Using the numbers in brackets as heuristic values, what is the search path from node A to node I using the Hill Climbing algorithm?

Question

BlackTom AI · Accepted Answer

First, identify the heuristic values at each node shown: A(10) has neighbors B(5) and C(8). B has D(3) and E(4). D has G(6) and H(7). C has F(5). F has J(1) and K(0). I is under E, but the immediate paths available from A must follow Hill Climbing rules.

Option 1: A – B – D
- From A, Hill Climbing selects the neighbor with the smallest heuristic value. Between B(5) and C(8), B is chosen.
- From B, again pick the neighbor with the smallest heuristic: D(3) vs E(4) gives D as the choice.
- Now at D, consider its neighbors G(6) and H(7). Both have higher heuristic values than D(3), so Hill Climbing would not move to either since they are worse than the current node. Since there is no neighbor with a better (lower) heuristic, the algorithm would stop at D in this greedy step.
- Therefore, the search path under pure Hill Climbing up to termination is A → B → D. It does not proceed to I, because the algorithm would stop when no neighboring node improves the current state.

Option 2: A – B – C – D – E – F – G – H – I
- This path tries to move from B to C, but C is not a direct neighbor of B in the given tree, so this sequence is not a valid Hill Climbing step-by-step path.
- Even if it were, Hill Climbing would not backtrack through a longer chain like this unless explicitly allowed by a different variant (not standard Hill Climbing).

Option 3: A – C – F – J
- From A, the correct first move is to B (5) rather than C (8) since B has the smaller heuristic. Moving to C first contradicts the Hill Climbing choice at the root.
- Therefore, this path violates the basic greedy choice rule from the initial node.

Option 4: A – B – D – G
- This follows the same initial steps as option 1: A → B (choose B over C), B → D (choose D over E).
- From D, the next step would be to a neighbor with a lower heuristic than D, but both G(6) and H(7) are higher than D(3). Hill Climbing would stop at D rather than proceed to G.
- Hence A – B – D – G represents a move to a worse state, which is not consistent with Hill Climbing’s rule of only moving to a better neighbor.

Conclusion: Based on standard Hill Climbing rules (always move to the neighboring node with the lowest heuristic value, and stop when no neighbor has a lower heuristic than the current node), the valid search path until termination is A – B – D. The other options violate the neighbor-choice rule, misrepresent valid neighbor relationships, or require backtracking not allowed in basic Hill Climbing.

Introduction to Artificial Intelligence (082025-VTK)

Using the numbers in brackets as heuristic values, what is the search path from node A to node I using the Hill Climbing algorithm?

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