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

Auther Marco Dorigo IRIDIA Université Libre de Bruxelles Belgium Luca Maria Gambardella IDSIA ,Department of Electronics and Informatics of Politecnico di Milano 2006/05/22 OPLab, Dept. of IM, NTU 2

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

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

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

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

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

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

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) 2006/05/22 OPLab, Dept. of IM, NTU 9

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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