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Avascular Necrosis (AVN) || Early Detection, Better Outcomes || ~xRay Pixy

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Avascular Necrosis (AVN) is a condition where blood flow to the bone is reduced, causing bone cells to die. This leads to pain, joint damage, and difficulty in movement, especially in the hip. Early diagnosis and proper treatment can prevent permanent bone damage and improve quality of life. Video Chapter: AVN 00:00 Introduction 00:45 What is AVN? 01:55 About Bone Tissue 02:49 AVN Causes 03:38 AVN Symptoms 04:11 AVN Diagnosis 04:56 AVN of femoral head 05:33 How AVN Develops 07:28 Conclusions #optimization #algorithm #metaheuristic #robotics #deeplearning #ArtificialIntelligence #MachineLearning #computervision #research #projects #thesis #Python #optimizationproblem #optimizationalgorithms 
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Find Maxima of Function using PSO Method || Numerical Example || ~xRay Pixy

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Find the maximum value for the objective function using Particle Swarm Optimization Step-By-Step.
Video Chapters: Find the Maxima of Function using the PSO Method
00:00 Introduction
02:18 Objective
03:17 Maximization Problem
04:22 Particle Swarm Optimization Steps
05:22 Step 1 - Objective Function
05:30 Step 2 - Position and Velocity Initialization
06:00 Step 3 - Fitness Calculation
07:06 Step 4 - Update Personal Best
07:16 Step 5 - Update Global Best
07:42 Step 6 - Position Update
10:34 Step 7 - Solution Boundary Checking
10:53 Step 8 - New Solution Evaluation
11:31 Step 9 - Update Personal Best
12:12 Step 10 - Update Global Best
13:24 Iteration 2 Start - Position Update
14:45 New Solution Boundary Checking
15:24 New Solution Fitness Calculation
15:48 Update Personal Best
16:32 Update Global Best
17:42 Conclusion

Problem: Find the Maxima of the function

�(�)=�2+2�+11�(�)=�2+2�+11f(x)=x

in the range -2<=x<=2 using PSO method. Use 4 particles (N = 4) with the initial

Calculation for Iteration 01

Step 1: Define Objective Function
�(�)=�2+2�+11

Step 2: Initialize Position and Velocity for Each Particle (N = 1,2,3,4)

Initial Positions: x1 = -1.5, x2 = 0.0, x3 = 0.5, x4 = 1.25
Initial Velocities: v1 = v2 = v3 = v4 = 0
Weight Inertia (w) = 0.8
Acceleration Coefficients c1 = c2 = 2.05

Step 3: Evaluate Performance using Objective Function

f(x1) = -(-1.5)^2 + 2 (-1.5) + 11 = 5.75

f(x2) = -(0.0)^2 + 2(0.0) + 11 = 11

f(x3) = -(0.5)^2 + 2(0.5) + 11 = 11.75

f(x4) = -(1.25) ^2 + 2(1.25) + 11 = 11.93

Step 4: Update Personal Best Positions

Pbest(x1) = -1.5

Pbest(x2) = 0.0

Pbest(x3) = 0.5

Pbest(x4) = 1.25

Step 5: Update Global Best Position
Gbest = (x4) = 1.25

Step 6: Update the Velocity and Position for each Particle

Particle (x1) New Velocity

v1 = 0.8 * 0 + 0.3 * 2.05 * (-1.5 - (-1.5)) + 0.6 (2.05)*(1.25-(-1.5))

v1 = 3.3825

Particle (x1) New Position

x(1) = -1.5 + 3.3825= 1.88

Particle (x2) New Velocity

v2 = 0.8 * 0 + 0.2 * 2.05 * (0.0 - 0.0) + 0.6 * (2.05)*(1.25-0.0)

v2 = 1.537

Particle (x2) New Position

x(2) = 0.0 + 1.537  = 1.537

Particle (x3) New Velocity

v3 = 0.8 * 0 + 0.4 * 2.05 * (0.5 - 0.5) + 0.1 * (2.05)*(1.25-0.5))

v3 = 0.1537

Particle (x3) New Position

x(3) = 0.5 + 0.1537 = 0.6537

Particle (x4) New Velocity

v4 = 0.8 * 0 + 0.9 * 2.05 * (1.25 - 1.25) + 0.2 * (2.05)*(1.25-1.25))

v4 = 0

Particle (x4) New Position

x(4) = 1.25 - 0  = 1.25

Step 07: Ensure New Solutions are within range

Step 08: Evaluate New Solution Performance using Objective Function

f(x1) = -(1.88)^2 + 2 (1.88) + 11 = 11.23

f(x2) = -(1.53)^2 + 2(1.53) + 11 = 11.72

f(x3) = -(0.65)^2 + 2(0.65) + 11 = 11.87

f(x4) = -(1.25) ^2 + 2(1.25) + 11 = 11.9

Step 09: Update Personal Best Positions

Pbest(x1) = 1.88

Pbest(x2) = 1.53

Pbest(x3) = 0.65

Pbest(x4) = 1.25

Step 10: Update Global Best Position

Gbest = (x4) = 1.25        Check Fitness (Old_Gbest) > Fitness (New_Gbest)

Check (11.93) > (11.23)

            (11.93) > (11.72)

            (11.93) > (11.87)

            (11.93) > (11.93)

Step 11: Update Global Best Position
Gbest = (x4) = 1.25 

Step 12: Check Stopping Condition

Check (Current_itr <= Max_iter)

Repeat Steps from Step 6 to Step 11

For Iteration 01 Gbest Position = (x4) = 1.25  and Fitness = 11.93

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