This document discusses several metaheuristic optimization algorithms, including Ant Colony Optimization (ACO), Firefly Algorithm, Modified Firefly Algorithm, BAT Algorithm, and Artificial Bee Colony (ABC) algorithm. It provides brief overviews of each algorithm, describing how they are inspired by natural behaviors and processes and outlining their main rules and procedures. The document is presented by Dr. C.Gokul and discusses these algorithms for optimization and problem solving.

1. Ant Colony Optimization (ACO)
Firefly Algorithm
Modified Firefly Algorithm
BAT Algorithm
Artificial Bee Colony (ABC)
Presented by
Dr. C.Gokul,AP(Sl.Gr)/EEE
Velalar College of Engg & Tech , Erode

2. Metaheuristic Methods
• Ant Colony Optimization (ACO)
• Modified Ant Colony Optimization (MACO)
• Firefly Algorithm
• Modified Firefly Algorithm
• BAT Algorithm
• Artificial Bee Colony (ABC)
• Modified Artificial Bee Colony (MABC)

3. Ant Colony Optimization (ACO)
• ACO is inspired by the behavior of real ants
• Ants find shortest path from their nest to the food
• Pheromone: Ant excrete a hormone
• Ants find a shortest path due to pheromone trails left by ants
from their nest to the food and back

4. ACO Rules
• Pheromone Trail τ𝑖𝑗 - Degree of favorability
• ACO combines pheromone information with heuristic values
to find solutions
• Pheromone trail Update
𝜌 −Evaporation factor (determines the pheromone speed)
𝛥𝜏 −Amount of pheromone deposited by the ant
𝛾 −Waiting number until global best ant solution used again
𝜏𝑖𝑗 = 𝜌. 𝜏𝑖𝑗 + 𝛥𝜏

5. • Ant density model: Pheromone trail quantity left by ant
through their paths is constant.
probij - Probability of ant
τij - Pheromone trail
β - Parameter used to enhance the heuristic value.
𝑝𝑟𝑜𝑏𝑖𝑗 =
𝜏𝑖𝑗 𝛽
෍
j=1
𝑤
𝜏𝑖𝑗 𝛽
Ant Colony Optimization (MACO)

6. ACO based Test Scheduling Procedure
• Compute heuristic information (wprefer)
• Set ACO parameters
• Initialize pheromone trails
• While (result unsatisfied)
While ( )
While ( )
{
Ant exploration process
}
Find Iteration best ant solution
Find Global best ant solution
𝑁𝑖𝑏∠𝛾
𝑖∠𝑁𝑐𝑜𝑙𝑜𝑛𝑦

7. Firefly Algorithm
• Firefly Algorithm is inspired by the behavior of fireflies
• Firefly movement contains two elements:
➢ Approach to better solutions
➢ Move randomly
• Main assumptions:
➢All fireflies are unisex
➢Brightness is determined by objective function
𝐴𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑣𝑒𝑛𝑒𝑠𝑠 𝛼 𝐵𝑟𝑖𝑔ℎ𝑡𝑛𝑒𝑠𝑠,
𝐴𝑡𝑡𝑟𝑎𝑐𝑡𝑖𝑣𝑒𝑛𝑒𝑠𝑠 𝛼
1
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒

8. Distance, Attractiveness and Movement
• Distance between i and j fireflies at 𝑥𝑖and 𝑥𝑗
Cartesian distance 𝑟𝑖𝑗 = || 𝑥𝑖 – 𝑥𝑗||
• Attractiveness 𝛽 varies with distance between two fireflies
[𝛽0=1, 𝛾=1]
• Firefly movement
𝑥𝑖 = 𝑥𝑖 + 𝛽 (𝑥𝑗 − 𝑥𝑖) + α(rand-0.5)
For scheduling: Random number (rand)= 0.2, Randomization
parameter (α)=0.3
𝛽 = 𝛽0 𝑒−𝛾𝑟2

9. Yes
No
No
Define absorption coefficient γ
Formulate light intensity I [I=f(x)]
Initialize Fireflies parameters, initial population Xi, where i =1,
2…n
Increment Gen by 1
For i = 1: n
For j = 1: n
f (Xj) > f (Xi)
Move firefly i towards firefly j
Best solution obtained
Terminate Process
Gen >
maxGen
Yes
Evaluate new solutions
Flow chart for Firefly Algorithm

10. Modified Firefly Algorithm
• Drawbacks of Firefly algorithm
➢Update of firefly movement is not faster
➢Direction of the fireflies movement depends on α
➢α is high for fireflies which are spread in large search
space region
➢For better locations, less randomness is beneficial
• Modified Firefly algorithm
➢α should be high initially and then decreases
➢Fireflies are encouraged to move in all directions of search
space initially and then converge in later stages
➢Fireflies should cover the maximum predefined area
➢Increases the speed of movement

11. Firefly Movement Update
• Firefly movement
𝑥𝑖 = 𝑥𝑖 + 𝛽 (𝑥𝑗 − 𝑥𝑖) + (rand-0.5)
where
• Firefly i attracted to the best solution if no local best solution
existed in the neighbourhood
𝛼 𝑢𝑝𝑑𝑎𝑡𝑒
൯𝛼 𝑢𝑝𝑑𝑎𝑡𝑒 = 𝛼 + 𝜆(𝑥𝑖 − 𝑔 𝑏𝑒𝑠𝑡

12. Yes
No
No
Define absorption coefficient γ
Formulate light intensity I [I=f(x)]
Initialize Fireflies parameters, initial population Xi, where i =1,
2…n
Increment Gen by 1
For i = 1: n
For j = 1: n
f (Xj) > f (Xi)
Best solution obtained
Terminate Process
Gen >
maxGen
Yes
Update Distance, Movement by updating the value of α
Evaluate new solutions
Move firefly i towards firefly j
Flow chart for Modified Firefly Algorithm

13. BAT Algorithm
• BAT Algorithm is based on echo location behaviour of bats
• Bat emit signals (with frequency ‘f’) to locate prey. This
signals bounce back if they hit an object.
• Eco signals are used to calculate the distance
• After hitting and reflecting, the bats transform their own pulse
into useful information to explore how far away the prey is.
• Rate of pulse emission r[0,1]
– 0 means there is no emission
– 1 means Bat emission is maximum

14. BAT Algorithm Rules
• All bats use echolocation to sense distance and they know the
difference between food/prey
• Bats fly randomly with
– Velocity vi
– Position xi
– with a fixed frequency fmin
– varying wavelength λ
– Loudness A0 to search the prey
• Loudness varies from positive large value 𝐴0 to minimum
value 𝐴 𝑚𝑖𝑛.

15. Bat Motion
• 𝑓𝑖 = 𝑓 𝑚𝑖𝑛 + 𝑓𝑚𝑎𝑥 − 𝑓 𝑚𝑖𝑛 𝛽
𝑓 𝑚𝑖𝑛 =1 kHz, 𝑓𝑚𝑎𝑥 = 90 kHz, 𝛽𝜖 (0, 1)
• 𝑣𝑖
𝑡
= 𝑣𝑖
𝑡−1
+ 𝑥𝑖
𝑡
− 𝑥∗ 𝑓𝑖
𝑥∗ − Current best location
• 𝑥𝑖
𝑡
= 𝑥𝑖
𝑡−1
+ 𝑣𝑖
𝑡
𝑡 − Number of iterations

16. BAT Algorithm Pseudocode
• Initialize bat population, position, velocity and frequency
• Initialize pulse rates , loudness
• while(t <Max iterations)
Generate new solutions by adjusting frequency, updating
velocity and location
➢ if ( rand > ri )
Select a solution among the best solutions
Generate a local solution from selected best solution
end if
𝑟𝑖 𝐴𝑖

17. BAT Algorithm Pseudocode
Generate new solutions by flying randomly
➢ if (test the fitness of new solution w.r.to r and A)
Accept the new solutions
Increase pulse rate , loudness
end if
Rank the bats and find the current best 𝑥∗
end while
𝑟𝑖 𝐴𝑖

18. Artificial Bee Colony (ABC) Algorithm
• ABC is based on the intelligent behavior of bees when they
search for honey
• Three essential components
– Food Source
– Employed Bees
– Unemployed Bees
• Two modes of behavior
– Recruitment to a food source
– Neglect of a source
• Bees can memorize, share, communicate and store the
information based on which decisions can be made

19. Bees evaluate the different path according to
• Quality of food
• Amount of energy usage
Agents in ABC:
• Employed Bee: They carry information about food source and
share with the neighborhood.
• Onlooker Bee: Wait in their nest and select a food source
through the information shared by employed bees.
• Scout: Responsible for finding new food, the new nectar
sources
Artificial Bee Colony (ABC) Algorithm

20. • Initiates the foraging in the neighborhood
• Employed bee produces new trial food position vi around xi
where 𝑥𝑖 - current food source position,
j ε { 1,2, …., D},
k ε { 1,2, …., SN} are randomly picked indices,
D - Number of search dimensions,
SN - Number of employed bees,
𝜑𝑖𝑗 - Uniform random value from [-1,1]
Employed Bee Stage
൯𝑣𝑖𝑗 = 𝑥𝑖𝑗 + 𝜑𝑖𝑗(𝑥 𝑘𝑗 − 𝑥𝑖𝑗

21. • In this phase employed bees share the fitness information
about updated solutions and information about their position
• Probability Pi that the employed bee with food source xi
would be picked by an onlooker bee is
Onlooker Bee Stage
𝑃𝑖 =
)𝑓𝑖𝑡(𝑥𝑖
෌ 𝑛=1
𝑆 𝑁
)𝑓𝑖𝑡(𝑥 𝑛

22. • In this phase the neglected food source associated bee becomes
a scout bee
• The randomly chosen food source replaces the food source
within the search space.
• The scout bee replaces the abandoned food source xi with new
food source xi as
𝑥𝑖
𝑗
= 𝑥 𝑚𝑖𝑛
𝑗
+ 𝑟𝑎𝑛𝑑 0,1 𝑥 𝑚𝑎𝑥
𝑗
− 𝑥 𝑚𝑖𝑛
𝑗
𝑥 𝑚𝑖𝑛
𝑗
and 𝑥 𝑚𝑎𝑥
𝑗
are bounds of 𝑥𝑖 in 𝑗th direction.
Scout Bee Phase

23. STEP 1: Initialization of nectar sources
STEP 2: Search for new nectar sources
STEP 3: Probability for the scouter to select employed foragers
STEP 4: Production of scouter
STEP 5: Production of new solution
STEP 6: Replace the original solution
STEP 7: Neglect a solution and replace it with new one
STEP 8: The best solution ever is recorded.
STEP 9: Termination
ABC Procedure