Regulatory Alerts2014-03-09
The detailed memorandum on the real estate financing initiative for the benefit of low- and middle-income people
The output table represents the probability of different events occurring at each level for both algorithms (Hill-Climbing and Random Search). Here, you can see that as the problem size increases, the success rate of finding the optimal solution using Hill-Climbing decreases significantly. On the other hand, the success rate of Random Search remains relatively constant across all problem sizes. For smaller problems (up to 40%), the success rate of Hill-Climbing is quite high, but as we go beyond this threshold, the chances of finding an optimal solution decrease dramatically. At 100%, both algorithms have a 100% success rate, which means they can always find the optimum solution for these problems. In contrast, Random Search has consistent performance across different problem sizes, with a slight improvement at larger scales (80-90% and above). This is because, as the problem size increases, the search space expands, making it more difficult to find an optimal solution using Hill-Climbing but not affecting the ability of Random Search to explore the entire search space. The results also show that even for very large problems (over 90%), there is still a chance for both algorithms to find the optimum solution, albeit at a much lower probability (around 14-15% for Hill-Climbing and around 20% for Random Search). Lastly, you can notice that the success rate of finding an optimal solution is always greater than or equal to the problem size percentage. This means that even when considering a small portion of the total search space (e.g., 30%), both algorithms have a chance to find the optimum solution.