Overview
Multi-Goal A* is a heuristic search method for multi-target pathfinding. It works by searching toward the best among several goals using admissible goal estimates.
ExtendedSource checked
Multi-Goal A*
Multi-Goal A* addresses multi-target pathfinding by searching toward the best among several goals using admissible goal estimates.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Pathfinding
- Difficulty
- Intermediate
- Family
- Heuristic Search
- Tier
- Extended
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 0
- Relationships
- 1
- Code example
- Ready
- Visualization
- Ready
Core Concepts
multi-target pathfindingheuristic searchpathfinding
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(1)
Average
O(n)
Worst
O(n)
Space
O(1)
When to Use
- Use Multi-Goal A* when solving multi-target pathfinding and you want to benefit from searching toward the best among several goals using admissible goal estimates.
- Choose it when O(n) average/worst-case time and O(1) memory match your workload profile.
- Prefer it over Visibility Graph Roadmap or 0-1 BFS when the problem structure favors multi-target pathfinding.
When Not to Use
- Avoid when path costs or obstacles change in ways the method cannot update efficiently.
- Avoid when approximate paths are unacceptable and the method does not guarantee optimality.
What It Does
- Computes multi-target pathfinding within Heuristic Search workloads (O(n) time, O(1) space).
- Works by searching toward the best among several goals using admissible goal estimates.
- Maintains key invariants across multi-target pathfinding, heuristic search, pathfinding.
Use Cases
- Production and research workloads requiring multi-target pathfinding via searching toward the best among several goals using admissible goal estimates.
- Heuristic Search pipelines where O(n) time and O(1) space fit system constraints.
- Engineering comparisons against Visibility Graph Roadmap and 0-1 BFS when tuning multi-target pathfinding.
Inputs
- Heuristic Search input instance for multi-target pathfinding
- Configuration parameters controlling multi-target pathfinding
Outputs
- Computed multi-target pathfinding solution produced by Multi-Goal A*
- Diagnostic state over multi-target pathfinding and heuristic search
Pseudocode
- 1.Initialize the search space, start/goal states, and cost/priority tables for Multi-Goal A*.
- 2.Insert the initial state into the open frontier or roadmap with its baseline cost and heuristic estimate.
- 3.Expand or sample candidate transitions by searching toward the best among several goals using admissible goal estimates.
- 4.Update path costs, parent pointers, or conflict constraints whenever an improved trajectory is found.
- 5.Reconstruct and return the collision-free path from start to goal once the termination criterion holds.
Canonical Example
- Input
- Heuristic Search input instance for multi-target pathfinding configured for a representative multi-target pathfinding test case
- Output
- Computed multi-target pathfinding solution produced by Multi-Goal A* satisfying Multi-Goal A* invariants
- Explanation
- Multi-Goal A* processes the input by searching toward the best among several goals using admissible goal estimates, tracking multi-target pathfinding and heuristic search to produce the verified multi-target pathfinding result.
Implementation Notes
- Separate search state from world state so changes can be tested.
- Use small maps with known optimal answers before large scenarios.
- Track whether returned paths are optimal, bounded, or heuristic.
Common Pitfalls
- Using an inadmissible heuristic where optimality is expected.
- Ignoring dynamic obstacles, time-dependent costs, or changing edge weights.
- Testing only open grids and missing narrow-passage cases.
Interactive Mechanism Walkthrough
2D Grid Wavefront & TrajectoryShow searching toward the best among several goals using admissible goal estimates on a small multi-target pathfinding example.
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Step 1 of 5: Initialize the search space, start/goal states, and cost/priority tables for Multi-Goal A*.
pathfinding-mechanismNotes
Multi-Goal A* operates in O(n) time and O(1) space within the Heuristic Search family. Often compared with Visibility Graph Roadmap and 0-1 BFS.
Sources (1)
What each reference supports for this entry.
Artificial Intelligence: A Modern Approach
BookAI search reference supporting Multi-Goal A* heuristic evaluation, frontier ordering, replanning behavior, or completeness tradeoffs.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageConceptual neighborGreedy Best-First Search
Both use heuristic priorities to guide search, while Multi-Goal A* evaluates termination against multiple targets.
Tags
PathfindingGraph