Thank you for sharing this comprehensive guide! The explanation of the Hill-Climbing Algorithm is very clear, especially how it iteratively moves from the current state to a neighboring state that improves the objective function. I appreciate the inclusion of advantages and limitations, as it helps to understand where the algorithm works best and where it might fail, such as getting stuck in local maxima.
The step-by-step breakdown makes it easy to follow, and the examples, like minimizing error in machine learning or solving routing problems, show practical applications. Including a visual diagram could further enhance understanding, particularly for illustrating the current state, neighbors, and movement toward the optimum.
Overall, this is an excellent summary for anyone learning optimization using hill-climbing!