Is incremental heuristic search always optimal?

Some algorithms provide optimality under stated assumptions; other variants use different quality guarantees. The specific method and conditions matter.

Does it only apply to robots?

No. The general idea applies to sequences of related search problems, although robotics is an important application area.

Is it the same as anytime search?

No. Anytime search concerns improving a solution with additional time; incremental search concerns reusing work across related problems.

AI Glossary / AI and machine learning / Intermediate

Incremental heuristic search

Definition

Incremental heuristic search solves a sequence of related search problems by reusing information from earlier searches and using a heuristic to guide the work. It is especially useful when a graph or the system's knowledge of it changes and a previous solution must be revised.

What it means

Ordinary heuristic search, such as A*, uses an estimate of remaining cost to focus exploration toward a goal. If the problem changes, starting the entire search again may repeat work that remains valid.

Incremental methods retain useful search information and update what the changes affect. The aim is to repair or adapt the solution more efficiently than recomputing everything from scratch, although the actual benefit depends on the changes and algorithm.

Examples include Lifelong Planning A* and D* Lite. They belong to a family of methods, so not every incremental search algorithm stores or updates the same quantities in the same way.

Incremental does not mean taking tiny physical movements, learning from streaming examples or always returning an immediate answer. It refers to reuse across related search problems. Separate terms such as real-time search and anytime search describe other properties.

How it works

Solve an initial search problem while retaining the information required by the chosen algorithm. This may include estimated path costs, predecessor relationships and a priority queue of states needing attention.

When edge costs or other relevant problem details change, identify the affected states. Some previous cost estimates remain valid, while others must be corrected and their consequences propagated.

Use the heuristic and update rules to focus the repair process. In methods such as Lifelong Planning A*, consistency relationships help determine which states require further processing.

Stop when the algorithm's conditions establish the required solution quality. Guarantees depend on assumptions about costs, heuristics and the particular variant. Reusing old information is beneficial only when it is kept consistent with the revised problem.

Three practical examples

1. A robot learns that a previously available corridor is blocked. An incremental planner revises its route using retained search information instead of necessarily rebuilding the entire plan from the beginning.

2. A route-planning simulation changes a small number of travel costs between queries. Researchers compare search reuse with repeated independent A* runs on the same sequence of changes.

3. A game-development experiment updates navigation costs as doors open or close. The team measures whether incremental repair helps under its actual map size and change frequency.

Think of it this way

Think of revising a journey plan after one road closes while keeping the parts of the map and reasoning that still apply. The analogy is limited because an algorithm must formally update affected costs and stopping conditions; simply retaining the old route and making a plausible detour is not enough to guarantee a best path.

Worked example

Suppose the current route S - A - G costs 2 plus 3, totaling 5. An alternative S - B - G costs 4 plus 4, totaling 8. Initially, the route through A is preferable.

Now the A - G edge cost changes from 3 to 10. The old route's cost becomes 12, making the route through B cheaper at 8. An incremental algorithm can use stored information about unaffected connections while updating the consequences of the changed edge.

This miniature example shows why repair is necessary and what can remain useful. It does not demonstrate a measured speedup: in a tiny graph, bookkeeping may cost as much as a new search, and large changes can invalidate much of the earlier work.

Illustrative case study

Fictional case: Oak Navigation Lab studies a mobile-robot simulator with changing obstacles. The team records a sequence of map updates and replays it for both incremental planning and fresh-search baselines.

Researchers measure total planning time, number of processed states and route cost. They include cases with a few local changes and cases with widespread changes, because the expected benefit of reuse differs.

The team verifies route validity after every update and keeps sensing errors separate from planning errors. This invented case illustrates fair comparison and correct state updates, not a guaranteed performance advantage for every robot or map.

Common misconceptions and mistakes

Mistake: Assuming incremental search means incremental machine learning. One reuses search work; the other updates a learned model from additional data.

Mistake: Believing reuse always makes the next search faster. Extensive changes and maintenance overhead can reduce or eliminate the benefit.

Mistake: Keeping old costs without checking consistency. Outdated search information can lead to invalid routes or incorrect quality claims.

Business use

Incremental heuristic search can help applications that repeatedly replan over related states, especially when changes are limited enough for previous computation to remain useful. Navigation and scheduling research provide natural settings for evaluation.

Business teams should assess the complete update workload rather than a single static query. Include how changes are detected, how quickly they reach the planner and what happens when the retained state becomes invalid. A fast repair algorithm cannot compensate for an inaccurate or outdated world model.

Check your understanding

An edge cost changes, but most of the graph remains the same. What is the main opportunity for an incremental planner?

Answer: Reuse valid previous search information and concentrate computation on the affected parts of the problem.

Related terms

Heuristic
Lifelong Planning A*
Shortest Paths
A* search
replanning
D* Lite
shortest path
search-state reuse

Learn next

Learn A* and admissible heuristics. Solve a small weighted graph, change one edge cost, and identify which earlier distance conclusions remain valid and which need to be reconsidered.

Weighted graph

Sources

Koenig, Likhachev, Liu and Furcy, Incremental Heuristic Search in Artificial Intelligence: https://publications.ri.cmu.edu/incremental-heuristic-search-in-artificial-intelligence. Lifelong Planning A* primary paper: https://www.cs.cmu.edu/afs/cs/Web/People/maxim/files/aij04.pdf. Primary research overview consulted; path calculation and fictional case are original.

Previous: Incremental Few-shot Learning Next: Indefinite reference