[Solved]-Q4 Following Algorithms State Justify Whether Guaranteed Converge Global Maximum Assume St Q37160162

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Q4 (a) For each of the following algorithms, state and justify whether it is guaranteed to converge to the global maximum. Assume that the state space is finite. i. Hill-climbing from a randomly chosen initial condition. [2 Marks] ii. Simulated annealin 2 Marks] iii. Genetic algorithm search. 2 Marks] (b) Identify a shortcoming of hill climbing algorithms. [1 Mark] (c) In Simulated Annealing, only one move is evaluated in each iteration. i. How is that move selected? ii. Argue whether an evaluated move is always discarded if it is worse than the current state and another move is chose. iii. Is it possible to get stuck in a local maximum in Simulated Annealing? 3 Marks] (d) Describe the operation procedure of a Genetic Algorithm (GA) including [5 Marks] (e) A genetic algorithm uses chromosomes of the form – abcdefgh with a each of the main components/elements of GA fixed length of eight genes. Each gene can be any digit between O and 9. The fitness of individual x be calculated as: x)-(a+b) – (cd)+ le+D-(g+ h) The initial population consists of 4 individuals with the following Ху 65413532 x2- 8712660 x,-23921285 x4-41852094 i. By showing your working, evaluate the fitness of each individual and 2 Marks] arrange them in order with the fittest first and the least fit last. Show the result of the following crossover operations: a. Cross the fittest two individuals using one-point crossover at the middle ii. point l Mark] b. Cross the 2nd and 3rd fittest individuals using a two-point crossover [1 Mark] c. Cross the first and third fittest individuals (ranked 1 and 3rd usinga [1 Mark] iii. Determine whether the overall fitness has improved by evaluating the fitness (points b and f). uniform crossover. of the new population of the six offspring individuals produced by the [2 Marks] iv. By looking at the fitness function and considering that genes can only be crossover operations in question 4(e).ii above. digits between 0 and 9, find the chromosome representing the optimal Mark] v. Explain whether it is possible to reach the optimal solution without the 2 Marks] solution (i.e. with the maximum fitness). mutation operator? Show transcribed image text Q4 (a) For each of the following algorithms, state and justify whether it is guaranteed to converge to the global maximum. Assume that the state space is finite. i. Hill-climbing from a randomly chosen initial condition. [2 Marks] ii. Simulated annealin 2 Marks] iii. Genetic algorithm search. 2 Marks] (b) Identify a shortcoming of hill climbing algorithms. [1 Mark] (c) In Simulated Annealing, only one move is evaluated in each iteration. i. How is that move selected? ii. Argue whether an evaluated move is always discarded if it is worse than the current state and another move is chose. iii. Is it possible to get stuck in a local maximum in Simulated Annealing? 3 Marks] (d) Describe the operation procedure of a Genetic Algorithm (GA) including [5 Marks] (e) A genetic algorithm uses chromosomes of the form – abcdefgh with a each of the main components/elements of GA fixed length of eight genes. Each gene can be any digit between O and 9. The fitness of individual x be calculated as: x)-(a+b) – (cd)+ le+D-(g+ h) The initial population consists of 4 individuals with the following Ху 65413532 x2- 8712660 x,-23921285 x4-41852094 i. By showing your working, evaluate the fitness of each individual and 2 Marks] arrange them in order with the fittest first and the least fit last. Show the result of the following crossover operations: a. Cross the fittest two individuals using one-point crossover at the middle ii. point l Mark]
b. Cross the 2nd and 3rd fittest individuals using a two-point crossover [1 Mark] c. Cross the first and third fittest individuals (ranked 1 and 3rd usinga [1 Mark] iii. Determine whether the overall fitness has improved by evaluating the fitness (points b and f). uniform crossover. of the new population of the six offspring individuals produced by the [2 Marks] iv. By looking at the fitness function and considering that genes can only be crossover operations in question 4(e).ii above. digits between 0 and 9, find the chromosome representing the optimal Mark] v. Explain whether it is possible to reach the optimal solution without the 2 Marks] solution (i.e. with the maximum fitness). mutation operator?

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Answer to Q4 (a) For each of the following algorithms, state and justify whether it is guaranteed to converge to the global maximu… . . .