Consider the straight$-$line distances for the map of Romania $($Figure $3\mathrm{.}2)$ contained in Figure $3\mathrm{.}22.$ Assume that you are in Zerind and wish to travel to Bucharest. a$)$ Does Greedy Best$-$First Search using the straight$-$line distance heuristic find a solution? Explain. b$)$ Assume that we use an explored set along with Greedy Best$-$First Search. What is the order of nodes visited by the algorithm using the straight$-$line distance heuristic? What is the optimal path? Does the search find the optimal path? Problem $2$: A$*$ Search $(5$ pts$.)$ Consider the straight$-$line distances for the map of Romania $($Figure $3\mathrm{.}2)$ contained in Figure $3\mathrm{.}22.$ Assume that you are in Lugoj and want to go to Bucharest. What is the order of nodes visited by A$*$ Search using the straight$-$line distances heuristic? For each node visited, note the path distance traveled, the estimated distance to go$,$ and the total path estimate. What is the optimal path? Does the search find the optimal path? Problem $3$: Hill Climbing $[3$ pts$]$ a$)$ Explain the hill climbing algorithm. How does it explore the search space, and how does it choose the next move? b$)$ What are the advantages and disadvantages of hill climbing? Provide examples of scenarios where hill climbing may or may not be effective. Problem $4$: Simulated Annealing $[3$ pts$]$ a$)$ Describe the simulated annealing algorithm. How does it differ from hill climbing in terms of exploration? b$)$ Discuss the key parameters in simulated annealing, such as temperature and cooling schedule. How do these parameters impact the algorithm's performance? Problem $5$: Genetic Algorithms $[3$ pts$]$ a$)$ Briefly explain how genetic algorithms work. What are the three main components of a genetic algorithm? b$)$ Compare and contrast genetic algorithms with local search algorithms like hill climbing. In what types of problems are genetic algorithms more suitable?