Learn Markov Chains step-by-step using real-life examples. Video Chapters: Markov Chains 00:00 Introduction 00:19 Topics Covered 01:49 Markov Chains Applications 02:04 Markov Property 03:18 Example 1 03:54 States, State Space, Transition Probabilities 06:17 Transition Matrix 08:17 Example 02 09:17 Example 03 10:26 Example 04 12:25 Example 05 14:16 Example 06 16:49 Example 07 18:11 Example 08 24:56 Conclusion
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Krill Herd Optimization Algorithm
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Krill Herd Optimization Algorithm Numerical Example
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.
Movement Induced by the position of other Krill’s.
Foraging Activity: Krill’s Searching for Food.
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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