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Ant colonies for traveling salesman problem

This study explores the use of artificial ant colonies to solve the Traveling Salesman Problem (TSP) in BioSystems. The paper introduces the TSP problem, discusses ACO (artificial ant) algorithms, presents simulations, and shares comparative results. It also outlines future research directions for ACO applications. The authors, Sherry Y.T. Chen, Marco Dorigo, and Luca Maria Gambardella, provide insights into how ACO mimics real ant behavior to optimize TSP solutions efficiently. The paper showcases ACO's effectiveness compared to traditional TSP algorithms.

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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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