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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JAYA Optimization Algorithm Step-by-Step with Numerical Example ~xRay Pixy
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JAYA Optimization Algorithm Step-by-Step with Numerical Example
JAYA Algorithm is very simple and new optimization algorithm used for solving constrained and unconstrained optimization problems.
Jaya: An Advanced Optimization Algorithm.
JAYA Algorithm is very simple and new optimization algorithm used for solving constrained and unconstrained optimization problems. It is Simple, Unique and Powerful Optimization Algorithm.
JAYA algorithm is introduced by R.V. Rao in 2016. JAYA is a SANSKRIT word it means VICTORY. That's why this algorithm always tries to get closer to the source (i.e., reaching the BEST Solution) and at the same time tries to avoid the WORST Solution. All values at the end of iteration are maintained and these values become the INPUT to the next iteration. JAYA Algorithm is simpler than TLBO (Teaching Learning Based Optimization) algorithm. Author also compared this algorithm with latest approaches and found JAYA algorithm at RANK 01 for BEST and MEAN solution for different Constrained Problems.
JAYA Algorithm KEY CONCEPT: It is based on the concept that solution obtained for any given problem should move towards the BEST Solution and should avoid WORST Solution.
ADVANTAGES: Using JAYA optimization algorithm we can solve different Engineering Design Problems, Constrained and Unconstrained optimization problems. We can use this algorithm in different research areas such as: Economic Load Dispatch Problems, Optimal Power Flow Solution, In Linear Power System (to find interconnection), In Modern Matching Process, and Optimization Heat Exchanger.
JAYA Algorithm : PSEUDOCODE
Initialize Parameters [JAYA Algorithm, Optimization Problem
Initialize Population Size (N) Randomly.
Calcuate Fitness Values for each candidate.
Sort the Population (Best and Worst Soltuion respectively).
Set Current_Iteration = 1
Check While (Current_Iteration <= Maximum_Iteration)
For i = 1,2,...,N do
For j = 1,2,...,D do
Set r1, r2 [0,1].
Using Equation update values for each candidate.
End For
If (New Solution)<=(Old Solution)
Update Solution.
End If
End For
Current_Iteration = Current_Iteration + 1.
End While
JAYA ALGORITHM Numerical Example
Step 01: Initialize the Algorithm Parameters.
Suppose, Population Size = 05;
Design Variable = 02;
Maximum Iteration = 06;
LB = -100, UB =100;
Step 02: Initialize Population for 5 individuals.
Step 03: Using Cost Function Calculate the Fitness values for each individual.
Here, sphere function is used for the Cost Calculation.
Step 04: Select Best and Worst Solution in current population.
Step 05: Update Current Solution [Position, Fitness Values].
Step 06: Compare New Solution with Old Solution and Replace if New solutions are better else no change.
Step 07: Find out Best and Worst Solution among all.
Step 08: Increment counter. If stopping criteria is not satisfy repeat loop.
Step 09: Display Best Solution obtained.
Swarm Intelligence based Population-based MetaheuristicsWATCH NOW!
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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...
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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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