MIN-Fakult¨at Fachbereich Informatik Ant Colony Optimization · Theoretical Approach - Ant System Ant Colony Optimization Ant System (AS) (cont.) Pheromone Update Pheromone update

Universitat Hamburg

MIN-FakultatFachbereich Informatik

Ant Colony Optimization

Ant Colony OptimizationAlgorithm and Approaches in Robot Path Planning

Katinka Bohm

Universitat HamburgFakultat fur Mathematik, Informatik und NaturwissenschaftenFachbereich Informatik

Technische Aspekte Multimodaler Systeme

January 4th, 2016

Katinka Bohm 1

Universitat Hamburg


Ant Colony Optimization

Structure

1. Introduction

2. Theoretical Approach

3. Robot Path Planning with ACO

4. Analysis

5. Interesting Applications

6. Recap

7. References

Katinka Bohm 2

Universitat Hamburg


Introduction - Motivation Ant Colony Optimization

Motivation

Natural Inspiration! based on the the behavior of ants seeking a path between theircolony and a source of food

Stigmergy

Unorganized actions of individuals serve as a stimuli for other individuals bymodifying their environment and result in a single outcome .

In short: A group of individuals that behave as a sole entity.

Katinka Bohm 3

Universitat Hamburg


Introduction - Motivation Ant Colony Optimization

Motivation (contd.)

I Swarm Intelligence method

I probabilistic technique ! non-deterministic

I solve hard combinatorial optimization problems

Definition

Combinatorial Optimization Problem P = (S ,⌦, f )S . . . finite set of decision variables,⌦ . . . constraints,f . . . objective function to be minimized

Prominent example: Traveling Salesman

Katinka Bohm 4

Universitat Hamburg


Introduction - Metaheuristic Ant Colony Optimization

Metaheuristic

Ant Colony Optimization (ACO)

Set parameters

Initialize pheromone trails

while termination condition not met do

ConstructAntSolutions

DaemonActions (optional)

UpdatePheromones

endwhile

Katinka Bohm 5

Universitat Hamburg


Theoretical Approach - Ant System Ant Colony Optimization

Ant System (AS)

I oldest most basic algorithm

I by Marco Dorigo in the 90s

Ant Movement

Probability for ant k to move from i to j in the next step:

pkij =

⌧↵ij · ⌘�ijP8cil

cil feasible

⌧↵il · ⌘�il

where ↵ and � control importance of pheromone ⌧ vs. heuristic value ⌘

Standard heuristic: ⌘ij = 1dij

where dij is the distance between i and j

Katinka Bohm 6

Universitat Hamburg


Theoretical Approach - Ant System Ant Colony Optimization

Ant System (AS) (cont.)

Pheromone Update

Pheromone update for all ants that have built a solution in that iteration:

⌧ij (1� ⇢) · ⌧ij +mX

k=1

�⌧ kij

where ⇢ is the evaporation rate and �⌧ kij is the quantity of pheromone laid onedge (ij) with

�⌧ kij =Q

L k

where Q is a constant and Lk is the total length of the tour of ant k

Katinka Bohm 7

Universitat Hamburg


Theoretical Approach - Max-Min Ant System Ant Colony Optimization

Max-Min Ant System (MMAS)

I pheromone values are bound

I only the best ant updates its pheromone trails after solutionshave been found

Pheromone Update

⌧ij h(1� ⇢) · ⌧ij +�⌧ bestij

i⌧max

⌧min

where �⌧ bestij = 1Lbest

Lbest can be the iteration best or global best tour

Katinka Bohm 8

Universitat Hamburg


Theoretical Approach - Ant Colony System Ant Colony Optimization

Ant Colony System (ACS)

I diversify the search through a local pheromone update

I pseudorandom proportional rule for ant movement

Local Pheromone Update

Performed by all ants after each construction step to the last traversed edge

⌧ij = (1� ) · ⌧ij + · ⌧0

where 2 (0, 1] is the pheromone decay coe�cient

and 0 is the initial pheromone value

Pheromone Update

⌧ij ((1� ⇢) · ⌧ij + ⇢ ·�⌧ij if (i , j) belongs to the best tour

⌧ij otherwise

Katinka Bohm 9

Universitat Hamburg


Theoretical Approach - Overview Ant Colony Optimization

Theoretical ApproachOverview

Algorithm Ant Movement Pheromones UpdateEvaporation

Ant System (AS)1991

random proportional ⌧ij (1� ⇢) · ⌧ij +Pm

k=1 �⌧kij all paths

Max-Min Ant Sys-tem (MMAX)2000

random proportional

⌧ij h(1� ⇢) · ⌧ij + �⌧bestij

i⌧max

⌧min

best-so-far tourmin/max bound

Ant Colony System(ACS)1997

pseudorandomproportional

local: ⌧ij = (1� ) · ⌧ij + · ⌧0global:

⌧ij ((1� ⇢) · ⌧ij + ⇢ · �⌧ij⌧ij

last stepbest-so-far tour

Katinka Bohm 10

Universitat Hamburg


Problem Types Ant Colony Optimization

Problem Types

I Routing Problems! Traveling Salesman, Vehicle Routing, Network Routing

I Assignment Problems! Graph Coloring

I Subset Problems! Set Covering, Knapsack Problem

I Scheduling! Project Scheduling, Timetable Scheduling

I Constraint Satisfaction Problems

I Protein Folding

Katinka Bohm 11

Universitat Hamburg


Robot Path Planning with ACO Ant Colony Optimization

Robot Path Planning

I NP-complete problemI static vs. dynamic environmentI known vs. unknown environmentI rerouting on collisionI shortest path

Katinka Bohm 12

Universitat Hamburg



Robot Path Planning Alg1Mohamad Z. et al. [8]

Shortest Path in a static environmentMap ConstructionGenerate a global free space map where the robot can traversebetween the yellow nodesFree space nodes (white) can be traversed by the robot

Katinka Bohm 13

Universitat Hamburg




Ant Movement

Probability

pij = ⌘�ij · ⌧↵ij with ↵ = 5, � = 5

Heuristic ⌘ =1

distance between next point withintersect point at reference line

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Universitat Hamburg




Pheromone Updatelocal ! after each step from one node to anotherglobal ! after path calculation is finished

Local Evaporation

prevents accumulation of pheromone⌧ij = (1� ⇢) · ⌧ij with ⇢ = 0.5

Global Reinforcement (AS)

⌧ij = ⌧ij +Pm

k=1 �⌧kij , �⌧ij = Q

LkwhereQ . . . number of nodes

Lk . . . length of path chosen by ant k

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Universitat Hamburg




Results

I comparison to a standard GA algorithmI ACO faster with smaller number of iterations

(due to good state transition rule - distance to baseline)

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Universitat Hamburg



Robot Path Planning Alg2Michael Brand et al. [2]

Shortest path in a dynamic environment

I grid world of 20x20, 30x30 and 40x40four possible movement directions: left, right, up, down

I basic AS approachI re-routing after obstacles are addedI focus on re-initialization of pheromones

Global Initialization

⌧ij = 0.1 for every transition between blocks

Local Initialization

Gradient of pheromones around every objectPheromone levels are decreased in a cyclic fashion by a certain fraction (50%)

Katinka Bohm 17

Universitat Hamburg



Robot Path Planning Alg2Michael Brand et al. [2]

Results

Global Initialization

Map Size 20x20 30x30 40x40

Iterations 151 277 148Path Length 39 66 138

Local Initialization

Map Size 20x20 30x30 40x40

Iterations 122 84 69Path Length 39 64 128

Local Initialization: 1st iteration

Local Initialization: 1000th iteration

Katinka Bohm 18

Universitat Hamburg


Analysis - Comparison Ant Colony Optimization

Comparison to other meta-heuristic techniques

I other techniques:Genetic Algorithms (GA), Simulated Annealing (SA),Particle Swarm Optimization (PSO), Tabu Search (TS)

I hard to compare in general ! dependent on specific probleminstance, algorithm implementation and parameter settings(No free lunch theorem)

I slow convergence compared to other approaches! long runtime for small easy instances and fast, pretty goodresults for complex instances

I ACO often performs really bad or really good

Katinka Bohm 19

Universitat Hamburg


Analysis - TSP Ant Colony Optimization

Traveling Salesman Problem

results for a small TSP instance with 20 nodes over multiple runs

MeasuresACO GA SA PSO TS

Parameters pheromone eva-poration

population,crossover,mutation

temperatureannealing rate

population size,velocity

tabu list length

Convergence slow due to phe-romone evapo-ration

rapid avoids trappingby deteriorationmoves

less rapid tabulist avoidstrappingin local optima

IntensificationDiversification

ant movement,pheromone up-date

crossover,mutation

cooling,solution accep-tance strategy

local search,fitness

tabulist,neighbor selecti-on

CPUTime(s)

250 200 101 220 140

Path Length 300 200 99 250 97

Katinka Bohm 20

Universitat Hamburg


Analysis - Advantages and Drawbacks Ant Colony Optimization

Advantages and Drawbacks

AdvantagesI inherent parallelism

I easy to implement on a basiclevel ! few parameters

I possible to solve NP-hardproblems

I fast in finding near optimalsolutions in comparison toclassical approaches

I robust ! suitable fordynamic applications

Drawbacks

I randomness ! notguaranteed to find theoptimal solution

I slow convergence

I theoretical research is hard! mostly rely onexperimental results

Katinka Bohm 21

Universitat Hamburg


Interesting Applications Ant Colony Optimization

Interesting Applications

Dexterous Manipulation:Gripper Configuration

Determine forces extracted by robotgrippers to guarantee stability of thegrip without causing defect or damageto the object.Non-linear problem containing fiveobjective functions, nine constraintsand seven variables.

Image Processing: Edge Detection

Ants move from one pixel to anotherand are directed by the local variationof the images intensity values stored ina heuristics matrix. The highest densityof the pheromone is deposited at theedges.

Katinka Bohm 22

Universitat Hamburg


Recap Ant Colony Optimization

Recap

I Swarm Intelligence

I Inspired by ant colony movementI Three basic approaches

I Ant SystemI Min-Max Ant SystemI Ant Colony System

I Application: Robot Path PlanningI Shortest path in static environment with free space mapI Shortest path in dynamic environment

I slow convergence but fast good solutions for complex problems

Katinka Bohm 23

Universitat Hamburg


References Ant Colony Optimization

References

[1] Toolika Arora and Yogita Gigras.A Survey of Comarison Between Various Meta-Heuristic Techniques for Path Planning Problem.International Journal of Computer Engineering & Science, 3(2):62–66, November 2013.

[2] Michael Brand, Michael Masuda, Michael Masuda, Nicole Wehner, and Xiao-Hua Yu.Ant Colony Optimization Algorithm for Robot Path Planning.International Conference On Computer Design And Appliations (ICCDA 2010), 3:436–440, 2010.

[3] Marco Dorigo and Thomas Stutzle.Ant colony optimization.MIT Press, 2004.

[4] Marco Dorigo and Thomas Stutzle.International Series in Operations Research & Management Science 146, Ant Colony Optimization: Overviewand Recent Advances, chapter 8, pages 227–263.Springer Science+Business Media, 2010.

[5] Yogita Gigras and Kusum Gupta.Ant Colony Based Path Planning Algorithm for Autonomous Robotic Vehicles.International Journal of Artificial Intelligence & Applications (IJAIA), 3(6), November 2012.

[6] Mauro Birattari Marco Dorigo and Thomas Stutzle.Ant Colony Optimization Artificial Ants as a Computational Intelligence Technique.IEEE Computational Intelligence Magazine, 1556-603X(06):28–39, 2006.

Katinka Bohm 24

Universitat Hamburg


References Ant Colony Optimization

References (cont.)

[7] Seedarla Moses Mullar and R. Satya Meher.Optimizing of Robot Gripper Configurations Using Ant Colony Optimization.International Journal of Engineering Research & Technology (IJERT), 2(9), September 2013.

[8] Buniyamin N., Sari↵ N., Wan Ngah W.A.J., and Mohamad Z.Robot global path planning overview and a variation of ant colony system algorithm.International Journal of Mathematics and Computers in Simulation, 5(1), 2011.

[9] Alpa Reshamwala and Deepika P Vinchurkar.Robot Path Planning using An Ant Colony Optimization Approach: A Survey.International Journal of Advanced Research in Artificial Intelligence, 2(3), 2013.

Katinka Bohm 25

Documents

MIN-Fakult¨at Fachbereich Informatik Ant Colony Optimization · Theoretical Approach - Ant System Ant Colony Optimization Ant System (AS) (cont.) Pheromone Update Pheromone update