The LAMA Planner: Guiding Cost-Based Anytime Planning with Landmarks

LAMA is a classical planning system based on heuristic forward search. Its core feature is the use of a pseudo-heuristic derived from landmarks, propositional formulas that must be true in every solution of a planning task. LAMA builds on the Fast Downward planning system, using finite-domain rather than binary state variables and multi-heuristic search. The latter is employed to combine the landmark heuristic with a variant of the well-known FF heuristic. Both heuristics are cost-sensitive, focusing on high-quality solutions in the case where actions have non-uniform cost. A weighted A* search is used with iteratively decreasing weights, so that the planner continues to search for plans of better quality until the search is terminated. LAMA showed best performance among all planners in the sequential satisficing track of the International Planning Competition 2008. In this paper we present the system in detail and investigate which features of LAMA are crucial for its performance. We present individual results for some of the domains used at the competition, demonstrating good and bad cases for the techniques implemented in LAMA. Overall, we find that using landmarks improves performance, whereas the incorporation of action costs into the heuristic estimators proves not to be beneficial. We show that in some domains a search that ignores cost solves far more problems, raising the question of how to deal with action costs more effectively in the future. The iterated weighted A* search greatly improves results, and shows synergy effects with the use of landmarks.

💡 Research Summary

The paper presents LAMA (Landmark‑Aware Multi‑heuristic Planner), a classical planning system that achieved the best results in the sequential satisficing track of the International Planning Competition (IPC) 2008. Built on top of the Fast Downward framework, LAMA combines two cost‑sensitive heuristics— a landmark‑derived heuristic and a variant of the well‑known FF heuristic— within a multi‑heuristic forward‑search architecture, and it employs an iterated weighted A* search strategy to produce high‑quality plans in an anytime fashion.

Core Concepts

1. Landmark Heuristic: Landmarks are propositions that must hold in every valid plan. LAMA extracts landmarks, builds a partial order among them, and estimates the minimum cost required to achieve each yet‑unreached landmark from the current state. The sum of these minimal costs constitutes a lower‑bound heuristic (h_land) that guides the search toward states that satisfy critical intermediate goals.
2. Cost‑Sensitive FF Heuristic: The classic FF heuristic is adapted to incorporate action costs. During the construction of a relaxed planning graph, each action is assigned its true cost, and the relaxed plan’s total cost becomes the heuristic value (h_FF). This yields a cost‑aware estimate of the distance to the goal.
3. Multi‑Heuristic Search: For every node LAMA computes both h_land and h_FF. The node’s evaluation function is f = g + w·h, where g is the accumulated real cost and w is the current weight. The open list is ordered by the smaller of the two f‑values, allowing the planner to exploit whichever heuristic is currently more informative.

Iterated Weighted A*
LAMA starts with a relatively large weight (e.g., w = 5) to obtain a quick, albeit suboptimal, solution. After a solution is found, the weight is reduced (e.g., 5 → 3 → 1) and the search resumes, using the best solution found so far as an upper bound on g. This process repeats until a time limit is reached, delivering a sequence of improving plans— the hallmark of an anytime planner.

Experimental Evaluation
The authors evaluated LAMA on the full set of IPC‑2008 benchmark domains (approximately 20 domains, including Satellite, Logistics, Driverlog, Blocksworld, etc.). They performed an ablation study with four configurations: (a) full LAMA (landmarks + cost‑FF + iterated weighted A*), (b) landmarks disabled, (c) cost‑FF disabled, and (d) both heuristics disabled (plain FF).

Key findings include:

• Landmarks dramatically increase coverage and reduce runtime across almost all domains. By explicitly representing necessary intermediate goals, the search space is pruned effectively.
• Incorporating action costs into the heuristic does not uniformly help. In several domains (notably Satellite and some logistics variants) the cost‑sensitive FF heuristic actually hurts performance, because it over‑penalises expensive actions and restricts the search to narrow corridors that may not contain a feasible plan.
• Iterated weighted A* consistently improves plan quality. The initial high‑weight phase yields a feasible plan quickly; subsequent lower‑weight phases refine it, often achieving near‑optimal cost without a dramatic increase in search time.
• A surprising observation is that a planner that completely ignores action costs sometimes solves more problems than a cost‑aware version, raising questions about how to integrate cost information more effectively.

Insights and Future Directions
The authors conclude that landmarks are the primary driver of LAMA’s success, while the current method of embedding costs into the FF heuristic is insufficient. They suggest several avenues for improvement: (1) develop more sophisticated cost‑aware heuristics (e.g., cost‑augmented planning graphs, cost‑weighted landmarks), (2) devise domain‑adaptive weight‑reduction schedules for weighted A*, possibly using learning techniques, and (3) explore hybrid strategies that switch between cost‑aware and cost‑agnostic search depending on the observed difficulty of a problem.

Overall, the paper provides a thorough description of LAMA’s architecture, a detailed empirical analysis of each component’s contribution, and a clear set of research questions that remain open for the planning community. The synergy between landmarks and iterated weighted A* emerges as a powerful paradigm for anytime, cost‑sensitive planning, while the challenges associated with cost integration highlight an important frontier for future work.