Ordered Landmarks in Planning

Abstract

Many known planning tasks have inherent constraints concerning the best order in which to achieve the goals. A number of research efforts have been made to detect such constraints and to use them for guiding search, in the hope of speeding up the planning process. We go beyond the previous approaches by considering ordering constraints not only over the (top-level) goals, but also over the sub-goals that will necessarily arise during planning. Landmarks are facts that must be true at some point in every valid solution plan. We extend Koehler and Hoffmann's definition of reasonable orders between top level goals to the more general case of landmarks. We show how landmarks can be found, how their reasonable orders can be approximated, and how this information can be used to decompose a given planning task into several smaller sub-tasks. Our methodology is completely domain- and planner-independent. The implementation demonstrates that the approach can yield significant runtime performance improvements when used as a control loop around state-of-the-art sub-optimal planning systems, as exemplified by FF and LPG.

Monotone Temporal Planning: Tractability, Extensions and Applications

“…The first one is the conception of heuristic functions to guide search algorithms (Richter, Helmert & Westphal, 2008;Richter & Westphal, 2010;Helmert & Domshlak, 2009). Another use of landmarks is to partition the problem into easier subproblems whose goals are disjunctions of landmarks (Hoffmann, Porteous & Sebastia, 2004;Sebastia, Onaindia & Marzal, 2006). More recently, Vernhes, Infantes and Vidal (2013) define a landmark-based meta best-first search algorithm.…”

“…However, some landmarks can be found more efficiently by using various techniques: Porteous and Cresswell (2002) and Hoffmann, Porteous and Sebastia (2004) present methods for detecting landmarks and relations between landmarks based on backchaining from the goals in the relaxed planning graph, whereas Zhu and Givan (2003) use forward propagation in the same graph and Richter, Helmert and Westphal (2008) use the domain transition graph, a graph whose nodes represent the possible values of the variable and edges represent the possible transitions between values induced by actions.…”

“…Different orderings between landmarks have been studied in non-temporal planning. Some of these orderings are guaranteed to hold in every solution-plan and do not prune the solution space (they are sound): "Natural" (Koehler & Hoffmann, 2000), "Necessary" and "Greedy-necessary" (Hoffmann, Porteous & Sebastia, 2004). The natural ordering is the most general and then greedy-necessary ordering and necessary ordering.…”

“…An obvious application of temporal relaxation is the detection of action landmarks by the following classic technique which applies to any valid relaxation (Hoffmann, Porteous & Sebastia, 2004;Cooper, de Roquemaurel & Régnier, 2011). Let P [-a] represent the planning problem P without a particular action a.…”

Divide-and-Evolve: a Sequential Hybridization Strategy Using Evolutionary Algorithms

“…The idea to divide the plan trajectory into small chunks has been studied with success in [11]. The authors have shown the existence of landmarks 4 and the impact of ordering them on search efficiency.…”