Iterative deepening a* algorithm example
Posted: Wed Aug 16, 2023 11:53 am
The Iterative Deepening A* (IDA*) algorithm is a variant of the A* search algorithm that addresses the limitations of memory consumption in traditional A* search while still guaranteeing optimality. IDA* iteratively increases the search depth while performing a depth-first search, effectively trading off memory usage for increased computational time. Here's a simplified example of how the Iterative Deepening A* algorithm works:
Consider a grid-based pathfinding problem where you need to find the shortest path from the start node 'S' to the goal node 'G'. Each cell in the grid is either passable or impassable, and you can only move to adjacent passable cells (up, down, left, right).
Legend:
'S': Start node
'G': Goal node
'x': Impassable cell
Let's outline the steps of the Iterative Deepening A* algorithm for this example:
Initialization:
Initialize the start node 'S' and goal node 'G'.
Set the initial depth limit to 0.
Iterative Search:
Begin an iterative loop where you repeatedly perform a depth-limited search using A*.
For each iteration, increment the depth limit by 1 and perform a depth-first search using A* until the depth limit is reached.
Depth-Limited A Search:*
Perform A* search with a depth limit. In this example, we'll assume a depth limit of 1 for simplicity.
Expand nodes at each depth, considering only adjacent passable cells.
Calculate the f-cost (estimated total cost) for each expanded node.
Add nodes to the open list based on their f-cost.
Node Expansion and Goal Check:
If the goal node 'G' is reached at the current depth limit, the search is successful. The algorithm terminates, and you've found the optimal path.
Increment Depth Limit:
If the goal is not found at the current depth limit, increment the depth limit by 1 and repeat the depth-limited A* search.
Termination:
Continue the iterative loop until the goal node is found or until the depth limit exceeds a predefined maximum depth.
Path Reconstruction:
If the goal node is found, reconstruct the optimal path from the start node to the goal node using parent pointers.
The key idea of IDA* is to perform a series of depth-limited searches while gradually increasing the depth limit. This approach ensures that the algorithm explores progressively deeper parts of the search space while using a limited amount of memory. Although the example provided here is simplified, the actual implementation of IDA* involves more intricate details, such as heuristics, data structures, and optimizations.
Consider a grid-based pathfinding problem where you need to find the shortest path from the start node 'S' to the goal node 'G'. Each cell in the grid is either passable or impassable, and you can only move to adjacent passable cells (up, down, left, right).
Code: Select all
| S | | | |
| x | | x | |
| | | | |
| | x | | G |
'S': Start node
'G': Goal node
'x': Impassable cell
Let's outline the steps of the Iterative Deepening A* algorithm for this example:
Initialization:
Initialize the start node 'S' and goal node 'G'.
Set the initial depth limit to 0.
Iterative Search:
Begin an iterative loop where you repeatedly perform a depth-limited search using A*.
For each iteration, increment the depth limit by 1 and perform a depth-first search using A* until the depth limit is reached.
Depth-Limited A Search:*
Perform A* search with a depth limit. In this example, we'll assume a depth limit of 1 for simplicity.
Expand nodes at each depth, considering only adjacent passable cells.
Calculate the f-cost (estimated total cost) for each expanded node.
Add nodes to the open list based on their f-cost.
Node Expansion and Goal Check:
If the goal node 'G' is reached at the current depth limit, the search is successful. The algorithm terminates, and you've found the optimal path.
Increment Depth Limit:
If the goal is not found at the current depth limit, increment the depth limit by 1 and repeat the depth-limited A* search.
Termination:
Continue the iterative loop until the goal node is found or until the depth limit exceeds a predefined maximum depth.
Path Reconstruction:
If the goal node is found, reconstruct the optimal path from the start node to the goal node using parent pointers.
The key idea of IDA* is to perform a series of depth-limited searches while gradually increasing the depth limit. This approach ensures that the algorithm explores progressively deeper parts of the search space while using a limited amount of memory. Although the example provided here is simplified, the actual implementation of IDA* involves more intricate details, such as heuristics, data structures, and optimizations.