem
BioSystems 1997
Present Sherry Y.T.Chen

2. Auther Marco Dorigo IRIDIA Université Libre de Bruxelles Belgium
Luca Maria Gambardella IDSIA ,Department of Electronics and Informatics of Politecnico di Milano
2006/05/ OPLab, Dept. of IM, NTU

3. Outline Introduction TSP problem ACO (artificial ant)
Simulation & Results
Conclusion & Future work
Reference
2006/05/ OPLab, Dept. of IM, NTU

4. Outline Introduction TSP problem ACO (artificial ant)
Simulation & Results
Conclusion
Future work
2006/05/ OPLab, Dept. of IM, NTU

5. Introduction Ants and positive feedback (Dorigo 1992)
Pheromone trail deposited on TSP graph
Assumption：TSP graph is completely connected
2006/05/ OPLab, Dept. of IM, NTU

6. Outline Introduction TSP problem ACO (artificial ant)
Simulation & Results
Conclusion & Future work
Reference
2006/05/ OPLab, Dept. of IM, NTU

7. TSP problem What is TSP problem? All cities were visited once
returns to the starting city
cheapest round-trip
2006/05/ OPLab, Dept. of IM, NTU

8. TSP problem Algorithms (I) The Greedy Method Divide-&-Conquer
Enumerating
Branch & Bound
Dynamic Programming
Approximation
2006/05/ OPLab, Dept. of IM, NTU

9. TSP problem Algorithms (II) Simulated annealing (SA) Neural nets (NNs)
Annealing-genetic algorithm (AG)
Neural nets (NNs)
Elastic net (EN) 
Self organizing map (SOM)
Evolutionary programming (EP)
Genetic algorithm (GA)
2006/05/ OPLab, Dept. of IM, NTU

10. Outline Introduction TSP problem ACO (artificial ant)
Simulation & Results
Conclusion & Future work
Reference
2006/05/ OPLab, Dept. of IM, NTU

11. ACO (artificial ant) Real ants Real ants seems have some memory
Real ants are completely blind
Real ants live in an discrete environment
2006/05/ OPLab, Dept. of IM, NTU

12. ACO (artificial ant) Example for real ants
2006/05/ OPLab, Dept. of IM, NTU

13. ACO (artificial ant) Example for artificial ants  t=0.5 t= 1
2006/05/ OPLab, Dept. of IM, NTU

14. ACO (artificial ant) From real to artificial
(i) the preference for paths with a high pheromone level
(ii) the higher rate of growth of the amount of pheromone on shorter paths
(iii) the trail mediated communication among ants.
2006/05/ OPLab, Dept. of IM, NTU

15. ACO (artificial ant) :Euclidean distance between i and j
:the number of ants in
town i at time t
:total number of ants.
2006/05/ OPLab, Dept. of IM, NTU

16. ACO (artificial ant) ：intensity of trail on edge (i,j) （1） （2） （3）
2006/05/ OPLab, Dept. of IM, NTU

17. ACO (artificial ant)
transition probability from town i to town j for the k-th ant
（4）
2006/05/ OPLab, Dept. of IM, NTU

18. ACO-Algorithm Initialize, set value Loop and updating NC reached?
2006/05/ OPLab, Dept. of IM, NTU

19. ACO-Algorithm 1. Initialize: Set t:=0 Set NC:=0
For every edge (i,j) set an initial value τij(t)=c for trail intensity and Δτij= 0
Place the m ants on the n nodes
2. Set s:=1
For k:=1 to m do
Place the starting town of the k-th ant in tabuk(s)
2006/05/ OPLab, Dept. of IM, NTU

20. ACO-Algorithm 3. Repeat until tabu list is full Set s:=s+1
For k:=1 to m do
Choose the town j to move to, with probability pkij (t) given by equation (4)
Move the k-th ant to the town j
Insert town j in tabuk(s)
2006/05/ OPLab, Dept. of IM, NTU

21. ACO-Algorithm 4. For k:=1 to m do
Move the k-th ant from tabuk(n) to tabuk(1)
Compute the length Lk of the tour described by the k-th ant τij(t+n)=ρ×τij(t)+ Δτij
Update the shortest tour found
2006/05/ OPLab, Dept. of IM, NTU

22. ACO-Algorithm 5. If (NC < NCMAX) and (not stagnation behavior) then
Empty all tabu lists
Goto step 2
else
Print shortest tour
Stop
2006/05/ OPLab, Dept. of IM, NTU

23. ACO (artificial ant)
ACS
TSP 
2006/05/ OPLab, Dept. of IM, NTU

24. Outline Introduction TSP problem ACO (artificial ant)
Simulation & Results
Conclusion & Future work
Reference
2006/05/ OPLab, Dept. of IM, NTU

25. Simulation & Results Compared with other optimization methods
2006/05/ OPLab, Dept. of IM, NTU

26. Simulation & Results Compared with TSPLIB
TSPLIB (maintained by G. Reinelt):
2006/05/ OPLab, Dept. of IM, NTU

27. Simulation & Results Compared with different candidate lists
2006/05/ OPLab, Dept. of IM, NTU

28. Simulation & Results Communication determines a synergistic C No-C
2006/05/ OPLab, Dept. of IM, NTU

29. Outline Introduction TSP problem ACO (artificial ant)
Simulation & Results
Conclusion & Future work
Reference
2006/05/ OPLab, Dept. of IM, NTU

30. Conclusion & Future work
ACO is appropriate to TSP problem
Improvement
Local optimization
Number of ants
Specialized ants, tighter reinforcement
2006/05/ OPLab, Dept. of IM, NTU

31. Reference
Ant System_Optimization by a colony of cooperating agents, M Dorigo, LM Gambardella - Evolutionary Computation, IEEE Transactions on, 1997
螞蟻演算法在即時戰略遊戲上的應用－以美式足球為例, 尹邦嚴
2006/05/ OPLab, Dept. of IM, NTU

32. Q&A
Thanks for your listening
2006/05/ OPLab, Dept. of IM, NTU

33. Are arcs limited the solution? Only ACS + greedy ?
2018/11/13
OPLab, Dept. of IM, NTU

34. TSP problem
Elastic net (EN) 
2006/05/ OPLab, Dept. of IM, NTU