Showing papers on "Admissible heuristic published in 2014"

Heuristic Planning with Time and Resources

Abstract: We present an algorithm for planning with time and resources, based on heuristic search. The algorithm minimizes makespan using an admissible heuristic derived automatically from the problem instance. Estimators for resource consumption are derived in the same way. The goals are twofold: to show the flexibility of the heuristic search approach to planning and to develop a planner that combines expressivity and performance. Two main issues are the definition of regression in a temporal setting and the definition of the heuristic estimating completion time. A number of experiments are presented for assessing the performance of the resulting planner.

Flow-based heuristics for optimal planning: landmarks and merges

Abstract: We describe a flow-based heuristic for optimal planning that exploits landmarks and merges. The heuristic solves a linear programming (LP) problem that represents variables in SAS+ planning as a set of interacting network flow problems. The solution to the LP provides a reasonable admissible heuristic for optimal planning, but we improve it considerably by adding constraints derived from action landmarks and from variable merges. Merged variables, however, can quickly grow in size and as a result introduce many new variables and constraints into the LP. In order to control the size of the LP we introduce the concept of dynamic merging that allows us to partially and incrementally merge variables, thus avoiding the formation of cross products of domains as done when merging variables in the traditional way. The two types of improvements (action landmarks and variable merges) to the LP formulation are orthogonal and general. We measure the impact on performance for optimal planning of each improvement in isolation, and also when combined, for a simple merge strategy. The results show that the new heuristic is competitive with the current state of the art.

Online Speedup Learning for Optimal Planning

Abstract: Domain-independent planning is one of the foundational areas in the field of Artificial Intelligence. A description of a planning task consists of an initial world state, a goal, and a set of actions for modifying the world state. The objective is to find a sequence of actions, that is, a plan, that transforms the initial world state into a goal state. In optimal planning, we are interested in finding not just a plan, but one of the cheapest plans. A prominent approach to optimal planning these days is heuristic state-space search, guided by admissible heuristic functions. Numerous admissible heuristics have been developed, each with its own strengths and weaknesses, and it is well known that there is no single "best heuristic for optimal planning in general. Thus, which heuristic to choose for a given planning task is a difficult question. This difficulty can be avoided by combining several heuristics, but that requires computing numerous heuristic estimates at each state, and the tradeoff between the time spent doing so and the time saved by the combined advantages of the different heuristics might be high. We present a novel method that reduces the cost of combining admissible heuristics for optimal planning, while maintaining its benefits. Using an idealized search space model, we formulate a decision rule for choosing the best heuristic to compute at each state. We then present an active online learning approach for learning a classifier with that decision rule as the target concept, and employ the learned classifier to decide which heuristic to compute at each state. We evaluate this technique empirically, and show that it substantially outperforms the standard method for combining several heuristics via their pointwise maximum.

Heuristic Search for Scheduling Flexible Manufacturing Systems Using Multiple Heuristic Functions

Abstract: To cope with the complexities of flexible manufacturing system FMS scheduling, this paper proposes and evaluates an improved search strategy and its application to FMS scheduling in a Petri net framework. Petri nets can concisely model multiple lot sizes for each job, the strict precedence constraint, multiple kinds of resources and concurrent activities. On the execution of the Petri nets, our algorithm can use both admissible heuristic functions and nonadmissible heuristic functions having the upper supports of the relative errors in A * heuristic search algorithm. In addition, the search scheme can ensure the results found are optimal and invokes quicker termination conditions. To demonstrate it, the scheduling results are derived and evaluated through a simple FMS with multiple lot sizes for each job. The algorithm is also applied to a set of randomly-generated FMSs with such characteristics as multiple resources and alternative routings.

Cost optimal planning with LP-based multi-valued landmark heuristic

Abstract: Landmark based heuristics are among the most accurate current known admissible heuristics for cost optimal planning. Disjunctive action landmarks can be considered as at-least-one constraints on the actions they contains. In many planning domains, there are many critical propositions which have to be established for a number of times. Previous landmarks fail to express this kind of general cardinality constraints. In this paper, we propose to generalize landmarks to multi-valued landmarks to model general cardinality constraints in cost optimal planning. We show existence of complete multi-valued landmark sets by explicitly constructing complete multi-valued action landmark sets for general planning tasks. However, it's computationally intractable to extract and exploit exact lower bounds of general multi-valued action landmarks. We devise a linear programming based multi-valued landmark heuristic hlpml which extracts and exploits multi-valued landmarks using a linear programming solver. The heuristic hlpml is guaranteed to be admissible and can be computed in polynomial time. Experimental evaluation on benchmark domains shows hlpml beats state-of-the-art admissible heuristic in terms of heuristic accuracy and achieves better overall coverage performance at the cost of using more CPU time.

A Heuristic Search Approach to Planning with Continuous Resources in Stochastic Domains

Abstract: We consider the problem of optimal planning in stochastic domains with resource constraints, where the resources are continuous and the choice of action at each step depends on resource availability. We introduce the HAO* algorithm, a generalization of the AO* algorithm that performs search in a hybrid state space that is modeled using both discrete and continuous state variables, where the continuous variables represent monotonic resources. Like other heuristic search algorithms, HAO* leverages knowledge of the start state and an admissible heuristic to focus computational effort on those parts of the state space that could be reached from the start state by following an optimal policy. We show that this approach is especially effective when resource constraints limit how much of the state space is reachable. Experimental results demonstrate its effectiveness in the domain that motivates our research: automated planning for planetary exploration rovers.

A Heuristic Search Algorithm for Solving First-Order MDPs

Abstract: We present a heuristic search algorithm for solving first-order MDPs (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, we apply state abstraction directly on the FOMDP avoiding propositionalization. Such kind of abstraction is referred to as firstorder state abstraction. Secondly, guided by an admissible heuristic, the search is restricted only to those states that are reachable from the initial state. We demonstrate the usefullness of the above techniques for solving FOMDPs on a system, referred to as FCPlanner, that entered the probabilistic track of the International Planning Competition (IPC'2004).