Artificial intelligence homework help

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Artificial intelligence homework help

  1. 1. 1 Game Playing (a) UsetheMinimaxalgorithmtocomputetheminimaxvalueat each node for the game tree below. 4 -11 1 1 14 1 -15 8 -15 -11 -11 -5 -11 -12 -12 5 4 5 5 5 10 -6 14 -6 4 4 9 4 -13 -13 3 min max min max (b) UseAlpha-BetaPruningtocomputetheminimaxvalueateach node for the game tree below, assuming children are visited left to right. Show the alpha and beta values at each node. Show which branches are pruned. 1 ARTIFICIAL INTELLIGENCE Our online Tutors are available 24*7 to provide Help with Artificial Intelligence Homework/Assignment or a long term Graduate/Undergraduate Artificial Intelligence Project. Our Tutors being experienced and proficient in Artificial Intelligence ensure to provide high quality Artificial Intelligence Homework Help. Upload your Artificial Intelligence Assignment at ‘Submit Your Assignment’ button or email it to info@assignmentpedia.com. You can use our ‘Live Chat’ option to schedule an Online Tutoring session with our Artificial Intelligence Tutors.
  2. 2. −∞, ∞ −∞, ∞ −∞, ∞ −∞, ∞ 8 -14 −14, ∞ -5 -13 −∞, −13 −∞, −13 15 15 pruned 6 4 −13, ∞ −13, ∞ −13, ∞ -12 -1 −12, ∞ 2 15 −13, 2 −13, 2 11 0 0, 2 10 13 min max min max Figure 1: Upon Arrival 2, ∞ −∞, −13 −13, ∞ −∞, −14 8 -14 −14, −13 -5 -13 −13, −13 −∞, −13 15 15 pruned 6 4 −13, 2 2, ∞ −13, −12 -12 -1 −12, 2 2 15 2, 2 −13, 0 11 0 0, 2 10 13 min max min max Figure 2: Upon Departure 2
  3. 3. 2 A∗ A B C D E F G 8 3 9 2 7 10 3 5 1 1 (a) Inthefigureabove,letAbethestartstateandEbethegoal state. The weights on the edges reflect the cost to traverse them. Show the ordered contents of the open and closed queues for each stage of the A∗ algorithm. The heuristic function values are given by the table below. node A B C D E F G h(n) 10 3 9 5 0 1 1 The following shows the state of the queues after each round. The queue objects are in the form XY (z) where X is the node identity, Y is the pre- ceding node in the path under consideration to reach X, and z is the value f(z) = g(z) + h(z) where h is given above and g is the cost of the path being considered that leads to X. Open Closed {A(10)} {} {BA(11), DA(14)} {A(10)} {DA(14), EB(15), CB(20)} {A(10), BA(11)} {FD(13), EB(15), CB(20)} {A(10), BA(11), DA(14)} {GF (14), EB(15), CB(20)} {A(10), BA(11), DA(14), FD(13)} {EG(14), CB(20)} {A(10), BA(11), DA(14), FD(13), GF (14)} After this round, EG is pulled off the queue and the algorithm ends. Fol- lowing backpointers will yield the path ADFGE. 3
  4. 4. (b) Whatpathisproducedbyrunningthebestfirstgreedyalgo- rithm? A → B → E This can be seen by repeating the above algorithm but using f = h to compute the z value. Open Closed {A(10)} {} {BA(3), DA(5)} {A(10)} {EB(0), DA(5), CB(9)} {A(10), BA(3)} 3 Simulated Annealing f(x) = max{(4−|x|, 2−|x−6|, 2−|x+6|}. It has three peaks with one forming a unique global maximum. Perform 8 rounds of simulated annealing using 4 as your start point, letting the temperature decrease by a factor of 0.9 each round. A point x has four successors: {x + 2, x + 1, x − 1, x − 2}. Show all of your work, including the current point, the successor chosen, the round temperature, and the probability of changing position given the successor and the temperature. Answers will respect the following constraints. 1. 0 ≤ i ≤ 7 2. Xi+1 ∈ {Xi, Yi} 3. |Yi − Xi| ∈ {1, 2} 4. Ti = 2(0.9)i 5. Pi ∈ {1, e−1/Ti , e−2/Ti } 6. Pi = min{1, e(f(Yi)−f(Xi))/Ti } 7. F(Yi) ≥ f(Xi) ⇒ Xi+1 = Yi, Pi = 1 This can also be interpreted using the following table. Note that here we assume an initial temperature of 2. As this was not specified in the original assignment wording, it will not be enforced during grading. 4
  5. 5. i Xi Yi Ti Pi 0 4 Y0 2.0000 {1} 1 {X0, Y0} Y1 1.8000 {1, 0.3292, 0.5738} 2 {X1, Y1} Y2 1.6200 {1, 0.2910, 0.5394} 3 {X2, Y2} Y3 1.4580 {1, 0.2537, 0.5037} 4 {X3, Y3} Y4 1.3122 {1, 0.2178, 0.4667} 5 {X4, Y4} Y5 1.1810 {1, 0.1839, 0.4288} 6 {X5, Y5} Y6 1.0629 {1, 0.1523, 0.3903} 7 {X6, Y6} Y7 0.9566 {1, 0.1236, 0.3516} 8 {X7, Y7} My sample run through the algorithm produced the following answer. i Xi Yi Ti Pi move? 0 4 3 2.0000 1 yes 1 3 5 1.8000 1 yes 2 5 3 1.6200 1 yes 3 3 4 1.4580 0.5037 yes 4 4 5 1.3122 1 yes 5 5 6 1.1810 1 yes 6 6 7 1.0629 0.3903 no 7 6 5 0.9566 0.3516 no 8 6 This particular run converged to the local maximum at 6. 5 visit us at www.assignmentpedia.com or email us at info@assignmentpedia.com or call us at +1 520 8371215

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