Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony OptimizationAre bugs smart?

Daniel Hallin Marlon Etheredge

Utrecht University

MAA, 2014

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Outline

IntroductionHistory & Analogy

AlgorithmAnt System (AS)MAX −MIN Ant System (MMAS)Ant Colony System (ACS)

Break

Examples & SimulationsDouble Bridge ExperimentTravelling Salesman Application

ClassificationMetaheuristicSwarm Intelligence

Applications

Discussion

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Outline

IntroductionHistory & Analogy

AlgorithmAnt System (AS)MAX −MIN Ant System (MMAS)Ant Colony System (ACS)

Break

Examples & SimulationsDouble Bridge ExperimentTravelling Salesman Application

ClassificationMetaheuristicSwarm Intelligence

Applications

Discussion

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

IntroductionHistory

I Pierre-Paul Grass discovered ”significant stimuli”beneficial to both the individual ant as well as thecolony, stigmergy

I In the 1980’s the collective behavior of ants was studiedby Deneubourg and others, double bridge experiment

I Initially proposed by Marco Dorigo in his docotral thesisin 1992

I Swarm intelligence, mimic behavior of animals

I Extensive topic of additional research (protein folding,scheduling problems, etc.)

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

IntroductionHistory

I Pierre-Paul Grass discovered ”significant stimuli”beneficial to both the individual ant as well as thecolony, stigmergy

I In the 1980’s the collective behavior of ants was studiedby Deneubourg and others, double bridge experiment

I Initially proposed by Marco Dorigo in his docotral thesisin 1992

I Swarm intelligence, mimic behavior of animals

I Extensive topic of additional research (protein folding,scheduling problems, etc.)

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

IntroductionHistory

I Pierre-Paul Grass discovered ”significant stimuli”beneficial to both the individual ant as well as thecolony, stigmergy

I In the 1980’s the collective behavior of ants was studiedby Deneubourg and others, double bridge experiment

I Initially proposed by Marco Dorigo in his docotral thesisin 1992

I Swarm intelligence, mimic behavior of animals

I Extensive topic of additional research (protein folding,scheduling problems, etc.)

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

IntroductionHistory

I Pierre-Paul Grass discovered ”significant stimuli”beneficial to both the individual ant as well as thecolony, stigmergy

I In the 1980’s the collective behavior of ants was studiedby Deneubourg and others, double bridge experiment

I Initially proposed by Marco Dorigo in his docotral thesisin 1992

I Swarm intelligence, mimic behavior of animals

I Extensive topic of additional research (protein folding,scheduling problems, etc.)

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

IntroductionHistory

I Pierre-Paul Grass discovered ”significant stimuli”beneficial to both the individual ant as well as thecolony, stigmergy

I In the 1980’s the collective behavior of ants was studiedby Deneubourg and others, double bridge experiment

I Initially proposed by Marco Dorigo in his docotral thesisin 1992

I Swarm intelligence, mimic behavior of animals

I Extensive topic of additional research (protein folding,scheduling problems, etc.)

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

IntroductionAnalogy

I In nature, ants walk randomly while laying downpheromone trails

I Ants are more likely to follow paths with higherpheromone levels

I Whenever an ant finds food, the path is thus reinforced

I Eventually, the probabilities of other paths being chosenwill converge to the strongest reinforced path

I Video:https://www.youtube.com/watch?v=5CAjWaZx2Ks

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

IntroductionAnalogy

I In nature, ants walk randomly while laying downpheromone trails

I Ants are more likely to follow paths with higherpheromone levels

I Whenever an ant finds food, the path is thus reinforced

I Eventually, the probabilities of other paths being chosenwill converge to the strongest reinforced path

I Video:https://www.youtube.com/watch?v=5CAjWaZx2Ks

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

IntroductionAnalogy

I In nature, ants walk randomly while laying downpheromone trails

I Ants are more likely to follow paths with higherpheromone levels

I Whenever an ant finds food, the path is thus reinforced

I Eventually, the probabilities of other paths being chosenwill converge to the strongest reinforced path

I Video:https://www.youtube.com/watch?v=5CAjWaZx2Ks

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

IntroductionAnalogy

I In nature, ants walk randomly while laying downpheromone trails

I Ants are more likely to follow paths with higherpheromone levels

I Whenever an ant finds food, the path is thus reinforced

I Eventually, the probabilities of other paths being chosenwill converge to the strongest reinforced path

I Video:https://www.youtube.com/watch?v=5CAjWaZx2Ks

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

IntroductionAnalogy

I In nature, ants walk randomly while laying downpheromone trails

I Ants are more likely to follow paths with higherpheromone levels

I Whenever an ant finds food, the path is thus reinforced

I Eventually, the probabilities of other paths being chosenwill converge to the strongest reinforced path

I Video:https://www.youtube.com/watch?v=5CAjWaZx2Ks

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Model

A model P = (S ,Ω, f ) of a combinatorial optimizationproblem consists of:

I a search space S defined over a finite set of discretedecision variables Xi , i = 1, ..., n;

I a set Ω of constraints among the variables;

I an objective function f : S → R+0 to be minimized.

The generic variable Xi takes values in Di = v1i , ..., v

|Di |i . A

feasible solution s ∈ S is a complete assignment of values tovariables that satisfies all constraints in Ω. A solutions∗ ∈ S is called a global optimum if and only if:f (s∗) ≤ f (s)∀s ∈ S

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Model

A model P = (S ,Ω, f ) of a combinatorial optimizationproblem consists of:

I a search space S defined over a finite set of discretedecision variables Xi , i = 1, ..., n;

I a set Ω of constraints among the variables;

I an objective function f : S → R+0 to be minimized.

The generic variable Xi takes values in Di = v1i , ..., v

|Di |i . A

feasible solution s ∈ S is a complete assignment of values tovariables that satisfies all constraints in Ω. A solutions∗ ∈ S is called a global optimum if and only if:f (s∗) ≤ f (s)∀s ∈ S

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Model

A model P = (S ,Ω, f ) of a combinatorial optimizationproblem consists of:

I a search space S defined over a finite set of discretedecision variables Xi , i = 1, ..., n;

I a set Ω of constraints among the variables;

I an objective function f : S → R+0 to be minimized.

The generic variable Xi takes values in Di = v1i , ..., v

|Di |i . A

feasible solution s ∈ S is a complete assignment of values tovariables that satisfies all constraints in Ω. A solutions∗ ∈ S is called a global optimum if and only if:f (s∗) ≤ f (s)∀s ∈ S

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Model

A model P = (S ,Ω, f ) of a combinatorial optimizationproblem consists of:

I a search space S defined over a finite set of discretedecision variables Xi , i = 1, ..., n;

I a set Ω of constraints among the variables;

I an objective function f : S → R+0 to be minimized.

The generic variable Xi takes values in Di = v1i , ..., v

|Di |i . A

feasible solution s ∈ S is a complete assignment of values tovariables that satisfies all constraints in Ω. A solutions∗ ∈ S is called a global optimum if and only if:f (s∗) ≤ f (s)∀s ∈ S

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Model

A model P = (S ,Ω, f ) of a combinatorial optimizationproblem consists of:

I a search space S defined over a finite set of discretedecision variables Xi , i = 1, ..., n;

I a set Ω of constraints among the variables;

I an objective function f : S → R+0 to be minimized.

The generic variable Xi takes values in Di = v1i , ..., v

|Di |i .

Afeasible solution s ∈ S is a complete assignment of values tovariables that satisfies all constraints in Ω. A solutions∗ ∈ S is called a global optimum if and only if:f (s∗) ≤ f (s)∀s ∈ S

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Model

A model P = (S ,Ω, f ) of a combinatorial optimizationproblem consists of:

I a search space S defined over a finite set of discretedecision variables Xi , i = 1, ..., n;

I a set Ω of constraints among the variables;

I an objective function f : S → R+0 to be minimized.

The generic variable Xi takes values in Di = v1i , ..., v

|Di |i . A

feasible solution s ∈ S is a complete assignment of values tovariables that satisfies all constraints in Ω.

A solutions∗ ∈ S is called a global optimum if and only if:f (s∗) ≤ f (s)∀s ∈ S

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Model

A model P = (S ,Ω, f ) of a combinatorial optimizationproblem consists of:

I a search space S defined over a finite set of discretedecision variables Xi , i = 1, ..., n;

I a set Ω of constraints among the variables;

I an objective function f : S → R+0 to be minimized.

The generic variable Xi takes values in Di = v1i , ..., v

|Di |i . A

feasible solution s ∈ S is a complete assignment of values tovariables that satisfies all constraints in Ω. A solutions∗ ∈ S is called a global optimum if and only if:f (s∗) ≤ f (s)∀s ∈ S

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

AlgorithmPseudo Code

beginInitialization;while termination condition not met do

ConstructAntSolutions;DaemonActions; /* optional */

UpdatePheromones;

end

end

Initialization Set parameters, reset pheromone variables

ConstructAntSolutions Let ants construct solutions

DaemonActions Optionally improve candidate solutions

UpdatePheromones Make solution components belonging togood solutions more desirable for ants infollowing iterations

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

AlgorithmPseudo Code

beginInitialization;while termination condition not met do

ConstructAntSolutions;DaemonActions; /* optional */

UpdatePheromones;

end

end

Initialization Set parameters, reset pheromone variables

ConstructAntSolutions Let ants construct solutions

DaemonActions Optionally improve candidate solutions

UpdatePheromones Make solution components belonging togood solutions more desirable for ants infollowing iterations

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

AlgorithmPseudo Code

beginInitialization;while termination condition not met do

ConstructAntSolutions;DaemonActions; /* optional */

UpdatePheromones;

end

end

Initialization Set parameters, reset pheromone variables

ConstructAntSolutions Let ants construct solutions

DaemonActions Optionally improve candidate solutions

UpdatePheromones Make solution components belonging togood solutions more desirable for ants infollowing iterations

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

AlgorithmPseudo Code

beginInitialization;while termination condition not met do

ConstructAntSolutions;DaemonActions; /* optional */

UpdatePheromones;

end

end

Initialization Set parameters, reset pheromone variables

ConstructAntSolutions Let ants construct solutions

DaemonActions Optionally improve candidate solutions

UpdatePheromones Make solution components belonging togood solutions more desirable for ants infollowing iterations

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

AlgorithmPseudo Code

beginInitialization;while termination condition not met do

ConstructAntSolutions;DaemonActions; /* optional */

UpdatePheromones;

end

end

Initialization Set parameters, reset pheromone variables

ConstructAntSolutions Let ants construct solutions

DaemonActions Optionally improve candidate solutions

UpdatePheromones Make solution components belonging togood solutions more desirable for ants infollowing iterations

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Outline

IntroductionHistory & Analogy

AlgorithmAnt System (AS)MAX −MIN Ant System (MMAS)Ant Colony System (ACS)

Break

Examples & SimulationsDouble Bridge ExperimentTravelling Salesman Application

ClassificationMetaheuristicSwarm Intelligence

Applications

Discussion

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmConstruct solutions

When ant k is in node i and has constructed partialsolution sp, the probability of going to node j is:

pkij =

ταij ·η

βij∑

cij∈N(sp) ταij ·η

βij

if cij ∈ N(sp),

0 otherwise

I N(sp) is the set of feasible components

I α and β control the relative importance of pheromoneversus the heuristic information ηij .

What happens if α or β are 0 respectively?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmConstruct solutions

When ant k is in node i and has constructed partialsolution sp, the probability of going to node j is:

pkij =

ταij ·ηβij∑

cij∈N(sp) ταij ·η

βij

if cij ∈ N(sp),

0 otherwise

I N(sp) is the set of feasible components

I α and β control the relative importance of pheromoneversus the heuristic information ηij .

What happens if α or β are 0 respectively?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmConstruct solutions

When ant k is in node i and has constructed partialsolution sp, the probability of going to node j is:

pkij =

ταij ·η

βij∑

cij∈N(sp) ταij ·η

βij

if cij ∈ N(sp),

0 otherwise

I N(sp) is the set of feasible components

I α and β control the relative importance of pheromoneversus the heuristic information ηij .

What happens if α or β are 0 respectively?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmConstruct solutions

When ant k is in node i and has constructed partialsolution sp, the probability of going to node j is:

pkij =

ταij ·η

βij∑

cij∈N(sp) ταij ·η

βij

if cij ∈ N(sp),

0 otherwise

I N(sp) is the set of feasible components

I α and β control the relative importance of pheromoneversus the heuristic information ηij .

What happens if α or β are 0 respectively?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmConstruct solutions

When ant k is in node i and has constructed partialsolution sp, the probability of going to node j is:

pkij =

ταij ·η

βij∑

cij∈N(sp) ταij ·η

βij

if cij ∈ N(sp),

0 otherwise

I N(sp) is the set of feasible components

I α and β control the relative importance of pheromoneversus the heuristic information ηij .

What happens if α or β are 0 respectively?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmConstruct solutions

When ant k is in node i and has constructed partialsolution sp, the probability of going to node j is:

pkij =

ταij ·η

βij∑

cij∈N(sp) ταij ·η

βij

if cij ∈ N(sp),

0 otherwise

I N(sp) is the set of feasible components

I α and β control the relative importance of pheromoneversus the heuristic information ηij .

What happens if α or β are 0 respectively?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmConstruct solutions

When ant k is in node i and has constructed partialsolution sp, the probability of going to node j is:

pkij =

ταij ·η

βij∑

cij∈N(sp) ταij ·η

βij

if cij ∈ N(sp),

0 otherwise

I N(sp) is the set of feasible components

I α and β control the relative importance of pheromoneversus the heuristic information ηij .

What happens if α or β are 0 respectively?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmConstruct solutions

When ant k is in node i and has constructed partialsolution sp, the probability of going to node j is:

pkij =

ταij ·η

βij∑

cij∈N(sp) ταij ·η

βij

if cij ∈ N(sp),

0 otherwise

I N(sp) is the set of feasible components

I α and β control the relative importance of pheromoneversus the heuristic information ηij .

What happens if α or β are 0 respectively?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmPheromone update

τij is the pheromone level on edge cij .

Global pheromone update:

τij ← (1− ρ) · τij

+m∑

k=1

∆τkij

I ρ is the evaporation rate

I ∆τkij is the amount of pheromone deposited by ant k

∆τkij =

Q/Lk if ant k used edge (i , j)0 otherwise

I Q is a constant.

I Lk is a value associated with ant k ’s solution candidate.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmPheromone update

τij is the pheromone level on edge cij .Global pheromone update:

τij ←

(1− ρ) · τij

+m∑

k=1

∆τkij

I ρ is the evaporation rate

I ∆τkij is the amount of pheromone deposited by ant k

∆τkij =

Q/Lk if ant k used edge (i , j)0 otherwise

I Q is a constant.

I Lk is a value associated with ant k ’s solution candidate.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmPheromone update

τij is the pheromone level on edge cij .Global pheromone update:

τij ← (1− ρ) · τij

+m∑

k=1

∆τkij

I ρ is the evaporation rate

I ∆τkij is the amount of pheromone deposited by ant k

∆τkij =

Q/Lk if ant k used edge (i , j)0 otherwise

I Q is a constant.

I Lk is a value associated with ant k ’s solution candidate.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmPheromone update

τij is the pheromone level on edge cij .Global pheromone update:

τij ← (1− ρ) · τij +m∑

k=1

∆τkij

I ρ is the evaporation rate

I ∆τkij is the amount of pheromone deposited by ant k

∆τkij =

Q/Lk if ant k used edge (i , j)0 otherwise

I Q is a constant.

I Lk is a value associated with ant k ’s solution candidate.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmPheromone update

τij is the pheromone level on edge cij .Global pheromone update:

τij ← (1− ρ) · τij +m∑

k=1

∆τkij

I ρ is the evaporation rate

I ∆τkij is the amount of pheromone deposited by ant k

∆τkij =

Q/Lk if ant k used edge (i , j)0 otherwise

I Q is a constant.

I Lk is a value associated with ant k ’s solution candidate.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmPheromone update

τij is the pheromone level on edge cij .Global pheromone update:

τij ← (1− ρ) · τij +m∑

k=1

∆τkij

I ρ is the evaporation rate

I ∆τkij is the amount of pheromone deposited by ant k

∆τkij =

Q/Lk if ant k used edge (i , j)

0 otherwise

I Q is a constant.

I Lk is a value associated with ant k ’s solution candidate.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmPheromone update

τij is the pheromone level on edge cij .Global pheromone update:

τij ← (1− ρ) · τij +m∑

k=1

∆τkij

I ρ is the evaporation rate

I ∆τkij is the amount of pheromone deposited by ant k

∆τkij =

Q/Lk if ant k used edge (i , j)0 otherwise

I Q is a constant.

I Lk is a value associated with ant k ’s solution candidate.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmPheromone update

τij is the pheromone level on edge cij .Global pheromone update:

τij ← (1− ρ) · τij +m∑

k=1

∆τkij

I ρ is the evaporation rate

I ∆τkij is the amount of pheromone deposited by ant k

∆τkij =

Q/Lk if ant k used edge (i , j)0 otherwise

I Q is a constant.

I Lk is a value associated with ant k ’s solution candidate.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant System AlgorithmPheromone update

τij is the pheromone level on edge cij .Global pheromone update:

τij ← (1− ρ) · τij +m∑

k=1

∆τkij

I ρ is the evaporation rate

I ∆τkij is the amount of pheromone deposited by ant k

∆τkij =

Q/Lk if ant k used edge (i , j)0 otherwise

I Q is a constant.

I Lk is a value associated with ant k ’s solution candidate.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Question 2

What would motivate some ants having greater influencethan others?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Outline

IntroductionHistory & Analogy

AlgorithmAnt System (AS)MAX −MIN Ant System (MMAS)Ant Colony System (ACS)

Break

Examples & SimulationsDouble Bridge ExperimentTravelling Salesman Application

ClassificationMetaheuristicSwarm Intelligence

Applications

Discussion

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail

andpheromone levels are bound.The pheromone update:

τij ←[(1− ρ) · τij + ∆τbest

ij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.

The pheromone update:

τij ←[(1− ρ) · τij + ∆τbest

ij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.The pheromone update:

τij ←

[(1− ρ) · τij + ∆τbest

ij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.The pheromone update:

τij ←

[

(1− ρ) · τij

+ ∆τbestij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.The pheromone update:

τij ←

[

(1− ρ) · τij + ∆τbestij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.The pheromone update:

τij ←[(1− ρ) · τij + ∆τbest

ij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.The pheromone update:

τij ←[(1− ρ) · τij + ∆τbest

ij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.The pheromone update:

τij ←[(1− ρ) · τij + ∆τbest

ij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,

b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.The pheromone update:

τij ←[(1− ρ) · τij + ∆τbest

ij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,

x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.The pheromone update:

τij ←[(1− ρ) · τij + ∆τbest

ij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.The pheromone update:

τij ←[(1− ρ) · τij + ∆τbest

ij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.The pheromone update:

τij ←[(1− ρ) · τij + ∆τbest

ij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,

0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

MAX −MIN Ant SystemPheromone update

Only the best ant updates the pheromone trail andpheromone levels are bound.The pheromone update:

τij ←[(1− ρ) · τij + ∆τbest

ij

]τmaxτmin

[x ]ab is defined as:

[x ]ab =

a if x > a,b if x < b,x otherwise

and

∆τbestij =

1/Lbest if (i , j) belongs to the best solution,0 otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Outline

IntroductionHistory & Analogy

AlgorithmAnt System (AS)MAX −MIN Ant System (MMAS)Ant Colony System (ACS)

Break

Examples & SimulationsDouble Bridge ExperimentTravelling Salesman Application

ClassificationMetaheuristicSwarm Intelligence

Applications

Discussion

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony System (ACS)Daemon Action and Pheromone update

All ants perform a local pheromone update after eachconstruction step.

Each ant applies it only to the last edgetraversed:

τij = (1− ϕ) · τij + ϕ · τ0,

I ϕ ∈ (0, 1) is the pheromone decay coefficient.

I τ0 is the initial value of the pheromone

Global (Offline) pheromone update:

τij ←

(1− ρ) · τij + ∆τbestij if (i , j) ∈ best solution,

τij otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony System (ACS)Daemon Action and Pheromone update

All ants perform a local pheromone update after eachconstruction step. Each ant applies it only to the last edgetraversed:

τij = (1− ϕ) · τij + ϕ · τ0,

I ϕ ∈ (0, 1) is the pheromone decay coefficient.

I τ0 is the initial value of the pheromone

Global (Offline) pheromone update:

τij ←

(1− ρ) · τij + ∆τbestij if (i , j) ∈ best solution,

τij otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony System (ACS)Daemon Action and Pheromone update

All ants perform a local pheromone update after eachconstruction step. Each ant applies it only to the last edgetraversed:

τij = (1− ϕ) · τij + ϕ · τ0,

I ϕ ∈ (0, 1) is the pheromone decay coefficient.

I τ0 is the initial value of the pheromone

Global (Offline) pheromone update:

τij ←

(1− ρ) · τij + ∆τbestij if (i , j) ∈ best solution,

τij otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony System (ACS)Daemon Action and Pheromone update

All ants perform a local pheromone update after eachconstruction step. Each ant applies it only to the last edgetraversed:

τij = (1− ϕ) · τij + ϕ · τ0,

I ϕ ∈ (0, 1) is the pheromone decay coefficient.

I τ0 is the initial value of the pheromone

Global (Offline) pheromone update:

τij ←

(1− ρ) · τij + ∆τbestij if (i , j) ∈ best solution,

τij otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony System (ACS)Daemon Action and Pheromone update

All ants perform a local pheromone update after eachconstruction step. Each ant applies it only to the last edgetraversed:

τij = (1− ϕ) · τij + ϕ · τ0,

I ϕ ∈ (0, 1) is the pheromone decay coefficient.

I τ0 is the initial value of the pheromone

Global (Offline) pheromone update:

τij ←

(1− ρ) · τij + ∆τbestij if (i , j) ∈ best solution,

τij otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony System (ACS)Daemon Action and Pheromone update

All ants perform a local pheromone update after eachconstruction step. Each ant applies it only to the last edgetraversed:

τij = (1− ϕ) · τij + ϕ · τ0,

I ϕ ∈ (0, 1) is the pheromone decay coefficient.

I τ0 is the initial value of the pheromone

Global (Offline) pheromone update:

τij ←

(1− ρ) · τij + ∆τbestij if (i , j) ∈ best solution,

τij otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony System (ACS)Daemon Action and Pheromone update

All ants perform a local pheromone update after eachconstruction step. Each ant applies it only to the last edgetraversed:

τij = (1− ϕ) · τij + ϕ · τ0,

I ϕ ∈ (0, 1) is the pheromone decay coefficient.

I τ0 is the initial value of the pheromone

Global (Offline) pheromone update:

τij ←

(1− ρ) · τij + ∆τbestij if (i , j) ∈ best solution,

τij otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony System (ACS)Daemon Action and Pheromone update

All ants perform a local pheromone update after eachconstruction step. Each ant applies it only to the last edgetraversed:

τij = (1− ϕ) · τij + ϕ · τ0,

I ϕ ∈ (0, 1) is the pheromone decay coefficient.

I τ0 is the initial value of the pheromone

Global (Offline) pheromone update:

τij ←

(1− ρ) · τij + ∆τbestij if (i , j) ∈ best solution,

τij otherwise

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

ACO AlgorithmsComparission

AS MMAS ACS heightConstruct Solutions

pkij =ταij ·η

βij∑

cij∈N(sp) ταij ·ηij

Daemon Actions

opt opt τij = (1− ϕ) · τij + ϕ · τ0

Update Pheromones

(1− ρ) · τij +∑m

k=1 ∆τkij (1− ρ) · τij + ∆τbestij

τmaxτmin

(1− ρ) · τij + ∆τbestij

I In general ACS produces better solutions than MMASin the early iterations, while in the latter iterationsMMAS performs better.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

ACO AlgorithmsComparission

AS MMAS ACS height

Construct Solutions

pkij =ταij ·η

βij∑

cij∈N(sp) ταij ·ηij

Daemon Actions

opt opt τij = (1− ϕ) · τij + ϕ · τ0

Update Pheromones

(1− ρ) · τij +∑m

k=1 ∆τkij (1− ρ) · τij + ∆τbestij

τmaxτmin

(1− ρ) · τij + ∆τbestij

I In general ACS produces better solutions than MMASin the early iterations, while in the latter iterationsMMAS performs better.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

ACO AlgorithmsComparission

AS MMAS ACS heightConstruct Solutions

pkij =ταij ·η

βij∑

cij∈N(sp) ταij ·ηij

Daemon Actions

opt opt τij = (1− ϕ) · τij + ϕ · τ0

Update Pheromones

(1− ρ) · τij +∑m

k=1 ∆τkij (1− ρ) · τij + ∆τbestij

τmaxτmin

(1− ρ) · τij + ∆τbestij

I In general ACS produces better solutions than MMASin the early iterations, while in the latter iterationsMMAS performs better.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

ACO AlgorithmsComparission

AS MMAS ACS heightConstruct Solutions

pkij =ταij ·η

βij∑

cij∈N(sp) ταij ·ηij

Daemon Actions

opt opt τij = (1− ϕ) · τij + ϕ · τ0

Update Pheromones

(1− ρ) · τij +∑m

k=1 ∆τkij (1− ρ) · τij + ∆τbestij

τmaxτmin

(1− ρ) · τij + ∆τbestij

I In general ACS produces better solutions than MMASin the early iterations, while in the latter iterationsMMAS performs better.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

ACO AlgorithmsComparission

AS MMAS ACS heightConstruct Solutions

pkij =ταij ·η

βij∑

cij∈N(sp) ταij ·ηij

Daemon Actions

opt opt τij = (1− ϕ) · τij + ϕ · τ0

Update Pheromones

(1− ρ) · τij +∑m

k=1 ∆τkij (1− ρ) · τij + ∆τbestij

τmaxτmin

(1− ρ) · τij + ∆τbestij

I In general ACS produces better solutions than MMASin the early iterations, while in the latter iterationsMMAS performs better.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

ACO AlgorithmsComparission

AS MMAS ACS heightConstruct Solutions

pkij =ταij ·η

βij∑

cij∈N(sp) ταij ·ηij

Daemon Actions

opt opt τij = (1− ϕ) · τij + ϕ · τ0

Update Pheromones

(1− ρ) · τij +∑m

k=1 ∆τkij (1− ρ) · τij + ∆τbestij

τmaxτmin

(1− ρ) · τij + ∆τbestij

I In general ACS produces better solutions than MMASin the early iterations, while in the latter iterationsMMAS performs better.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Break

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Outline

IntroductionHistory & Analogy

AlgorithmAnt System (AS)MAX −MIN Ant System (MMAS)Ant Colony System (ACS)

Break

Examples & SimulationsDouble Bridge ExperimentTravelling Salesman Application

ClassificationMetaheuristicSwarm Intelligence

Applications

Discussion

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony OptimizationDouble bridge experiment

I Ants will move from nest to source and back

I Pheromone is dropped along the way

I After a suficient number of iterations, the colony willconverge to the shortest path

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony OptimizationDouble bridge experiment

I Ants will move from nest to source and back

I Pheromone is dropped along the way

I After a suficient number of iterations, the colony willconverge to the shortest path

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony OptimizationDouble bridge experiment

I Ants will move from nest to source and back

I Pheromone is dropped along the way

I After a suficient number of iterations, the colony willconverge to the shortest path

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony OptimizationDouble bridge experiment

I Ants will move from nest to source and back

I Pheromone is dropped along the way

I After a suficient number of iterations, the colony willconverge to the shortest path

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony OptimizationDouble bridge experiment

I Ants will move from nest to source and back

I Pheromone is dropped along the way

I After a suficient number of iterations, the colony willconverge to the shortest path

How will the ants behave if both paths have equal lenght?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Outline

IntroductionHistory & Analogy

AlgorithmAnt System (AS)MAX −MIN Ant System (MMAS)Ant Colony System (ACS)

Break

Examples & SimulationsDouble Bridge ExperimentTravelling Salesman Application

ClassificationMetaheuristicSwarm Intelligence

Applications

Discussion

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony OptimizationTravelling Salesman Problem (TSP)

Given a list of cities and the distances between each pair ofcities, what is the shortest possible route that visits each

city exactly once and returns to the origin city?

I Ant System (AS)I Some additional rules and recap:

I Each city can only be visited once

I A distant city is less likely to be chosenI Edges with stronger pheromone trail are more likely

to be selectedI More pheromones are deposited for short journeysI Trails are evaporated after each iteration

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony OptimizationTravelling Salesman Problem (TSP)

Given a list of cities and the distances between each pair ofcities, what is the shortest possible route that visits each

city exactly once and returns to the origin city?

I Ant System (AS)I Some additional rules and recap:

I Each city can only be visited onceI A distant city is less likely to be chosen

I Edges with stronger pheromone trail are more likelyto be selected

I More pheromones are deposited for short journeysI Trails are evaporated after each iteration

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony OptimizationTravelling Salesman Problem (TSP)

Given a list of cities and the distances between each pair ofcities, what is the shortest possible route that visits each

city exactly once and returns to the origin city?

I Ant System (AS)I Some additional rules and recap:

I Each city can only be visited onceI A distant city is less likely to be chosenI Edges with stronger pheromone trail are more likely

to be selected

I More pheromones are deposited for short journeysI Trails are evaporated after each iteration

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony OptimizationTravelling Salesman Problem (TSP)

Given a list of cities and the distances between each pair ofcities, what is the shortest possible route that visits each

city exactly once and returns to the origin city?

I Ant System (AS)I Some additional rules and recap:

I Each city can only be visited onceI A distant city is less likely to be chosenI Edges with stronger pheromone trail are more likely

to be selectedI More pheromones are deposited for short journeys

I Trails are evaporated after each iteration

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Ant Colony OptimizationTravelling Salesman Problem (TSP)

Given a list of cities and the distances between each pair ofcities, what is the shortest possible route that visits each

city exactly once and returns to the origin city?

I Ant System (AS)I Some additional rules and recap:

I Each city can only be visited onceI A distant city is less likely to be chosenI Edges with stronger pheromone trail are more likely

to be selectedI More pheromones are deposited for short journeysI Trails are evaporated after each iteration

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Outline

IntroductionHistory & Analogy

AlgorithmAnt System (AS)MAX −MIN Ant System (MMAS)Ant Colony System (ACS)

Break

Examples & SimulationsDouble Bridge ExperimentTravelling Salesman Application

ClassificationMetaheuristicSwarm Intelligence

Applications

Discussion

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Classification 1Why in MAA?

Why include ACO in Multi Agent Learning?

I Can be used to solve similar problems, under certainconditions

I Is in sense multi agent (swarm) based, and showslearning behaviour.

I Is very popular, due to its nice analogy, and wellresearched.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Classification 1Why in MAA?

Why include ACO in Multi Agent Learning?

I Can be used to solve similar problems, under certainconditions

I Is in sense multi agent (swarm) based, and showslearning behaviour.

I Is very popular, due to its nice analogy, and wellresearched.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Classification 1Why in MAA?

Why include ACO in Multi Agent Learning?

I Can be used to solve similar problems, under certainconditions

I Is in sense multi agent (swarm) based, and showslearning behaviour.

I Is very popular, due to its nice analogy, and wellresearched.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Classification 1Why in MAA?

Why include ACO in Multi Agent Learning?

I Can be used to solve similar problems, under certainconditions

I Is in sense multi agent (swarm) based, and showslearning behaviour.

I Is very popular, due to its nice analogy, and wellresearched.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Classification 2

Ant Colony Optimization (ACO) is a metaheuristic forsolving hard combinatorial optimization problems

I An heuristic algorithm trades optimality, completeness,accuracy and/or precision for speed.

I A metaheuristic is a top-level general strategy whichguides other heuristics to search for feasible solutions indomains where the task is hard.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Classification 2

Ant Colony Optimization (ACO) is a metaheuristic forsolving hard combinatorial optimization problems

I An heuristic algorithm trades optimality, completeness,accuracy and/or precision for speed.

I A metaheuristic is a top-level general strategy whichguides other heuristics to search for feasible solutions indomains where the task is hard.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Classification 2

Ant Colony Optimization (ACO) is a metaheuristic forsolving hard combinatorial optimization problems

I An heuristic algorithm trades optimality, completeness,accuracy and/or precision for speed.

I A metaheuristic is a top-level general strategy whichguides other heuristics to search for feasible solutions indomains where the task is hard.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Metaheuristics

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Game TheoryACO purpose in games

I Ant colony optimization alone does not seem to beparticularly useful for use in games

I Many iterations (or like with EA, evolutions) will beneeded to optimize strategies

I We know that a better strategy (better than a previoussolution) will be found

I There is no guarantee that a winning strategy will befound, within the time constraints

I Despite this, broader, more domain-specificimplementations, have shown promising results (see thetetris paper)

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Game TheoryACO purpose in games

I Ant colony optimization alone does not seem to beparticularly useful for use in games

I Many iterations (or like with EA, evolutions) will beneeded to optimize strategies

I We know that a better strategy (better than a previoussolution) will be found

I There is no guarantee that a winning strategy will befound, within the time constraints

I Despite this, broader, more domain-specificimplementations, have shown promising results (see thetetris paper)

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Game TheoryACO purpose in games

I Ant colony optimization alone does not seem to beparticularly useful for use in games

I Many iterations (or like with EA, evolutions) will beneeded to optimize strategies

I We know that a better strategy (better than a previoussolution) will be found

I There is no guarantee that a winning strategy will befound, within the time constraints

I Despite this, broader, more domain-specificimplementations, have shown promising results (see thetetris paper)

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Game TheoryACO purpose in games

I Ant colony optimization alone does not seem to beparticularly useful for use in games

I Many iterations (or like with EA, evolutions) will beneeded to optimize strategies

I We know that a better strategy (better than a previoussolution) will be found

I There is no guarantee that a winning strategy will befound, within the time constraints

I Despite this, broader, more domain-specificimplementations, have shown promising results (see thetetris paper)

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Game TheoryACO purpose in games

I Ant colony optimization alone does not seem to beparticularly useful for use in games

I Many iterations (or like with EA, evolutions) will beneeded to optimize strategies

I We know that a better strategy (better than a previoussolution) will be found

I There is no guarantee that a winning strategy will befound, within the time constraints

I Despite this, broader, more domain-specificimplementations, have shown promising results (see thetetris paper)

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Outline

IntroductionHistory & Analogy

AlgorithmAnt System (AS)MAX −MIN Ant System (MMAS)Ant Colony System (ACS)

Break

Examples & SimulationsDouble Bridge ExperimentTravelling Salesman Application

ClassificationMetaheuristicSwarm Intelligence

Applications

Discussion

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Classification 3

Ant Colony Optimization (ACO) belongs to the SwarmIntelligence discipline.

I Swarm intelligence ... deals with natural and artificialsystems composed of many individuals that coordinateusing decentralized control and self-organization.

I Informal: In principle, it should be a multi-agent systemthat has self-organized behaviour that shows someintelligent behaviour.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Classification 3

Ant Colony Optimization (ACO) belongs to the SwarmIntelligence discipline.

I Swarm intelligence ... deals with natural and artificialsystems composed of many individuals that coordinateusing decentralized control and self-organization.

I Informal: In principle, it should be a multi-agent systemthat has self-organized behaviour that shows someintelligent behaviour.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Classification 3

Ant Colony Optimization (ACO) belongs to the SwarmIntelligence discipline.

I Swarm intelligence ... deals with natural and artificialsystems composed of many individuals that coordinateusing decentralized control and self-organization.

I Informal: In principle, it should be a multi-agent systemthat has self-organized behaviour that shows someintelligent behaviour.

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Swarm intelligence

Advantages:

I Adaptable

I Evolvable

I Resilient

Disadvantages:

I Non-optimal

I Uncontrollable

I Unpredictable

I Non-understandable

I Non-immediate

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Swarm intelligence

Advantages:

I Adaptable

I Evolvable

I Resilient

Disadvantages:

I Non-optimal

I Uncontrollable

I Unpredictable

I Non-understandable

I Non-immediate

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Swarm intelligence

Advantages:

I Adaptable

I Evolvable

I Resilient

Disadvantages:

I Non-optimal

I Uncontrollable

I Unpredictable

I Non-understandable

I Non-immediate

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Swarm intelligence

Advantages:

I Adaptable

I Evolvable

I Resilient

Disadvantages:

I Non-optimal

I Uncontrollable

I Unpredictable

I Non-understandable

I Non-immediate

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Swarm intelligence

Advantages:

I Adaptable

I Evolvable

I Resilient

Disadvantages:

I Non-optimal

I Uncontrollable

I Unpredictable

I Non-understandable

I Non-immediate

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Swarm intelligence

Advantages:

I Adaptable

I Evolvable

I Resilient

Disadvantages:

I Non-optimal

I Uncontrollable

I Unpredictable

I Non-understandable

I Non-immediate

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Swarm intelligence

Advantages:

I Adaptable

I Evolvable

I Resilient

Disadvantages:

I Non-optimal

I Uncontrollable

I Unpredictable

I Non-understandable

I Non-immediate

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Swarm intelligence

Advantages:

I Adaptable

I Evolvable

I Resilient

Disadvantages:

I Non-optimal

I Uncontrollable

I Unpredictable

I Non-understandable

I Non-immediate

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Swarm intelligence

Advantages:

I Adaptable

I Evolvable

I Resilient

Disadvantages:

I Non-optimal

I Uncontrollable

I Unpredictable

I Non-understandable

I Non-immediate

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Applications

I Travelling salesman problem (Ant system)

I Scheduling problem

I Vehicle routing problem

I Protein folding

I Data mining

I Extensions:

MMAS, ACSElitist ant system The global solution transmits

pheromones along with the antsRank-based ant system Pheromone levels according to

weighted solutionsContinuous orthogonal ant colonyRecursive Ant Colony Optimization Nested ant systems

to increase precision of output

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Applications

I Travelling salesman problem (Ant system)

I Scheduling problem

I Vehicle routing problem

I Protein folding

I Data mining

I Extensions:

MMAS, ACSElitist ant system The global solution transmits

pheromones along with the antsRank-based ant system Pheromone levels according to

weighted solutionsContinuous orthogonal ant colonyRecursive Ant Colony Optimization Nested ant systems

to increase precision of output

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Applications

I Travelling salesman problem (Ant system)

I Scheduling problem

I Vehicle routing problem

I Protein folding

I Data mining

I Extensions:

MMAS, ACSElitist ant system The global solution transmits

pheromones along with the antsRank-based ant system Pheromone levels according to

weighted solutionsContinuous orthogonal ant colonyRecursive Ant Colony Optimization Nested ant systems

to increase precision of output

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Applications

I Travelling salesman problem (Ant system)

I Scheduling problem

I Vehicle routing problem

I Protein folding

I Data mining

I Extensions:

MMAS, ACSElitist ant system The global solution transmits

pheromones along with the antsRank-based ant system Pheromone levels according to

weighted solutionsContinuous orthogonal ant colonyRecursive Ant Colony Optimization Nested ant systems

to increase precision of output

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Applications

I Travelling salesman problem (Ant system)

I Scheduling problem

I Vehicle routing problem

I Protein folding

I Data mining

I Extensions:

MMAS, ACSElitist ant system The global solution transmits

pheromones along with the antsRank-based ant system Pheromone levels according to

weighted solutionsContinuous orthogonal ant colonyRecursive Ant Colony Optimization Nested ant systems

to increase precision of output

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Applications

I Travelling salesman problem (Ant system)

I Scheduling problem

I Vehicle routing problem

I Protein folding

I Data mining

I Extensions:

MMAS, ACSElitist ant system The global solution transmits

pheromones along with the antsRank-based ant system Pheromone levels according to

weighted solutionsContinuous orthogonal ant colonyRecursive Ant Colony Optimization Nested ant systems

to increase precision of output

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Applications

I Travelling salesman problem (Ant system)

I Scheduling problem

I Vehicle routing problem

I Protein folding

I Data mining

I Extensions:

MMAS, ACS

Elitist ant system The global solution transmitspheromones along with the ants

Rank-based ant system Pheromone levels according toweighted solutions

Continuous orthogonal ant colonyRecursive Ant Colony Optimization Nested ant systems

to increase precision of output

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Applications

I Travelling salesman problem (Ant system)

I Scheduling problem

I Vehicle routing problem

I Protein folding

I Data mining

I Extensions:

MMAS, ACSElitist ant system The global solution transmits

pheromones along with the ants

Rank-based ant system Pheromone levels according toweighted solutions

Continuous orthogonal ant colonyRecursive Ant Colony Optimization Nested ant systems

to increase precision of output

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Applications

I Travelling salesman problem (Ant system)

I Scheduling problem

I Vehicle routing problem

I Protein folding

I Data mining

I Extensions:

MMAS, ACSElitist ant system The global solution transmits

pheromones along with the antsRank-based ant system Pheromone levels according to

weighted solutions

Continuous orthogonal ant colonyRecursive Ant Colony Optimization Nested ant systems

to increase precision of output

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Applications

I Travelling salesman problem (Ant system)

I Scheduling problem

I Vehicle routing problem

I Protein folding

I Data mining

I Extensions:

MMAS, ACSElitist ant system The global solution transmits

pheromones along with the antsRank-based ant system Pheromone levels according to

weighted solutionsContinuous orthogonal ant colony

Recursive Ant Colony Optimization Nested ant systemsto increase precision of output

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Applications

I Travelling salesman problem (Ant system)

I Scheduling problem

I Vehicle routing problem

I Protein folding

I Data mining

I Extensions:

MMAS, ACSElitist ant system The global solution transmits

pheromones along with the antsRank-based ant system Pheromone levels according to

weighted solutionsContinuous orthogonal ant colonyRecursive Ant Colony Optimization Nested ant systems

to increase precision of output

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Additional reading

I Shiven Sharma, Ziad Kobti, and Scott Goodwin. 2008.”General Game Playing with Ants”

I Pablo Romero, Franco Robledo, Pablo Rodrguez-Bocca,Daro Padula, and Mara Elisa Bertinat. 2010. ”Acooperative network game efficiently solved via an antcolony optimization approach”

I Xingguo Chen, Hao Wang, Weiwei Wang, YinghuanShi, and Yang Gao. 2009. ”Apply ant colonyoptimization to Tetris”

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Additional reading

I Shiven Sharma, Ziad Kobti, and Scott Goodwin. 2008.”General Game Playing with Ants”

I Pablo Romero, Franco Robledo, Pablo Rodrguez-Bocca,Daro Padula, and Mara Elisa Bertinat. 2010. ”Acooperative network game efficiently solved via an antcolony optimization approach”

I Xingguo Chen, Hao Wang, Weiwei Wang, YinghuanShi, and Yang Gao. 2009. ”Apply ant colonyoptimization to Tetris”

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Additional reading

I Shiven Sharma, Ziad Kobti, and Scott Goodwin. 2008.”General Game Playing with Ants”

I Pablo Romero, Franco Robledo, Pablo Rodrguez-Bocca,Daro Padula, and Mara Elisa Bertinat. 2010. ”Acooperative network game efficiently solved via an antcolony optimization approach”

I Xingguo Chen, Hao Wang, Weiwei Wang, YinghuanShi, and Yang Gao. 2009. ”Apply ant colonyoptimization to Tetris”

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Additional reading

I Shiven Sharma, Ziad Kobti, and Scott Goodwin. 2008.”General Game Playing with Ants”

I Pablo Romero, Franco Robledo, Pablo Rodrguez-Bocca,Daro Padula, and Mara Elisa Bertinat. 2010. ”Acooperative network game efficiently solved via an antcolony optimization approach”

I Xingguo Chen, Hao Wang, Weiwei Wang, YinghuanShi, and Yang Gao. 2009. ”Apply ant colonyoptimization to Tetris”

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Discussion

I Do (artificial) ants learn?

I Additional extensions seem to get further away from theoriginal analogy, should we stop naming these thingsants?

I Can (artificial) ant colonies be considered intelligentsystems?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Discussion

I Do (artificial) ants learn?

I Additional extensions seem to get further away from theoriginal analogy, should we stop naming these thingsants?

I Can (artificial) ant colonies be considered intelligentsystems?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Discussion

I Do (artificial) ants learn?

I Additional extensions seem to get further away from theoriginal analogy, should we stop naming these thingsants?

I Can (artificial) ant colonies be considered intelligentsystems?

Ant ColonyOptimization

Daniel Hallin,Marlon Etheredge

Introduction

History & Analogy

Algorithm

Ant System (AS)

MAX −MINAnt System(MMAS)

Ant Colony System(ACS)

Break

Examples &Simulations

Double BridgeExperiment

Travelling SalesmanApplication

Classification

Metaheuristic

Swarm Intelligence

Applications

Additional reading

Discussion

Discussion

I Do (artificial) ants learn?

I Additional extensions seem to get further away from theoriginal analogy, should we stop naming these thingsants?

I Can (artificial) ant colonies be considered intelligentsystems?