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Ant colonies for traveling salesman problem

Ant colonies for traveling salesman problem. BioSystems 1997. Present Sherry Y.T.Chen. Auther. Marco Dorigo IRIDIA Universit é Libre de Bruxelles Belgium Luca Maria Gambardella IDSIA ,Department of Electronics and Informatics of Politecnico di Milano.

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Ant colonies for traveling salesman problem

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

  2. Auther • Marco DorigoIRIDIAUniversité Libre de BruxellesBelgium • Luca Maria GambardellaIDSIA,Department of Electronics and Informatics of Politecnico di Milano 2006/05/22 OPLab, Dept. of IM, NTU 2

  3. Outline • Introduction • TSP problem • ACO (artificial ant) • Simulation & Results • Conclusion & Future work • Reference 2006/05/22 OPLab, Dept. of IM, NTU 3

  4. Outline • Introduction • TSP problem • ACO (artificial ant) • Simulation & Results • Conclusion • Future work 2006/05/22 OPLab, Dept. of IM, NTU 4

  5. Introduction • Ants and positive feedback (Dorigo 1992) • Pheromone trail deposited on TSP graph • Assumption：TSP graph is completely connected 2006/05/22 OPLab, Dept. of IM, NTU 5

  6. Outline • Introduction • TSP problem • ACO (artificial ant) • Simulation & Results • Conclusion & Future work • Reference 2006/05/22 OPLab, Dept. of IM, NTU 6

  7. TSP problem • What is TSP problem? • All cities were visited once • returns to the starting city • cheapest round-trip 2006/05/22 OPLab, Dept. of IM, NTU 7

  8. TSP problem • Algorithms (I) • The Greedy Method • Divide-&-Conquer • Enumerating • Branch & Bound • Dynamic Programming • Approximation 2006/05/22 OPLab, Dept. of IM, NTU 8

  9. TSP problem • Algorithms (II) • Simulated annealing (SA) • Annealing-genetic algorithm (AG) • Neural nets (NNs) • Elastic net (EN)  • Self organizing map (SOM) • Evolutionary programming (EP) • Genetic algorithm (GA) 2006/05/22 OPLab, Dept. of IM, NTU 9

  10. Outline • Introduction • TSP problem • ACO (artificial ant) • Simulation & Results • Conclusion & Future work • Reference 2006/05/22 OPLab, Dept. of IM, NTU 10

  11. ACO (artificial ant) • Real ants • Real ants seems have some memory • Real ants are completely blind • Real ants live in an discrete environment 2006/05/22 OPLab, Dept. of IM, NTU 11

  12. ACO (artificial ant) • Example for real ants 2006/05/22 OPLab, Dept. of IM, NTU 12

  13. ACO (artificial ant) • Example for artificial ants •  t=0.5 t= 1 2006/05/22 OPLab, Dept. of IM, NTU 13

  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. 2006/05/22 OPLab, Dept. of IM, NTU 14

  15. ACO (artificial ant) • :Euclidean distance between i and j • :the number of ants in town i at time t • :total number of ants. 2006/05/22 OPLab, Dept. of IM, NTU 15

  16. ACO (artificial ant) • ：intensity of trail on edge (i,j) • （1） • （2） • （3） 2006/05/22 OPLab, Dept. of IM, NTU 16

  17. ACO (artificial ant) • transition probability from town i to town j for the k-th ant • （4） 2006/05/22 OPLab, Dept. of IM, NTU 17

  18. ACO-Algorithm • Initialize, set value • Loop and updating • NC reached? 2006/05/22 OPLab, Dept. of IM, NTU 18

  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) 2006/05/22 OPLab, Dept. of IM, NTU 19

  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) 2006/05/22 OPLab, Dept. of IM, NTU 20

  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 2006/05/22 OPLab, Dept. of IM, NTU 21

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

  23. ACO (artificial ant) • ACS • TSP  2006/05/22 OPLab, Dept. of IM, NTU 23

  24. Outline • Introduction • TSP problem • ACO (artificial ant) • Simulation & Results • Conclusion & Future work • Reference 2006/05/22 OPLab, Dept. of IM, NTU 24

  25. Simulation & Results • Compared with other optimization methods 2006/05/22 OPLab, Dept. of IM, NTU 25

  26. Simulation & Results • Compared with TSPLIB • TSPLIB (maintained by G. Reinelt): http://www.iwr.uniheidelberg.de/iwr/comopt/soft/TSPLIB95/TSPLIB.html 2006/05/22 OPLab, Dept. of IM, NTU 26

  27. Simulation & Results • Compared with different candidate lists 2006/05/22 OPLab, Dept. of IM, NTU 27

  28. Simulation & Results • Communication determines a synergistic C No-C 2006/05/22 OPLab, Dept. of IM, NTU 28

  29. Outline • Introduction • TSP problem • ACO (artificial ant) • Simulation & Results • Conclusion & Future work • Reference 2006/05/22 OPLab, Dept. of IM, NTU 29

  30. Conclusion & Future work • ACO is appropriate to TSP problem • Improvement • Local optimization • Number of ants • Specialized ants, tighter reinforcement 2006/05/22 OPLab, Dept. of IM, NTU 30

  31. Reference • Ant System_Optimization by a colony of cooperating agents, M Dorigo, LM Gambardella - Evolutionary Computation, IEEE Transactions on, 1997 • http://www.neotech-web.com/technology_03.html • http://en.wikipedia.org/ • http://uk.geocities.com/markcsinclair/aco.html • 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 2006/05/22 OPLab, Dept. of IM, NTU 31

  32. Q&A Thanks for your listening 2006/05/22 OPLab, Dept. of IM, NTU 32

  33. Are arcs limited the solution? • Only ACS + greedy ? OPLab, Dept. of IM, NTU

  34. TSP problem • Elastic net (EN)  2006/05/22 OPLab, Dept. of IM, NTU 33

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