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Markov Chains || Step-By-Step || ~xRay Pixy

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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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Firefly Optimization Algorithm

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Firefly algorithm is a swarm-based metaheuristic algorithm that was introduced by Yang. Firefly Algorithm is inspired by the FLASHING Behavior of Fireflies. 

Assumptions

  • Fireflies are attracted to each other.
  • Attractiveness is proportional to BRIGHTNESS. 
  • Less Brighter Firefly is attracted to the Brighter Firefly.
  • Attractiveness decrease as the distance between 2 fireflies increase.
  • If brightness for both is the same, fireflies move randomly.
  • New Solutions are generated by Random walks & the Attraction of fireflies.

Firefly Optimization Algorithm Steps
  1. Initialize Parameters.
  2. Generate Population of n Fireflies.
  3. Calculate Fitness Value for Each Firefly.
  4. Check stopping criteria if (CurrentIteration := 1 to MaximumIteration ).
  5.  Update Position and Light Intensity for Each Firefly.
  6. Report the Best Solution.
Initialize Parameters, Population of Fire Fly Swarm.
Population Size (n) = 20;
Maximum Iteration (Maxt) = 50;
Dimension (d) = 10;
Upper Bound [UB] = 100;
Lower Bound [LB] = -100;

Calculate Fitness Value [Light Intensity] for Each FireFly.
The light intensity of Firefly (i.e., 𝐼_𝑖) at 𝑥_𝑖 is computed by the Value of the Objective Function.

Firefly Position Updated as:
For i = 1 to n -1;
For j = i + 1 to n;
  IF ( 𝑰_𝒋 > 𝑰_𝒊 )
      Update Position. [move Firefly i towards Firefly j ];
    End IF
  End For
 End For

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