Learn how to implement an obstacle-avoiding path planning for a robot using the Grey Wolf Optimization (GWO) in a static environment. #optimization #algorithm #metaheuristic #robotics #deeplearning #ArtificialIntelligence #MachineLearning #computervision #research #projects #thesis #Python
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Neuro Fuzzy Hybrid System for Water Heater Control System ~xRay Pixy
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Water heater control system using Neuro Fuzzy Hybrid System.
Video Chapters:
00:00 Introduction
01:38 Hybrid Approach
02:37 Neural Network
03:08 Neural Network Components
05:38 Fuzzy Logic
12:09 Neuro-Fuzzy Hybrid System
14:16 Numerical Example
22:22 Conclusion
A neuro-fuzzy hybrid system, also known as a neuro-fuzzy system or fuzzy neural network, combines the principles of neural networks and fuzzy logic to create a more robust and versatile system for solving complex problems, particularly in the field of artificial intelligence and control systems. This hybrid approach aims to take advantage of the strengths of both neural networks and fuzzy logic to handle uncertainty, nonlinearities, and complex patterns effectively.
The key components and concepts involved in a neuro-fuzzy hybrid system:
Neural Networks
Neural networks are computational models inspired by the human brain's structure and functioning. They consist of interconnected nodes (neurons) organized into layers, including an input layer, one or more hidden layers, and an output layer. Neural networks can learn from data and adapt their internal parameters (weights and biases) through training using algorithms like backpropagation. Neural networks are well-suited for tasks involving pattern recognition, function approximation, and nonlinear mapping.
Fuzzy Logic
Fuzzy logic is a mathematical framework for dealing with uncertainty and imprecision in data and decision-making. It uses linguistic variables, membership functions, and fuzzy rules to represent and process information in a fuzzy manner. Fuzzy logic is particularly useful for handling vague or qualitative information and making decisions based on expert knowledge.
In a neuro-fuzzy hybrid system, these two components are integrated to address complex problems. Here's how it typically works:
Fuzzification
Input data is fuzzified to convert crisp values into fuzzy sets using linguistic variables and membership functions.
Rule-Based Fuzzy Inference
Fuzzy rules, which describe relationships between inputs and outputs in linguistic terms, are applied to the fuzzy inputs to produce fuzzy outputs.
Defuzzification
The fuzzy output is converted back into a crisp value using defuzzification methods, such as centroid or weighted average.
Neural Network Integration
The crisp output from the fuzzy system can be used as input to a neural network.
The neural network can further refine the output, learn from data, and handle complex patterns and nonlinear relationships.
Steps of a neuro-fuzzy system for stock price prediction with corrected numerical calculations:
Step 1: Fuzzification
In this step, we convert crisp input data into fuzzy sets using linguistic variables and membership functions. Here are the linguistic variables and membership functions for our example:
SPC (Stock Price Change):
Linguistic variables: Negative (N), Neutral (Z), Positive (P)
Membership functions:
Negative (N): SPC ∈ [-2, -1]
Neutral (Z): SPC ∈ [-1, 1]
Positive (P): SPC ∈ [1, 2]
TVC (Trading Volume Change):
Linguistic variables: Low (L), Medium (M), High (H)
Membership functions:
Low (L): TVC ∈ [0, 50]
Medium (M): TVC ∈ [30, 70]
High (H): TVC ∈ [50, 100]
Suppose we have the following data:
SPC = -0.5 (Negative)
TVC = 40 (Medium)
Step 2: Rule-Based Fuzzy Inference
Define fuzzy rules that describe the relationship between fuzzy input variables and the predicted stock price change. We use a simple set of rules:
If SPC is Negative (N) and TVC is Low (L), then Price Change is Negative (N).
If SPC is Neutral (Z) and TVC is Medium (M), then Price Change is Neutral (Z).
If SPC is Positive (P) and TVC is High (H), then Price Change is Positive (P).
Rule 1: SPC(N) = 0.5 (since SPC is halfway between -1 and -2), TVC(L) = 0.6 (since TVC is halfway between 0 and 50)
Rule 2: SPC(Z) = 0.5 (since SPC is halfway between -1 and 1), TVC(M) = 0.5 (since TVC is halfway between 30 and 70)
Rule 3: SPC(P) = 0 (since SPC is negative, and P doesn't apply), TVC(H) = 0 (since TVC is not in the high range)
Step 3: Defuzzification
Now that we have determined that Rule 2 is the most relevant, we defuzzify the output to get a crisp prediction. We can use the centroid method for defuzzification. The output membership functions for Price Change (N, Z, P) have centroids defined as:
Negative (N): -1.5
Neutral (Z): 0
Positive (P): 1.5
So, the centroid of the output membership function for "Price Change" is 0.
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Cuckoo Search Algorithm - Metaheuristic Optimization Algorithm What is Cuckoo Search Algorithm? Cuckoo Search Algorithm is a Meta-Heuristic Algorithm. Cuckoo Search Algorithm is inspired by some Cuckoo species laying their eggs in the nest of other species of birds. In this algorithm, we have 2 bird Species. 1.) Cuckoo birds 2.) Host Birds (Other Species) What if Host Bird discovered cuckoo eggs? Cuckoo eggs can be found by Host Bird. Host bird discovers cuckoos egg with Probability of discovery of alien eggs. If Host Bird Discovered Cuckoo Bird Eggs. The host bird can throw the egg away. Abandon the nest and build a completely new nest. Mathematically, Each egg represent a solution and it is stored in the host bird nest. In this algorithm Artificial Cuckoo Birds are used. Artificial Cuckoo can lay one egg at a time. We will replace New and better solutions with less fit solutions. It means eggs that are more similar to host bird has opportunity to develop in the new generation a
Particle Swarm Optimization (PSO) is a p opulation-based stochastic search algorithm. PSO is inspired by the Social Behavior of Birds flocking. PSO is a computational method that Optimizes a problem. PSO searches for Optima by updating generations. It is popular is an intelligent metaheuristic algorithm. In Particle Swarm Optimization the solution of the problem is represented using Particles. [Flocking birds are replaced with particles for algorithm simplicity]. Objective Function is used for the performance evaluation for each particle / agent in the current population. After a number of iterations agents / particles will find out optimal solution in the search space. Q. What is PSO? A. PSO is a computational method that Optimizes a problem. Q. How PSO will optimize? A. By Improving a Candidate Solution. Q. How PSO Solve Problems? A. PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). Local and global optimal solutions are used to upda
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Local Binary Pattern Introduction to Local Binary Pattern (LBP) Q. What is Digital Image? A. Digital images are collections of pixels or numbers ( range from 0 to 255). Q. What is Pixel? A. Pixel is the smallest element of any digital image. Pixel can be categorized as Dark Pixel and Bright Pixel. Dark pixels contain low pixel values and bright pixels contain high pixel values. Q. Explain Local Binary Pattern (LBP)? A. Local binary pattern is a popular technique used for image processing. We can use the local binary pattern for face detection and face recognition. Q. What is LBP Operator? A. LBP operator is an image operator. We can transform images into arrays using the LBP operator. Q. How LBP values are computed? A. LBP works in 3x3 (it contain a 9-pixel value ). Local binary pattern looks at nine pixels at a time. Using each 3x3 window in the digital image, we can extract an LBP code. Q. How to Obtain LBP operator value? A. LBP operator values can be obtained by using the simp
There are about 1000 species of Bats. Bat Algorithm is based on the echolocation behavior of Micro Bats with varying pulse rates of emission and loudness. All bats use echolocation to sense distance and background barriers. Microbats are small to medium-sized flying mammals. Micro Bats used a Sonar that is known as Echolocation to detect their prey. Bats fly randomly with the velocity at the position with a fixed frequency and loudness for prey. Q. Whats is Frequency? A. Frequency is the number of waves that pass a fixed point in unit time. Wavelength is the minimum distance between two nearest particles which are in the same phase. Here, Sound waves are used by microbats to detect prey. Q. What is Position? A. A place where something or someone is located. Q. What is Velocity? A. Speed of something in a given direction. Q. What is loudness. A. Loudness refers to how soft or loud sound seems to listeners. Q. What is pulse rate? A. Wave or vibration. In th
Grey Wolf Optimization Algorithm (GWO) Grey Wolf Optimization Grey Wolf Optimization Algorithm is a metaheuristic proposed by Mirjaliali Mohammad and Lewis, 2014. Grey Wolf Optimizer is inspired by the social hierarchy and the hunting technique of Grey Wolves. What is Metaheuristic? Metaheuristic means a High-level problem-independent algorithmic framework (develop optimization algorithms). Metaheuristic algorithms find the best solution out of all possible solutions of optimization. Who are the Grey Wolves? Wolf (Animal): Wolf Lived in a highly organized pack. Also known as Gray wolf or Grey Wolf, is a large canine. Wolf Speed is 50-60 km/h. Their Lifespan is 6-8 years (in the wild). Scientific Name: Canis Lupus. Family: Canidae (Biological family of dog-like carnivorans). Grey Wolves lived in a highly organized pack. The average pack size ranges from 5-12. 4 different ranks of wolves in a pack: Alpha Wolf, Beta Wolf, Delta Wolf, and Omega Wolf. How Grey Wolf Optimization Algorithm
Grey Wolf Optimization Algorithm Numerical Example Grey Wolf Optimization Algorithm Steps 1.) Initialize Grey Wolf Population. 2.) Initialize a, A, and C. 3.) Calculate the fitness of each search agent. 4.) 𝑿_𝜶 = best search agent 5.) 𝑿_𝜷 = second-best search agent 6.) 𝑿_𝜹 = third best search agent. 7.) while (t<Max number of iteration) 8.) For each search agent update the position of the current search agent by the above equations end for 9.) update a, A, and C 10.) Calculate the fitness of all search agents. 11.) update 𝑿_𝜶, 𝑿_𝜷, 𝑿_𝜹 12.) t = t+1 end while 13.) return 𝑿_𝜶 Grey Wolf Optimization Algorithm Numerical Example STEP 1. Initialize the Grey wolf Population [Initial Position for each Search Agent] 𝒙_(𝒊 ) (i = 1,2,3,…n) n = 6 // Number of Search Agents [ -100, 100] // Range Initial Wolf Position 3.2228 4.1553 -3.8197 4.2330 1.3554 -4.1212 STEP 2. Calculate Fitness for Each Search Agent. Objective Function: F6(x) = su
Whale Optimization Algorithm Code Implementation Whale Optimization Algorithm Code Files function obj_fun(test_fun) switch test_fun case 'F1' x = -100:2:100; y=x; case 'F2' x = -10:2:10; y=x; end end function [LB,UB,D,FitFun]=test_fun_info(C) switch C case 'F1' FitFun = @F1; LB = -100; UB = 100; D = 30; case 'F2' FitFun = @F2; LB = -10; UB = 10; D = 30; end % F1 Test Function function r = F1(x) r = sum(x.^2); end % F2 Test Function function r = F2(x) r = sum(abs(x))+prod(abs(x)); end end function Position = initialize(Pop_Size,D,UB,LB) SS_Bounds = size(UB,2); if SS_Bounds == 1 Position = rand(Pop_Size,D).*(UB-LB)+LB; end if SS_Bounds>1 for i = 1:D UB_i = UB(i); LB_i = LB(i); Position(:,i) = rand(Pop_Size,1).*(UB_i-LB_i)+LB_i; end end end function [Best_Val,Best_Pos,Convergence_Curve]=WOA(
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