Ant Colony Optimization

Slides:



Advertisements
Similar presentations
Computational Intelligence Winter Term 2011/12 Prof. Dr. Günter Rudolph Lehrstuhl für Algorithm Engineering (LS 11) Fakultät für Informatik TU Dortmund.
Advertisements

Computational Intelligence Winter Term 2013/14 Prof. Dr. Günter Rudolph Lehrstuhl für Algorithm Engineering (LS 11) Fakultät für Informatik TU Dortmund.
VEHICLE ROUTING PROBLEM
Swarm algorithms COMP308. Swarming – The Definition aggregation of similar animals, generally cruising in the same direction Termites swarm to build colonies.
1 Topic 7: Stigmergy, Swarm Intelligence and Ant Algorithms stigmergy swarm intelligence ant algorithms  AntNet: routing  AntSystem: TSP.
Ant colonies for the traveling salesman problem Eliran Natan Seminar in Bioinformatics (236818) – Spring 2013 Computer Science Department Technion - Israel.
Ant Colony Optimization. Brief introduction to ACO Ant colony optimization = ACO. Ants are capable of remarkably efficient discovery of short paths during.
Biologically Inspired Computation Lecture 10: Ant Colony Optimisation.
The Antnet Routing Algorithm - A Modified Version Firat Tekiner, Z. Ghassemlooy Optical Communications Research Group, The University of Northumbria, Newcastle.
Ant Colony Optimization Optimisation Methods. Overview.
Ant Colony Optimization Algorithms for the Traveling Salesman Problem ACO Kristie Simpson EE536: Advanced Artificial Intelligence Montana State.
D Nagesh Kumar, IIScOptimization Methods: M1L4 1 Introduction and Basic Concepts Classical and Advanced Techniques for Optimization.
Presented by: Martyna Kowalczyk CSCI 658
Ant Colony Optimization: an introduction
Ant Colony Optimization (ACO): Applications to Scheduling
1 IE 607 Heuristic Optimization Ant Colony Optimization.
FORS 8450 Advanced Forest Planning Lecture 19 Ant Colony Optimization.
Ant Colony Optimization
Ant colony optimization algorithms Mykulska Eugenia
L/O/G/O Ant Colony Optimization M1 : Cecile Chu.
Lecture: 5 Optimization Methods & Heuristic Strategies Ajmal Muhammad, Robert Forchheimer Information Coding Group ISY Department.
Part B Ants (Natural and Artificial) 8/25/ Real Ants (especially the black garden ant, Lasius niger)
Genetic Algorithms and Ant Colony Optimisation
By:- Omkar Thakoor Prakhar Jain Utkarsh Diwaker
Swarm Computing Applications in Software Engineering By Chaitanya.
Swarm Intelligence 虞台文.
Algorithms and their Applications CS2004 ( )
G5BAIM Artificial Intelligence Methods Graham Kendall Ant Algorithms.
-Abhilash Nayak Regd. No. : CS1(B) “The Power of Simplicity”
Design & Analysis of Algorithms Combinatory optimization SCHOOL OF COMPUTING Pasi Fränti
Kavita Singh CS-A What is Swarm Intelligence (SI)? “The emergent collective intelligence of groups of simple agents.”
Ant Colony Optimization. Summer 2010: Dr. M. Ameer Ali Ant Colony Optimization.
Ant Colony Optimization Theresa Meggie Barker von Haartman IE 516 Spring 2005.
Object Oriented Programming Assignment Introduction Dr. Mike Spann
Ant Colony Optimization Algorithms for TSP: 3-6 to 3-8 Timothy Hahn February 13, 2008.
Discrete optimization of trusses using ant colony metaphor Saurabh Samdani, Vinay Belambe, B.Tech Students, Indian Institute Of Technology Guwahati, Guwahati.
The Application of The Improved Hybrid Ant Colony Algorithm in Vehicle Routing Optimization Problem International Conference on Future Computer and Communication,
Topic 6: Stigmergy, Swarm Intelligence and Ant Algorithms swarm intelligence stigmergy ant algorithms  AntNet: routing  AntSystem: TSP.
Neural and Evolutionary Computing - Lecture 11 1 Nature inspired metaheuristics  Metaheuristics  Swarm Intelligence  Ant Colony Optimization  Particle.
Traveling Salesman Problem IEOR 4405 Production Scheduling Professor Stein Sally Kim James Tsai April 30, 2009.
Optimizing Pheromone Modification for Dynamic Ant Algorithms Ryan Ward TJHSST Computer Systems Lab 2006/2007 Testing To test the relative effectiveness.
Ant colony optimization. HISTORY introduced by Marco Dorigo (MILAN,ITALY) in his doctoral thesis in 1992 Using to solve traveling salesman problem(TSP).traveling.
Ant Colony Optimization Quadratic Assignment Problem Hernan AGUIRRE, Adel BEN HAJ YEDDER, Andre DIAS and Pascalis RAPTIS Problem Leader: Marco Dorigo Team.
Ant Colony Optimization 22c: 145, Chapter 12. Outline Introduction (Swarm intelligence) Natural behavior of ants First Algorithm: Ant System Improvements.
AntNet: A nature inspired routing algorithm
Ant Colony Optimization Andriy Baranov
M ulti m edia c omputing laboratory Biologically Inspired Cooperative Routing for Wireless Mobile Sensor Networks S. S. Iyengar, Hsiao-Chun Wu, N. Balakrishnan,
Biologically Inspired Computation Ant Colony Optimisation.
AUT- Department of Industrial Engineering Behrooz Karimi 1 Ant Colony Optimization By: Dr. Behrooz Karimi
What is Ant Colony Optimization?
B.Ombuki-Berman1 Swarm Intelligence Ant-based algorithms Ref: Various Internet resources, books, journal papers (see assignment 3 references)
Ant Colony Optimisation. Emergent Problem Solving in Lasius Niger ants, For Lasius Niger ants, [Franks, 89] observed: –regulation of nest temperature.
Swarm Intelligence. Content Overview Swarm Particle Optimization (PSO) – Example Ant Colony Optimization (ACO)
Ant Colony Optimisation: Applications
Ant Colony Optimization
Scientific Research Group in Egypt (SRGE)
Subject Name: Operation Research Subject Code: 10CS661 Prepared By:Mrs
Swarm Intelligence: From Natural to Artificial Systems
Ant colonies for traveling salesman problem
Computational Intelligence
Ant Colony Optimization Quadratic Assignment Problem
Metaheuristic methods and their applications. Optimization Problems Strategies for Solving NP-hard Optimization Problems What is a Metaheuristic Method?
Swarm Intelligence.
ANT COLONY OPTIMIZATION
Ant Colony Optimization
Design & Analysis of Algorithms Combinatorial optimization
traveling salesman problem
Ants and the TSP.
Computational Intelligence
Ant Colony Optimization
Presentation transcript:

Ant Colony Optimization

Swarm Intelligence (SI) Collective behavior of decentralized, self-organized systems. (G.Beni and J.Wang (1989, cellular robotics)

Swarm Intelligence Collective system capable of accomplishing difficult tasks in dynamic and varied environments without any external guidance or control and with no central coordination Achieving a collective performance which could not normally be achieved by an individual acting alone (ex) Ant colony optimization (ACO) algorithm, Artificial bee colony (ABC) algorithm, Artificial immune systems (AIS), Particle swarm optimization (PSO), ……..

Ant Colony Optimization A probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. A member of swarm intelligence methods, and it constitutes some metaheuristic optimization Initially proposed by Marco Dorico in 1992 in his PhD thesis Aims to search for an optimal path in a graph, based on the behavior of ants seeking a path between their colony and a source of food.

Ant Colony Optimization Problem name Authors Algorithm name Year Traveling salesman Dorigo, Maniezzo & Colorni AS 1991 Gamberdella & Dorigo Ant-Q 1995 Dorigo & Gamberdella ACS &ACS 3 opt 1996 Stutzle & Hoos MMAS 1997 Bullnheimer, Hartl & Strauss ASrank   Cordon, et al. BWAS 2000 Quadratic assignment Maniezzo, Colorni & Dorigo AS-QAP 1994 Gamberdella, Taillard & Dorigo HAS-QAP MMAS-QAP 1998 Maniezzo ANTS-QAP 1999 Maniezzo & Colorni Scheduling problems Colorni, Dorigo & Maniezzo AS-JSP Stutzle AS-SMTTP Barker et al ACS-SMTTP den Besten, Stutzle & Dorigo ACS-SMTWTP Merkle, Middenderf & Schmeck ACO-RCPS Vehicle routing AS-VRP Gamberdella, Taillard & Agazzi HAS-VRP

Ant Colony Optimization Problem name Authors Algorithm name Year Connection-oriented Schoonderwood et al. ABC 1996 network routing White, Pagurek & Oppacher ASGA 1998 Di Caro & Dorigo AntNet-FS Bonabeau et al. ABC-smart ants Connection-less AntNet & AntNet-FA 1997 Subramanian, Druschel & Chen Regular ants Heusse et al. CAF   van der Put & Rethkrantz ABC-backward Sequential ordering Gamberdella& Dorigo HAS-SOP Graph coloring Costa & Hertz ANTCOL Shortest common supersequence Michel & Middendorf AS_SCS Frequency assignment Maniezzo & Carbonaro ANTS-FAP Generalized assignment Ramalhinho Lourenco & Serra MMAS-GAP Multiple knapsack Leguizamon & Michalewicz AS-MKP 1999 Optical networks routing Navarro Varela & Sinclair ACO-VWP Redundancy allocation Liang & Smith ACO-RAP Constraint satisfaction Solnon Ant-P-solver 2000

Ant’s Foraging Behavior Experiments with Argentine ants (Goss et.al, 1989) Ants go from the nest to the food source and backwards after a while, the ants prefer the shortest path from the nest to the food source stigmercy: the ants communicate indirectly laying pheromone trails and following trails with higher pheromone length gradient  pheromone will accumulate on the shortest path food nest

Ant’s Foraging Behavior

Double Bridge Experiments Deneubourg et. al., 1990 Branches of equal length 𝑟= 𝑙 𝑙 𝑙 𝑠 =1 ants converges to one single path Initial random fluctuation 의 효과 Autocatalytic or positive feedback process

Double Bridge Experiments Branches of different length (1) 𝑟= 𝑙 𝑙 𝑙 𝑠 =2 ants converges to the short branch Initial random fluctuation 의 효과가 줄어듬 Positive feedback to shorter branch Shorter branch -> Higher level of pheromone -> faster accumulation of pheromone on shorter branch -> ….

Double Bridge Experiments Branches of different length (2) 𝑟= 𝑙 𝑙 𝑙 𝑠 =2 Short branch were added after 30 min the great majority of ants select the long branch High pheromone concentration Slow evaporation of pheromone Autocatalytic (自動觸媒) behavior

Double Bridge Experiments Stochastic Model Probability of choosing a branch Pheromone evaporation 𝑝 𝑖𝑎 (𝑡): probability that an ant arriving at decision point 𝑖∈{0,1} selects branch 𝑎∈{𝑠,𝑙} (s: short, l: long) 𝜑 𝑖𝑎 (𝑡): total amount of pheromone at instant t 𝑡 𝑠 : traverse time on short branch 𝑟 𝑡 𝑠 : traverse time on long branch 𝛼=2 𝜓: ants per second cross the bridge in each direction

Double Bridge Experiments Monte Carlo simulation 𝑟=1 𝑟=2

S-ACO Algorithm Ant’s path-searching behavior Graph 𝐺= 𝑁, 𝐴 , 𝑁: set of nodes, 𝐴:set of arcs 𝜏 𝑖𝑗 : pheromone trail on arc 𝑖,𝑗 = const. , ∀(𝑖,𝑗)∈𝐴 (at the beginning stage) Ant’s path-searching behavior If an ant 𝑘 is located at a node 𝑖, then the probability of choosing 𝑗 as next node is 𝑁 𝑖 𝑘 : neighborhood of ant 𝑘 when in node 𝑖 All nodes directly connected to node 𝑖 except for the predecessor of node 𝑖

S-ACO Algorithm Pheromone update 𝑘-th ant deposits an amount ∆𝜏 𝑘 of pheromone on arcs it has visited 𝜏 𝑖𝑗 = 𝜏 𝑖𝑗 +∆ 𝜏 𝑘 <Equivalent graph model> ∆𝜏 𝑘 : non-increasing function of path length ∆𝜏 𝑘 : constant

S-ACO Algorithm Pheromone evaporation After each ant 𝑘 has moved to a next node, pheromone trails are evaporated by Exponentially decreasing 𝜏 𝑖𝑗 ←(1−𝜌) 𝜏 𝑖𝑗 ∀(𝑖,𝑗)∈𝐴 𝜌∈[0, 1]

S-ACO Shortest Path Algorithm Given a directed acyclic graph 𝐺= 𝑁, 𝐴 , where 𝑁= 0,⋯,𝐺 0: source (nest), G: destination (food) for all ant 𝑘, ant position 𝑛 𝑘 ←0 ant state 𝑠 𝑘 ← forward for all arcs (𝑖,𝑗), 𝜏 𝑖𝑗 ← const repeat ant_step(𝑘) 𝜏 𝑖𝑗 ← (1−𝜌) 𝜏 𝑖𝑗 ant_step(𝑘) if 𝑛 𝑘 =𝐺, 𝑠 𝑘 ← backward if 𝑛 𝑘 =0, 𝑠 𝑘 ← forward if 𝑠 𝑘 = forward, choose next ant position 𝑛 𝑘 ←𝑗 with the probability of 𝑝 𝑘 𝑖𝑗 update pheromone 𝜏 𝑖𝑗 = 𝜏 𝑖𝑗 +𝜖 if 𝑠 𝑘 = backward, with the probability of 𝑝 𝑘 𝑗𝑖 update pheromone 𝜏 𝑗𝑖 = 𝜏 𝑗𝑖 +𝜖

S-ACO

Experiments with Double Bridge Number of ants 𝑚=1, ⋯, 512 Pheromone update ∆ 𝜏 𝑘 = constant (without considering path length) = 1 𝐿 𝑘 (with considering path length)

Experiments with Extended Double Bridge Pheromone evaporation Evaporation rate 𝜌={0, 0.01, 0.1} 𝜌=0 : no evaporation 𝜌=0.01: 10% of pheromone evaporated after 10 iterations 𝜌=0.1: 65% of pheromone evaporated after 10 iterations The larger 𝜌, the faster converges to suboptimal solution 𝜏 𝑖𝑗 ←(1−𝜌) 𝜏 𝑖𝑗 ∀(𝑖,𝑗)∈𝐴

Traveling Salesman Problem TSP PROBLEM Given N cities, and a distance function d between cities, find a tour that: 1. Goes through every city once and only once 2. Minimizes the total distance. Problem is NP-hard Classical combinatorial optimization problem to test.

Ant System (AS) for TSP Algorithm Initialize Place each ant in a randomly chosen city Choose NextCity(For Each Ant) more cities to visit For Each Ant Return to the initial cities Update pheromone level using the tour cost for each ant Print Best tour yes No Stopping criteria

Ant System (AS) for TSP Tour Construction Probability of ant 𝑘 , currently at city 𝑖 , choosing a next city 𝑗 𝑁 𝑘 𝑖 : feasible neighborhood of ant 𝑘 when being at city 𝑖 set of cities that ant 𝑘 has not visited yet 𝜂 𝑖𝑗 = 1 𝑑 𝑖𝑗 : heuristic value priori to closer city 𝑑 𝑖𝑗 : length of arc (𝑖,𝑗) 𝛼, 𝛽 : parameters 𝛼=0, 𝛽>1 : the closest city is selected 𝛼>1, 𝛽=0 : only pheromone is used ⇒ stagnation ⇒ strongly suboptimal solution

(𝛽=0) (𝛼=0)

Ant System (AS) for TSP Pheromone trail update Pheromone evaporation 𝜏 𝑖𝑗 ← 𝜏 𝑖𝑗 + 𝑘=1 𝑚 ∆ 𝜏 𝑘 𝑖𝑗 , ∀ 𝑖,𝑗 ∈𝐴 ∆𝜏 𝑘 𝑖𝑗 = 1 𝐶 𝑘 , if 𝑖,𝑗 ∈ 𝑇 𝑘 0 , otherwise 𝑇 𝑘 : tour of ant 𝑘, tabu 𝜏 𝑖𝑗 ←(1−𝜌) 𝜏 𝑖𝑗 ∀(𝑖,𝑗)∈𝐴

A simple TSP example A B C D E dAB =100;dBC = 60…;dDE =150 [] [] [] [] 2 [] A B 3 [] C 4 [] D E 5 [] dAB =100;dBC = 60…;dDE =150

Iteration 1 2 [B] 1 [A] A B 3 [C] C 5 [E] 4 [D] D E

How to build next sub-solution? 1 [A] A B 1 [A] 1 [A] C 1 [A,D] 1 [A] D E

Iteration 2 5 [E,A] 3 [C,B] A B 2 [B,C] C 1 [A,D] 4 [D,E] D E

Iteration 3 A B C D E [D,E,A] [E,A,B] [A,D,C] [B,C,D] [C,B,E] 4 5 1 2

Iteration 4 A B C D E [B,C,D,A] [D,E,A,B] [E,A,B,C] [C,B,E,D] [A,DCE] 2 [B,C,D,A] 4 [D,E,A,B] A B 5 [E,A,B,C] C 3 [C,B,E,D] 1 [A,DCE] D E

Iteration 5 A B C D E [A,D,C,E,B] [C,B,E,D,A] [D,E,A,B,C] [E,A,B,C,D] 1 [A,D,C,E,B] 3 [C,B,E,D,A] A B 4 [D,E,A,B,C] C 5 [E,A,B,C,D] 2 [B,C,D,A,E] D E

Pheromone Update 𝐶 1 =300 𝐶 2 =450 𝐶 3 =260 𝐶 4 =280 𝐶 5 =420 [A,D,C,E,B] 𝐶 1 =300 2 [B,C,D,A,E] 𝐶 2 =450 3 [C,B,E,D,A] 𝐶 3 =260 4 [D,E,A,B,C] 𝐶 4 =280 𝐶 5 =420 5 [E,A,B,C,D]

Ant Colony System (ACS) for TSP Dorigo & Gambardella (1997) introduced four modifications in AS : Different tour construction rule Different pheromone trail updates Global Local

ACS for TSP Tour Construction When located at city 𝑖, ant 𝑘 chooses a next city 𝑗 by the following rule 𝑗= arg max 𝑎𝑟𝑔𝑚𝑎𝑥 𝑙∈ 𝑁 𝑘 𝑖 𝜏 𝑖𝑗 𝜂 𝑖𝑙 𝛽 , if 𝑞 ≤ 𝑞 𝑜 𝐽 , otherwise 𝑞: random variable uniformly distributed in [0,1] 𝑞 𝑜 ∈(0,1] : parameter 𝐽: random variable selected by the following probability (𝛼=0)

ACS for TSP Tour Construction (Example) else choose If 𝑞≤ 𝑞 𝑜 choose A-B (15) else choose A-B with probability 15/26 A-C with probability 5/26 A-D with probability 6/26

ACS for TSP Global pheromone trail update Add and evaporate pheromone only to the best tour since trial began Computational complexity 𝑂 𝑛 2 → 𝑂(𝑛) 𝜏 𝑖𝑗 ← 1−𝜌 𝜏 𝑖𝑗 + 𝜌 ∆ 𝜏 𝑏𝑒𝑠𝑡 𝑖𝑗 ∀(𝑖,𝑗)∈ 𝑇 𝑏𝑒𝑠𝑡 ∆𝜏 𝑏𝑒𝑠𝑡 𝑖𝑗 = 1 𝐶 𝑏𝑒𝑠𝑡

ACS for TSP Local pheromone update Remove pheromone to the arc (𝑖,𝑗) immediately after having been crossed during tour construction Tabu effect The arc recently visited is not desirable for the following ants Increase the exploration of arcs that have not been visited yet ⇒ reduce stagnation behavior 𝜏 𝑖𝑗 ← 1−𝜉 𝜏 𝑖𝑗 + 𝜉 𝜏 𝑜 𝜉 ∈ 0,1 , 𝜏 𝑜 : initial pheromone

ACS for TSP Results for a 30 cities instance Results for larger cities (best tour) best average std.deviation ACS 420 420.4 1.3 Tabu-search 420.6 1.5 Sim. Annealing 422 459.8 25.1 ACO Gen.Alg. Evol.Prog. Sim.Ann. 50 cities 425 428 426 443 75 cities 535 545 542 580 100 cities 21282 21761

Conclusions ACO is a recently proposed metaheuristic approach for solving hard combinatorial optimization problems. Artificial ants implement a randomized construction heuristic which makes probabilistic decisions. ACO can find best solutions on smaller problems On larger problems converged to good solutions –but not the best In ACO Local search is extremely important to obtain good results.