SlideShare a Scribd company logo
1 of 28
Metaheuristic Algorithms for
Optimization
Francisco de Melo jr
Problem
Introduction
Research Question
Meta heuristics
Comparative evaluation
Conclusion
References
Outline
Problem
Generate data to test a program
<non linear function>
Solution
Consider the problem a minimization vs maximization problem
We can apply Simplex! (From Linear programing)
Solution
Simplex!
From Linear programing
Well, not quite
Research Question
How to optimize the generation?
Compare the several way to generate the data?
Introduction
Meta heuristic algorithms*
To solve the optimization problem (1), efficient search or optimization algorithms are needed. There are many optimization algorithms
which can be classified in many ways, depending on the focus and characteristics.
Name controversy*
Meta-heuristics
Components
Two major components of any metaheuristic algorithms are: intensification and diversification, or exploitation and
exploration (Blum and Roli, 2003).
Meta heuristic I
Particle Swarm Optimization
PSO searches the space of an objective function by adjusting the trajectories of individual agents, called particles.
Each particle traces a piecewise path which can be modelled as a time-dependent positional vector.
The movement of a swarming particle consists of two major components: a stochastic component and a deterministic component.
Each particle is attracted toward the position of the current global best g∗ and its own best known location x∗i , while exhibiting at the
same time a tendency to move randomly.
Meta heuristic I
Particles
Meta heuristic I
Algorithm
for each particle i = 1, ..., S do
Initialize the particle's position with a uniformly distributed random vector: xi ~ U(blo, bup)
Initialize the particle's best known position to its initial position: pi ← xi
if f(pi) < f(g) then
update the swarm's best known position: g ← pi
Initialize the particle's velocity: vi ~ U(-|bup-blo|, |bup-blo|)
while a termination criterion is not met do:
for each particle i = 1, ..., S do
for each dimension d = 1, ..., n do
Pick random numbers: rp, rg ~ U(0,1)
Update the particle's velocity: vi,d ← ω vi,d + φp rp (pi,d-xi,d) + φg rg (gd-xi,d)
Update the particle's position: xi ← xi + vi
if f(xi) < f(pi) then
Update the particle's best known position: pi ← xi
if f(pi) < f(g) then
Update the swarm's best known position: g ← pi
Meta heuristic I
Demo
Meta heuristic I
After finding the two best values, the particle updates its velocity and
positions with following equation (a) and (b).
Fitness function update
v[] = v[] + c1 * rand() * (pbest[] - present[]) + c2 * rand() * (gbest[] - present[]) (a)
present[] = persent[] + v[] (b)
Five principles of swarm intelligence
First is the proximity principle: the population should be able to carry out simple space and time
computations.
Second is the quality principle: the population should be able to respond to quality factors in the
environment.
Third is the principle of diverse response: the population should not commit its activities along excessively
narrow channels.
Fourth is the principle of stability: the population should not change its mode of behavior every time the
environment changes.
Fifth is the 1946 principle of adaptability: the population must be able to change behavior mode when it’s
worth the computational price.
Meta heuristic II
Bee Colony Optimization Metaheuristic (BCO)
Meta heuristic II
Agents (bees) collaborate in order to solve a difficult problem together
Problems that can be applied:
● Traveling Salesman Problem (TSP)
● Quadratic Assignment Problem (QAP)
● Binary Knapsack Problem
Meta heuristic II
Bees
During the search process, artificial bees communicate directly.
Each artificial bee makes a series of local moves, and in this way incrementally constructs
a solution of the problem.
Bees are adding solution components to the current partial solution until they create one or
more feasible solutions.
The search process is composed of iteration
Meta heuristic II
Algorithms Pseudocode for the standard bees algorithm[2]
1 for i=1,…,ns
i scout[i]=Initialise_scout()
ii flower_patch[i]=Initialise_flower_patch(scout[i])
2 do until stopping_condition=TRUE
i Recruitment()
ii for i =1,...,nb
1 flower_patch[i]=Local_search(flower_patch[i])
2 flower_patch[i]=Site_abandonment(flower_patch[i])
3 flower_patch[i]=Neighbourhood_shrinking(flower_patch[i])
iii for i = nb,...,ns
1 flower_patch[i]=Global_search(flower_patch[i])}
Meta heuristic II Traveling Salesman Problem
Meta heuristic II
Demo
Meta heuristic III
Ant Colony
Optimization
Meta heuristic III
Ant Colony Optimization - ACO
It is a probabilistic technique for solving computational problems which can be
reduced to finding good paths through graphs.
Meta heuristic IV
Cuckoo Search
Cuckoos are fascinating birds, not only because of the beautiful sounds they make, but also because of their aggressive reproduction
strategy. Some species named ani and Guira lay their eggs in communal nests, though they may remove others' eggs to increase the
hatching probability of their own eggs.
Quite a number of species engage in the mandatory brood parasitism by laying their eggs in the nests of other host birds (often other
species).
Cuckoo search (CS) is one of the latest nature-inspired metaheuristic algorithms, developed by Xin-She Yang and Suash Deb in 2009.
Comparative evaluation
CS is based on the brood parasitism of some cuckoo species (Yang and Deb 2009). In addition, this algorithm is enhanced by the so-
called Lévy flights, rather than by simple isotropic random walks (Pavlyukevich 2007). Recent studies show that CS is potentially far
more efficient than PSO and genetic algorithms (Yang and Deb 2010).
Summary
- GA and SA are not considered swarm methods
- Thousands of algorithms with Swarm optimization methods
- Each particle is a solution
- It is not guaranteed to find the best solution
Conclusion
- Metaheuristic vs heuristic
- “Standard” metaheuristic
- CS and recent developments
- Several other techniques
References
Blum and Roli, 2003
Yang and Deb 2009
Pavlyukevich 2007
Fred Glover in the 1970s
James McCaffrey from Microsoft Research
Contact
Francisco de Melo
francisco.melo.jr@gmail.com

More Related Content

What's hot

Particle swarm optimization
Particle swarm optimizationParticle swarm optimization
Particle swarm optimization
Hanya Mohammed
 
Particle Swarm Optimization
Particle Swarm OptimizationParticle Swarm Optimization
Particle Swarm Optimization
Stelios Petrakis
 
Particle Swarm Optimization
Particle Swarm OptimizationParticle Swarm Optimization
Particle Swarm Optimization
QasimRehman
 

What's hot (20)

An Introduction To Applied Evolutionary Meta Heuristics
An Introduction To Applied Evolutionary Meta HeuristicsAn Introduction To Applied Evolutionary Meta Heuristics
An Introduction To Applied Evolutionary Meta Heuristics
 
Optimization and particle swarm optimization (O & PSO)
Optimization and particle swarm optimization (O & PSO) Optimization and particle swarm optimization (O & PSO)
Optimization and particle swarm optimization (O & PSO)
 
Particle Swarm Optimization: The Algorithm and Its Applications
Particle Swarm Optimization: The Algorithm and Its ApplicationsParticle Swarm Optimization: The Algorithm and Its Applications
Particle Swarm Optimization: The Algorithm and Its Applications
 
Particle swarm optimization
Particle swarm optimizationParticle swarm optimization
Particle swarm optimization
 
Particle Swarm Optimization Matlab code Using 50, 5000 Swarms
Particle Swarm Optimization Matlab code Using 50, 5000 SwarmsParticle Swarm Optimization Matlab code Using 50, 5000 Swarms
Particle Swarm Optimization Matlab code Using 50, 5000 Swarms
 
Machine Learning Tools and Particle Swarm Optimization for Content-Based Sear...
Machine Learning Tools and Particle Swarm Optimization for Content-Based Sear...Machine Learning Tools and Particle Swarm Optimization for Content-Based Sear...
Machine Learning Tools and Particle Swarm Optimization for Content-Based Sear...
 
Particle swarm optimization on pacman game problem solving
Particle swarm optimization on pacman game problem solvingParticle swarm optimization on pacman game problem solving
Particle swarm optimization on pacman game problem solving
 
Particle swarm optimization
Particle swarm optimizationParticle swarm optimization
Particle swarm optimization
 
Whale optimizatio algorithm
Whale optimizatio algorithmWhale optimizatio algorithm
Whale optimizatio algorithm
 
Particle Swarm Optimization by Rajorshi Mukherjee
Particle Swarm Optimization by Rajorshi MukherjeeParticle Swarm Optimization by Rajorshi Mukherjee
Particle Swarm Optimization by Rajorshi Mukherjee
 
nature inspired algorithms
nature inspired algorithmsnature inspired algorithms
nature inspired algorithms
 
Particle Swarm Optimization
Particle Swarm OptimizationParticle Swarm Optimization
Particle Swarm Optimization
 
Grasshopper optimization algorithm
Grasshopper optimization algorithmGrasshopper optimization algorithm
Grasshopper optimization algorithm
 
Estimating Species Divergence Times in RevBayes – iEvoBio 2014
Estimating Species Divergence Times in RevBayes – iEvoBio 2014Estimating Species Divergence Times in RevBayes – iEvoBio 2014
Estimating Species Divergence Times in RevBayes – iEvoBio 2014
 
Particle Swarm Optimization
Particle Swarm OptimizationParticle Swarm Optimization
Particle Swarm Optimization
 
Particle swarm optimization
Particle swarm optimizationParticle swarm optimization
Particle swarm optimization
 
An Introduction to RevBayes and Graphical Models
An Introduction to RevBayes and Graphical ModelsAn Introduction to RevBayes and Graphical Models
An Introduction to RevBayes and Graphical Models
 
A new hybrid particle swarm optimization with variable neighborhood search fo...
A new hybrid particle swarm optimization with variable neighborhood search fo...A new hybrid particle swarm optimization with variable neighborhood search fo...
A new hybrid particle swarm optimization with variable neighborhood search fo...
 
Ant Colony Optimization: The Algorithm and Its Applications
Ant Colony Optimization: The Algorithm and Its ApplicationsAnt Colony Optimization: The Algorithm and Its Applications
Ant Colony Optimization: The Algorithm and Its Applications
 
Particle Swarm Optimization
Particle Swarm OptimizationParticle Swarm Optimization
Particle Swarm Optimization
 

Similar to Metaheuristics for software testing

Swarm intelligence pso and aco
Swarm intelligence pso and acoSwarm intelligence pso and aco
Swarm intelligence pso and aco
satish561
 

Similar to Metaheuristics for software testing (20)

Pso notes
Pso notesPso notes
Pso notes
 
Swarm intelligence pso and aco
Swarm intelligence pso and acoSwarm intelligence pso and aco
Swarm intelligence pso and aco
 
DriP PSO- A fast and inexpensive PSO for drifting problem spaces
DriP PSO- A fast and inexpensive PSO for drifting problem spacesDriP PSO- A fast and inexpensive PSO for drifting problem spaces
DriP PSO- A fast and inexpensive PSO for drifting problem spaces
 
swarm pso and gray wolf Optimization.pdf
swarm pso and gray wolf Optimization.pdfswarm pso and gray wolf Optimization.pdf
swarm pso and gray wolf Optimization.pdf
 
Metaheuristic Algorithms: A Critical Analysis
Metaheuristic Algorithms: A Critical AnalysisMetaheuristic Algorithms: A Critical Analysis
Metaheuristic Algorithms: A Critical Analysis
 
Particle swarm optimization
Particle swarm optimizationParticle swarm optimization
Particle swarm optimization
 
PSO-ACO-Presentation.pptx
PSO-ACO-Presentation.pptxPSO-ACO-Presentation.pptx
PSO-ACO-Presentation.pptx
 
A REVIEW OF PARTICLE SWARM OPTIMIZATION (PSO) ALGORITHM
A REVIEW OF PARTICLE SWARM OPTIMIZATION (PSO) ALGORITHMA REVIEW OF PARTICLE SWARM OPTIMIZATION (PSO) ALGORITHM
A REVIEW OF PARTICLE SWARM OPTIMIZATION (PSO) ALGORITHM
 
A Fast and Inexpensive Particle Swarm Optimization for Drifting Problem-Spaces
A Fast and Inexpensive Particle Swarm Optimization for Drifting Problem-SpacesA Fast and Inexpensive Particle Swarm Optimization for Drifting Problem-Spaces
A Fast and Inexpensive Particle Swarm Optimization for Drifting Problem-Spaces
 
Pso kota baru parahyangan 2017
Pso kota baru parahyangan 2017Pso kota baru parahyangan 2017
Pso kota baru parahyangan 2017
 
Enhanced abc algo for tsp
Enhanced abc algo for tspEnhanced abc algo for tsp
Enhanced abc algo for tsp
 
TEXT FEUTURE SELECTION USING PARTICLE SWARM OPTIMIZATION (PSO)
TEXT FEUTURE SELECTION  USING PARTICLE SWARM OPTIMIZATION (PSO)TEXT FEUTURE SELECTION  USING PARTICLE SWARM OPTIMIZATION (PSO)
TEXT FEUTURE SELECTION USING PARTICLE SWARM OPTIMIZATION (PSO)
 
SI and PSO --Machine Learning
SI and PSO --Machine Learning SI and PSO --Machine Learning
SI and PSO --Machine Learning
 
Two-Stage Eagle Strategy with Differential Evolution
Two-Stage Eagle Strategy with Differential EvolutionTwo-Stage Eagle Strategy with Differential Evolution
Two-Stage Eagle Strategy with Differential Evolution
 
Master of Science Thesis Defense - Souma (FIU)
Master of Science Thesis Defense - Souma (FIU)Master of Science Thesis Defense - Souma (FIU)
Master of Science Thesis Defense - Souma (FIU)
 
Eagle Strategy Using Levy Walk and Firefly Algorithms For Stochastic Optimiza...
Eagle Strategy Using Levy Walk and Firefly Algorithms For Stochastic Optimiza...Eagle Strategy Using Levy Walk and Firefly Algorithms For Stochastic Optimiza...
Eagle Strategy Using Levy Walk and Firefly Algorithms For Stochastic Optimiza...
 
Engineering Optimisation by Cuckoo Search
Engineering Optimisation by Cuckoo SearchEngineering Optimisation by Cuckoo Search
Engineering Optimisation by Cuckoo Search
 
AN IMPROVED MULTIMODAL PSO METHOD BASED ON ELECTROSTATIC INTERACTION USING NN...
AN IMPROVED MULTIMODAL PSO METHOD BASED ON ELECTROSTATIC INTERACTION USING NN...AN IMPROVED MULTIMODAL PSO METHOD BASED ON ELECTROSTATIC INTERACTION USING NN...
AN IMPROVED MULTIMODAL PSO METHOD BASED ON ELECTROSTATIC INTERACTION USING NN...
 
International Journal of Engineering Research and Development (IJERD)
International Journal of Engineering Research and Development (IJERD)International Journal of Engineering Research and Development (IJERD)
International Journal of Engineering Research and Development (IJERD)
 
UNIT-5 Optimization (Part-1).ppt
UNIT-5 Optimization (Part-1).pptUNIT-5 Optimization (Part-1).ppt
UNIT-5 Optimization (Part-1).ppt
 

More from Francisco de Melo Jr

More from Francisco de Melo Jr (12)

Presentation infonuagique/ cloud computing presentation
Presentation infonuagique/ cloud computing presentationPresentation infonuagique/ cloud computing presentation
Presentation infonuagique/ cloud computing presentation
 
Nutri App
Nutri AppNutri App
Nutri App
 
NeuroGames - TCC Mackenzie Univ
NeuroGames - TCC Mackenzie UnivNeuroGames - TCC Mackenzie Univ
NeuroGames - TCC Mackenzie Univ
 
Honour Thesis Gabriel Alabarse - TCC Anhembi Morumbi
Honour Thesis Gabriel Alabarse - TCC Anhembi MorumbiHonour Thesis Gabriel Alabarse - TCC Anhembi Morumbi
Honour Thesis Gabriel Alabarse - TCC Anhembi Morumbi
 
Automata research developed at Saint Mary's 2014
Automata research developed at Saint Mary's 2014Automata research developed at Saint Mary's 2014
Automata research developed at Saint Mary's 2014
 
Performance Analysis Using Automated Grouping Mechanisms - Conference Portuga...
Performance Analysis Using Automated Grouping Mechanisms - Conference Portuga...Performance Analysis Using Automated Grouping Mechanisms - Conference Portuga...
Performance Analysis Using Automated Grouping Mechanisms - Conference Portuga...
 
Comparative Framework for Education
Comparative Framework for EducationComparative Framework for Education
Comparative Framework for Education
 
H2HC Tracing Profiling Debugging
H2HC Tracing Profiling DebuggingH2HC Tracing Profiling Debugging
H2HC Tracing Profiling Debugging
 
Dreams
DreamsDreams
Dreams
 
Run time
Run timeRun time
Run time
 
Apresentação TDC Floripa 2014
Apresentação TDC Floripa 2014Apresentação TDC Floripa 2014
Apresentação TDC Floripa 2014
 
Projeto mpx
Projeto mpxProjeto mpx
Projeto mpx
 

Recently uploaded

Abortion Pills For Sale WhatsApp[[+27737758557]] In Birch Acres, Abortion Pil...
Abortion Pills For Sale WhatsApp[[+27737758557]] In Birch Acres, Abortion Pil...Abortion Pills For Sale WhatsApp[[+27737758557]] In Birch Acres, Abortion Pil...
Abortion Pills For Sale WhatsApp[[+27737758557]] In Birch Acres, Abortion Pil...
drm1699
 

Recently uploaded (20)

Transformer Neural Network Use Cases with Links
Transformer Neural Network Use Cases with LinksTransformer Neural Network Use Cases with Links
Transformer Neural Network Use Cases with Links
 
From Knowledge Graphs via Lego Bricks to scientific conversations.pptx
From Knowledge Graphs via Lego Bricks to scientific conversations.pptxFrom Knowledge Graphs via Lego Bricks to scientific conversations.pptx
From Knowledge Graphs via Lego Bricks to scientific conversations.pptx
 
Auto Affiliate AI Earns First Commission in 3 Hours..pdf
Auto Affiliate  AI Earns First Commission in 3 Hours..pdfAuto Affiliate  AI Earns First Commission in 3 Hours..pdf
Auto Affiliate AI Earns First Commission in 3 Hours..pdf
 
Weeding your micro service landscape.pdf
Weeding your micro service landscape.pdfWeeding your micro service landscape.pdf
Weeding your micro service landscape.pdf
 
The Evolution of Web App Testing_ An Ultimate Guide to Future Trends.pdf
The Evolution of Web App Testing_ An Ultimate Guide to Future Trends.pdfThe Evolution of Web App Testing_ An Ultimate Guide to Future Trends.pdf
The Evolution of Web App Testing_ An Ultimate Guide to Future Trends.pdf
 
Novo Nordisk: When Knowledge Graphs meet LLMs
Novo Nordisk: When Knowledge Graphs meet LLMsNovo Nordisk: When Knowledge Graphs meet LLMs
Novo Nordisk: When Knowledge Graphs meet LLMs
 
CERVED e Neo4j su una nuvola, migrazione ed evoluzione di un grafo mission cr...
CERVED e Neo4j su una nuvola, migrazione ed evoluzione di un grafo mission cr...CERVED e Neo4j su una nuvola, migrazione ed evoluzione di un grafo mission cr...
CERVED e Neo4j su una nuvola, migrazione ed evoluzione di un grafo mission cr...
 
Entropy, Software Quality, and Innovation (presented at Princeton Plasma Phys...
Entropy, Software Quality, and Innovation (presented at Princeton Plasma Phys...Entropy, Software Quality, and Innovation (presented at Princeton Plasma Phys...
Entropy, Software Quality, and Innovation (presented at Princeton Plasma Phys...
 
[GeeCON2024] How I learned to stop worrying and love the dark silicon apocalypse
[GeeCON2024] How I learned to stop worrying and love the dark silicon apocalypse[GeeCON2024] How I learned to stop worrying and love the dark silicon apocalypse
[GeeCON2024] How I learned to stop worrying and love the dark silicon apocalypse
 
Microsoft365_Dev_Security_2024_05_16.pdf
Microsoft365_Dev_Security_2024_05_16.pdfMicrosoft365_Dev_Security_2024_05_16.pdf
Microsoft365_Dev_Security_2024_05_16.pdf
 
Abortion Clinic In Pretoria ](+27832195400*)[ 🏥 Safe Abortion Pills in Pretor...
Abortion Clinic In Pretoria ](+27832195400*)[ 🏥 Safe Abortion Pills in Pretor...Abortion Clinic In Pretoria ](+27832195400*)[ 🏥 Safe Abortion Pills in Pretor...
Abortion Clinic In Pretoria ](+27832195400*)[ 🏥 Safe Abortion Pills in Pretor...
 
Abortion Pills For Sale WhatsApp[[+27737758557]] In Birch Acres, Abortion Pil...
Abortion Pills For Sale WhatsApp[[+27737758557]] In Birch Acres, Abortion Pil...Abortion Pills For Sale WhatsApp[[+27737758557]] In Birch Acres, Abortion Pil...
Abortion Pills For Sale WhatsApp[[+27737758557]] In Birch Acres, Abortion Pil...
 
architecting-ai-in-the-enterprise-apis-and-applications.pdf
architecting-ai-in-the-enterprise-apis-and-applications.pdfarchitecting-ai-in-the-enterprise-apis-and-applications.pdf
architecting-ai-in-the-enterprise-apis-and-applications.pdf
 
Workshop: Enabling GenAI Breakthroughs with Knowledge Graphs - GraphSummit Milan
Workshop: Enabling GenAI Breakthroughs with Knowledge Graphs - GraphSummit MilanWorkshop: Enabling GenAI Breakthroughs with Knowledge Graphs - GraphSummit Milan
Workshop: Enabling GenAI Breakthroughs with Knowledge Graphs - GraphSummit Milan
 
BusinessGPT - Security and Governance for Generative AI
BusinessGPT  - Security and Governance for Generative AIBusinessGPT  - Security and Governance for Generative AI
BusinessGPT - Security and Governance for Generative AI
 
Modern binary build systems - PyCon 2024
Modern binary build systems - PyCon 2024Modern binary build systems - PyCon 2024
Modern binary build systems - PyCon 2024
 
Prompt Engineering - an Art, a Science, or your next Job Title?
Prompt Engineering - an Art, a Science, or your next Job Title?Prompt Engineering - an Art, a Science, or your next Job Title?
Prompt Engineering - an Art, a Science, or your next Job Title?
 
Software Engineering - Introduction + Process Models + Requirements Engineering
Software Engineering - Introduction + Process Models + Requirements EngineeringSoftware Engineering - Introduction + Process Models + Requirements Engineering
Software Engineering - Introduction + Process Models + Requirements Engineering
 
OpenChain Webinar: AboutCode and Beyond - End-to-End SCA
OpenChain Webinar: AboutCode and Beyond - End-to-End SCAOpenChain Webinar: AboutCode and Beyond - End-to-End SCA
OpenChain Webinar: AboutCode and Beyond - End-to-End SCA
 
Abortion Pill Prices Mthatha (@](+27832195400*)[ 🏥 Women's Abortion Clinic In...
Abortion Pill Prices Mthatha (@](+27832195400*)[ 🏥 Women's Abortion Clinic In...Abortion Pill Prices Mthatha (@](+27832195400*)[ 🏥 Women's Abortion Clinic In...
Abortion Pill Prices Mthatha (@](+27832195400*)[ 🏥 Women's Abortion Clinic In...
 

Metaheuristics for software testing

  • 3. Problem Generate data to test a program <non linear function>
  • 4. Solution Consider the problem a minimization vs maximization problem We can apply Simplex! (From Linear programing)
  • 6. Research Question How to optimize the generation? Compare the several way to generate the data?
  • 7. Introduction Meta heuristic algorithms* To solve the optimization problem (1), efficient search or optimization algorithms are needed. There are many optimization algorithms which can be classified in many ways, depending on the focus and characteristics. Name controversy*
  • 8. Meta-heuristics Components Two major components of any metaheuristic algorithms are: intensification and diversification, or exploitation and exploration (Blum and Roli, 2003).
  • 9. Meta heuristic I Particle Swarm Optimization PSO searches the space of an objective function by adjusting the trajectories of individual agents, called particles. Each particle traces a piecewise path which can be modelled as a time-dependent positional vector. The movement of a swarming particle consists of two major components: a stochastic component and a deterministic component. Each particle is attracted toward the position of the current global best g∗ and its own best known location x∗i , while exhibiting at the same time a tendency to move randomly.
  • 11. Meta heuristic I Algorithm for each particle i = 1, ..., S do Initialize the particle's position with a uniformly distributed random vector: xi ~ U(blo, bup) Initialize the particle's best known position to its initial position: pi ← xi if f(pi) < f(g) then update the swarm's best known position: g ← pi Initialize the particle's velocity: vi ~ U(-|bup-blo|, |bup-blo|) while a termination criterion is not met do: for each particle i = 1, ..., S do for each dimension d = 1, ..., n do Pick random numbers: rp, rg ~ U(0,1) Update the particle's velocity: vi,d ← ω vi,d + φp rp (pi,d-xi,d) + φg rg (gd-xi,d) Update the particle's position: xi ← xi + vi if f(xi) < f(pi) then Update the particle's best known position: pi ← xi if f(pi) < f(g) then Update the swarm's best known position: g ← pi
  • 13. Meta heuristic I After finding the two best values, the particle updates its velocity and positions with following equation (a) and (b). Fitness function update v[] = v[] + c1 * rand() * (pbest[] - present[]) + c2 * rand() * (gbest[] - present[]) (a) present[] = persent[] + v[] (b)
  • 14. Five principles of swarm intelligence First is the proximity principle: the population should be able to carry out simple space and time computations. Second is the quality principle: the population should be able to respond to quality factors in the environment. Third is the principle of diverse response: the population should not commit its activities along excessively narrow channels. Fourth is the principle of stability: the population should not change its mode of behavior every time the environment changes. Fifth is the 1946 principle of adaptability: the population must be able to change behavior mode when it’s worth the computational price.
  • 15. Meta heuristic II Bee Colony Optimization Metaheuristic (BCO)
  • 16. Meta heuristic II Agents (bees) collaborate in order to solve a difficult problem together Problems that can be applied: ● Traveling Salesman Problem (TSP) ● Quadratic Assignment Problem (QAP) ● Binary Knapsack Problem
  • 17. Meta heuristic II Bees During the search process, artificial bees communicate directly. Each artificial bee makes a series of local moves, and in this way incrementally constructs a solution of the problem. Bees are adding solution components to the current partial solution until they create one or more feasible solutions. The search process is composed of iteration
  • 18. Meta heuristic II Algorithms Pseudocode for the standard bees algorithm[2] 1 for i=1,…,ns i scout[i]=Initialise_scout() ii flower_patch[i]=Initialise_flower_patch(scout[i]) 2 do until stopping_condition=TRUE i Recruitment() ii for i =1,...,nb 1 flower_patch[i]=Local_search(flower_patch[i]) 2 flower_patch[i]=Site_abandonment(flower_patch[i]) 3 flower_patch[i]=Neighbourhood_shrinking(flower_patch[i]) iii for i = nb,...,ns 1 flower_patch[i]=Global_search(flower_patch[i])}
  • 19. Meta heuristic II Traveling Salesman Problem
  • 21. Meta heuristic III Ant Colony Optimization
  • 22. Meta heuristic III Ant Colony Optimization - ACO It is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs.
  • 23. Meta heuristic IV Cuckoo Search Cuckoos are fascinating birds, not only because of the beautiful sounds they make, but also because of their aggressive reproduction strategy. Some species named ani and Guira lay their eggs in communal nests, though they may remove others' eggs to increase the hatching probability of their own eggs. Quite a number of species engage in the mandatory brood parasitism by laying their eggs in the nests of other host birds (often other species). Cuckoo search (CS) is one of the latest nature-inspired metaheuristic algorithms, developed by Xin-She Yang and Suash Deb in 2009.
  • 24. Comparative evaluation CS is based on the brood parasitism of some cuckoo species (Yang and Deb 2009). In addition, this algorithm is enhanced by the so- called Lévy flights, rather than by simple isotropic random walks (Pavlyukevich 2007). Recent studies show that CS is potentially far more efficient than PSO and genetic algorithms (Yang and Deb 2010).
  • 25. Summary - GA and SA are not considered swarm methods - Thousands of algorithms with Swarm optimization methods - Each particle is a solution - It is not guaranteed to find the best solution
  • 26. Conclusion - Metaheuristic vs heuristic - “Standard” metaheuristic - CS and recent developments - Several other techniques
  • 27. References Blum and Roli, 2003 Yang and Deb 2009 Pavlyukevich 2007 Fred Glover in the 1970s James McCaffrey from Microsoft Research