Video Link CLICK HERE... Learn Nash Equilibrium In Game Theory Step-By-Step Using Examples. Video Chapters: Nash Equilibrium 00:00 Introduction 00:19 Topics Covered 00:33 Nash Equilibrium 01:55 Example 1 02:30 Example 2 04:46 Game Core Elements 06:41 Types of Game Strategies 06:55 Prisoner’s Dilemma 07:17 Prisoner’s Dilemma Example 3 09:16 Dominated Strategy 10:56 Applications 11:34 Conclusion The Nash Equilibrium is a concept in game theory that describes a situation where no player can benefit by changing their strategy while the other players keep their strategies unchanged. No player can increase their payoff by changing their choice alone while others keep theirs the same. Example : If Chrysler, Ford, and GM each choose their production levels so that no company can make more money by changing their choice, it’s a Nash Equilibrium Prisoner’s Dilemma : Two criminals are arrested and interrogated separately. Each has two ...
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Transmission Expansion Planning (TEP) |AC Optimal Power Flow|
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Transmission Expansion Planning (TEP)
Transmission Systems are Large and Interconnected. Transmission Systems carry large quantities of electricity (from utility-scale to low voltage lines – distributed system). Transmission Expansion Planning (TEP) is process of identifying needed investment and expansion in transmission. Transmission Expansion Planning (TEP) is a complex decision-making process.
TEP Process include different analysis :
System Cost.
Reliability and Modeling.
Compute Risk and burden.
Number of Generators required.
The number of Equipment required.
How a transmission system should develop over time?
Determine the Number of Electric Power Transmission facilities required in the future power grid.
Transmission Expansion Planning (TEP): A list of types of equipment can be inserted on the grid:
Approaches in Transmission Expansion Planning Problems
Static Approach: System Information (i.e., load, types of equipment) is only considered at the planning horizon in one shot.
Dynamic Approach: System Information (i.e., load, types of equipment) is handled over sub-periods of the planning horizon
What is the Role of Metaheuristic Algorithms in TEP?
Bio-inspired Meta-heuristic algorithms are widely used to solve Transmission Expansion Problems. Metaheuristic algorithms provide the best solutions to TEP problems as compared to other traditional methods. Metaheuristic algorithms are problem independent [not dependent on particular information about the problem].
Evolutionary Particle Swarm Optimization is a powerful tool to solve complex TEP problems. Evolutionary Particle Swarm Optimization provides the best solutions. Evolutionary Particle Swarm Optimization combines the best features of the Genetic Algorithm (GA) and Particle Swarm Optimization Algorithm (PSO).
PARTICLE SWARM OPTIMIZATION ALGORITHM NUMERICAL EXAMPLE PSO is a computational method that Optimizes a problem. It is a Population-based stochastic search algorithm. PSO is inspired by the Social Behavior of Birds flocking. n 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. PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). Local and global optimal solutions are used to update particle position in each iteration. Particle Swarm Optimization (PSO) Algorithm step-by-step explanation with Numerical Example and source code implementation. - PART 2 [Example 2] 1.) Initialize Population [Current Iteration (t) = 0] Population Size = 4; 𝑥𝑖 : (i = 1,2,3,4) and (t = 0) 𝑥1 =1.3; 𝑥2=4.3; 𝑥3=0.4; 𝑥4=−1.2 2.) Fitness Function u...
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 de...
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 ...
Particle swarm optimization (PSO) What is meant by PSO? PSO is a computational method that Optimizes a problem. It is a Population-based stochastic search algorithm. PSO is inspired by the Social Behavior of Birds flocking. n 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. PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). Local and global optimal solutions are used to update particle position in each iteration. How PSO will optimize? By Improving a Candidate Solution. How PSO Solve Problems? PSO solved problems by having a Population (called Swarms) of Candidate Solutions (Particles). The population of Candidate Solutions (i.e., Particles). What is Search Space in PSO? It is the range in which the algorithm computes th...
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 ...
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 Optimiza...
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? ...
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 ...
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_Bo...
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