Hill Climbing Search Solved Example using Local and Global Heuristic Function by Dr. Mahesh Huddar

Summary

This video tutorial explains the Hill Climbing algorithm's application in transitioning from an initial state to a goal state using both local and global heuristic functions. It illustrates the process with a block-stacking example, highlighting the limitations of local heuristics leading to a local maximum and demonstrating how global heuristics can guide the algorithm to the optimal solution. The explanation clarifies the use of heuristic functions in overcoming local maxima and achieving the goal state.

Takeaways

• 📚 The video discusses the application of the hill climbing algorithm using both local and global heuristic functions to transition from an initial state to a goal state.
• 🔍 The example given involves moving blocks labeled A, B, C, and D to their correct positions on top of each other to reach the goal state.
• 🤖 Local heuristic functions consider immediate consequences and reward blocks that are resting on the correct block with a +1, while incorrectly placed blocks receive a -1.
• 🌐 Global heuristic functions take into account the overall support structure of each block, rewarding correct placements with +1 and penalizing incorrect ones with -1.
• 🔢 The start state's value is calculated by assigning points based on the local heuristic function, resulting in a total value of 0 for the given example.
• 🎯 The goal state's value is calculated as +4 using the local heuristic function, indicating all blocks are correctly placed.
• 🚫 A disadvantage of using local heuristic functions is the potential to reach a local maximum, where no further improvement is possible, as demonstrated when moving block D.
• 🔄 To overcome local maxima, the video switches to using a global heuristic function, which considers the entire structure of block placement.
• 📉 The initial state's value using the global heuristic function is -6, indicating that none of the blocks are correctly placed.
• 📈 By applying operators and moving blocks according to the global heuristic function, the algorithm successfully reaches the goal state with a value of +6.
• 🛠 The video illustrates the process of using hill climbing with heuristic functions to find a solution path from the start state to the goal state in a block puzzle scenario.

Q & A

What is the Hill Climbing algorithm?

The Hill Climbing algorithm is a heuristic search algorithm that aims to find the peak of a cost function, which represents the solution to a problem. It iteratively moves to the best local solution until it reaches a peak, which may or may not be the global optimum.

What is the difference between a local and a global heuristic function?

A local heuristic function considers only the immediate consequences of a move to decide the next step, whereas a global heuristic function takes into account the overall state of the problem to guide the search towards the goal.

What is the initial state in the context of the given script?

The initial state is the starting configuration of the blocks where the goal is to rearrange them so that each block is on top of the block it should be, according to the problem's goal state.

What is the goal state in the described scenario?

The goal state is the final configuration where block A is on the ground, block B is on top of A, block C is on top of B, and block D is on top of C.

How does the local heuristic function assign rewards in the given example?

The local heuristic function assigns a plus one reward for each block that is resting on the block it is supposed to be on, and a minus one reward if it is not in the correct position.

What is the problem with using only a local heuristic function in the script's example?

The problem with using only a local heuristic function is that it can lead to a local maximum, where no further improvements can be made based on immediate consequences, thus potentially failing to reach the global optimum or goal state.

How does the global heuristic function differ in assigning rewards compared to the local heuristic?

The global heuristic function assigns rewards based on the correct support structure of each block. It gives a plus one reward for each block with the correct support and a minus one reward for each block with an incorrect support structure.

What is the advantage of using a global heuristic function over a local heuristic function?

The advantage of using a global heuristic function is that it considers the overall state of the problem, which can help avoid local maxima and provide a better chance of reaching the global optimum or the goal state.

What does the script illustrate about the process of moving from the initial state to the goal state using heuristic functions?

The script illustrates that by applying different heuristic functions—local and global—one can evaluate the current state and choose the best next move. It shows that sometimes a local heuristic might not be sufficient, and a global heuristic might be necessary to reach the goal state.

What is the final outcome of applying the global heuristic function in the script's example?

The final outcome is that the algorithm successfully moves from the initial state with a value of minus six to the goal state with a value of plus six, indicating that all blocks are in their correct positions.