Assume that you are given an equation ax^4+bx^3+cx+d = 25. You are asked to find a suitable solution for x, a, b, c and d. Use genetic algorithm to model your problem. Define your population, initialization, parent selection, fitness, and other required steps. aksam 8:42
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- Fibonacci numbers F1, F2, F3, . . . are defined by the rule: F1 = F2 = 1 and Fk = Fk−2 + Fk−1 for k > 2. Lucas numbers L1, L2, L3, . . . are defined in a similar way by the rule: L1 = 1, L2 = 3 and Lk = Lk−2 + Lk−1 for k > 2. Show that Fibonacci and Lucas numbers satisfy the following equality for all n ≥ 2 Ln = Fn−1 + Fn+1.Exercise 2. Here is a classic geometric problem, in the same application domain as the Center Selection problem: Given n points with Cartesian coordinates (₁, 3) in the plane, and positive weights w, find one(!) point (x, y) that minimizes the weighted sum of the Euclidean distances to the given points. For formal clarity: We want to minimize n Σwi i-1 n •√(x- i-1 (x − x)² + (y - y₁)². This problem is at least not very easy to solve exactly. In the following we therefore propose a rough but rather quick and simple approximation algorithm: Instead of the Euclidean distance, take the Manhattan distance and minimize 1 w₁(x − x₂|+|y-yil). 2.1. Explain how the point that minimizes the weigthed sum of Manhattan distances can be found in polynonial time. That is: Sketch an algorithm, argue why it is correct, and explain your time bound. Try to keep the time bound as low as possible. 2.2. Show that this algorithm has an approximation ratio √2. More specifi- cally: The point found by the…Machine Learning Problem Perform the optimization problem of finding the minimum of J(x) = (2x-3)2 by: (i) defining theta, J(theta), h(theta) as defined in the Stanford Machine Learning videos in Coursera; (ii) plotting J(theta) vs theta by hand then use a program (iii) determining its minimum using gradient descent approach starting from a random initial value of theta = 5. Perform the search for the minimum using the gradient descent approach by hand calculations, i.e., step 1, step 2, etc. showing your work completely
- There are n bacteria and one virus in a Petri dish. Within the first minute, the virus kills one bacterium and produces another copy of itself, and all of the remaining bacteria reproduce, making 2 viruses and 2(n-1) bacteria. In the second minute, each of the viruses kills a bacterium and produces a new copy of itself, resulting in 4 viruses and 2(2(n-1)-2)) = 4n - 8 bacteria. Again, the remaining bacteria reproduce. This process continues every minute. Will the viruses eventually kill all the bacteria? If so, give an algorithm that computes how many steps it will take. How does the running time of your algorithm depend on n?Genetic algorithms are a particular class of evolutionary algorithms that use techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover (also called recombination).a) Optimization is a process that finds a best, or optimal, solution for a problem. Explain in your own words the three factors that are centered on optimization problems in genetic algorithms and illustrate your answers with appropriate examples. AN(6)b) In your own words, clearly discuss the five applications of genetic algorithms and provide appropriate examples to explain your answers.CR(7)c) Explain in details with practical examples how one-point crossover and two-point crossover operators work in your own words.Using Genetic Algorithms, we are required to solve the problem of finding out what a good car is. The information we have is as follows:Car Brand: Toyota, BMW, MercedesCar Engine: V6, V8 and normalCar Compact Size: small, medium, bigCar style: sport, normal iii. Propose some suitable values of those parameters for this problem. Provide a short explanation for each. iv. Provide the genetic algorithm pseudocode that will be followed.
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- A given system of linear equations Ax = b can be solved using Gaussian elimination. For the following A's and b's, perform as indicated: Problem 1: (3 1 2 A1 = 4 2 8 2 4 4. xv1= y b1 = 1 Problem 2: 12 1 2 3 3 4 x1 x2 Xv2= x3 A2 = b= 0 3 3 0 2 1 -4. x4 Script e H Save C Reset I MATLAB Documentation 1 %Encode A1, b1 and x1 as the vector of unknowns. 2 A1 = 3 b1 = 4 syms 5 xv1 = 6 7 %Check the size of A, set it as m1 and n1 8 [m1, n1] - 9 10 %Augment A and b to form AM1 11 AM1 = 12 13 %Solve the Reduced Rwo Echelon of AM1. 14 RREFA1 = 15 16 %Collect the last column and set as bnew1, set the remaining elements as Anew1 17 bnew1= 18 Anew1 = 19 20 %Check if Anew is an identity matrix, if it is, bnew is the solution 21 if Anew1 =eye(m1, n1) 22 Root1 - bnew1 23 else 24 display("No Solution") 25 end 26Correct answer will be upvoted else Multiple Downvoted. Computer science. Petya coordinated a peculiar birthday celebration. He welcomed n companions and relegated an integer ki to the I-th of them. Presently Petya might want to give a present to every one of them. In the close by shop there are m one of a kind presents accessible, the j-th present expenses cj dollars (1≤c1≤c2≤… ≤cm). It's not permitted to purchase a solitary present more than once. For the I-th companion Petya can either get them a present j≤ki, which costs cj dollars, or simply give them cki dollars straightforwardly. Assist Petya with deciding the base all out cost of facilitating his get-together. Input The originally input line contains a solitary integer t (1≤t≤103) — the number of experiments. The main line of each experiment contains two integers n and m (1≤n,m≤3⋅105) — the number of companions, and the number of interesting presents accessible. The accompanying line contains n integers…The world monarch in the new post-apocalyptic world is extremely worried about the birth rate. She therefore orders that every family must have at least one female or else pay hefty fines. What will the gender ratio of the next generation be if all families adhere to this policy, which requires them to keep having children until they have one girl, at which time they immediately stop? (Presume that all pregnancies have an equal chance of producing a male or a girl.) Write a computer simulation of this problem after you have rationally resolved it.