Can you please help me with the answer for the following question as a conitnuation for this Hill Climing questions. Part D: Discussion After completing your code, you will need to prepare a report in PDF format with answers to the following questions: 1. Did the hill-climbing algorithm find the globally-optimum solution to the objective function? Why or why not? 2. Did the random restart algorithm find the globally-optimum solution to the objective function? Why or why not? 3. Did the simulated annealing algorithm find the globally-optimum solution to the objective function? Why or why not? 4. Discuss anything else you have observed about the strengths and weaknesses of each algorithm. Which algorithm performed the best overall? Part E: 1. Implement an improvement to the hill-climbing algorithm and demonstrate that it is able to find a better solution. a. First-choice hill climbing: Generate successors randomly until one is generated that is better than the current state. b. Local beam search: Begin with k randomly generated states. At each step, all the successors of all k states are generated. If none of them are more optimal, the algorithm halts. Otherwise, select the k best successors from the complete list and repeat. c. Stochastic beam search: Similar to beam search, except that k successors are chosen at random, with the probability of choosing a given successor being an increasing function of its value. 2. Design your own objective function that has one or more local optima and one global optimum. This function could be based on a natural phenomena, physical law, or mathematical equation. Determine whether any or all of the local search algorithms implemented in this assignment are able to find the global optimum for your custom objective function. 3. Open-ended. Implement any visualization or algorithmic improvements to the program. In your report, justify the change and explain how it is advantageous compared to the original program.