Krill Herd Optimization NUMERICAL EXAMPLE ~xRay Pixy

 Krill Herd Optimization Algorithm Numerical Example

KRILL HERD OPTIMIZATION ALGORITHM STEPS

1. Initialize Algorithm Parameters.
2. Initialize Population for Krill's.
3. Evaluate Krill's Performance.
4. Selection Best Krill Among all.
5. Check While(Current Iteration <= Maximum Iteration)
6. Calculate Neighbors Krill Effect.
7. Movement Induced.
8. Calculate Food Attraction.
9. Calculate Best Position Attraction.
10. Foraging Motion.
11. Physical Diffusion.
12. Crossover and Mutation
13. Update Krill Position.
14. End While
15. Display Best Solution

Movement Induced Calculation

Foraging Motion Calculation

Physical Diffusion Calculation

What is Krill Herd Optimization Algorithm? 

Krill herd optimization algorithm is introduced in 2012 to solve the Global Optimization Function. This is a population-based Swarm Intelligence Search Algorithm based on the Herding behavior of krill.  In the Krill herd optimization algorithm, we have a Group of Krill individuals and they are Searching for Food. 

Krill Herd Optimization Algorithm Working.

In real life, Krill move through Multidimensional Space to search for Food and High-Density herd. Three main Calculations to update Krill's Position. 

1. Movement Induced by the position of other Krill’s.
2. Foraging Activity: Krill’s Searching for Food.
3. Random Diffusion: Net movement of each Krill based on Density.

KRILL MOTION CALCULATION

• The movement led by Other Krill
• Foraging Activity/Motion
• Random Physical Diffusion

FOR KRILL Individual Movement is Calculated as:

𝑁_𝑖^𝑁𝑒𝑤=𝑁^𝑀𝑎𝑥 𝛼_𝑖+𝜔_𝑛 𝑁_𝑖^𝑜𝑙𝑑

Where,

𝑁^𝑀𝑎𝑥 = Maximum Induced Motion

 𝜔_𝑛 =Inertia Weight [0,1]

𝑁_𝑖^𝑜𝑙𝑑 =Inertia Weight [0,1]

 i = Krill Individual

N = Movement 

w = Weight Inertia

α = Local Swarm Density

Krill Movement is influenced by other krill’s.

What is 𝜶_𝒊?

𝛼_𝑖 = Local Swarm Density. 

𝛼_𝑖= 𝛼_𝑖^𝑙𝑜𝑐𝑎𝑙+ 𝛼_𝑖^𝑡𝑎𝑟𝑔𝑒𝑡

 𝛼_𝑖^𝑡𝑎𝑟𝑔𝑒𝑡: Target Direction affected by jth Individual movement. 

If ( krill is Closest to the Food )

{

Then Density is High.

}

Each Krill Move towards the Best Solution by searching for the herd (group) with high density (similar groups) & Closest Food

FOR KRILL Individual Foraging Activity/Motion is Formulated by using 2 main parameters: 

• The Food Location.
• Prior knowledge about the Food Location.

Krill Herd Optimization Algorithm Steps

Step 1. Initialize the Population of N Krill Randomly.

Step 2. Calculate Fitness Value for Each Krill.

Step 3. Perform Motion Calculations. 

Step 4. Update Each Krill Position.

Step 5. Find New Position (t+1) for each Krill.

Step 6. Evaluate Each Krill according to their New Position.

Crossover Component: Each member of krill update its current position using the position of other

Mutation Component: Controlled by mutation parameter.  [change in best solution]

For more details please watch Krill herd optimization Part 1 and Part 2.

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