Showing papers on "Admissible heuristic published in 2007"

An LP-based heuristic for optimal planning

Abstract: One of the most successful approaches in automated planning is to use heuristic state-space search. A popular heuristic that is used by a number of state-space planners is based on relaxing the planning task by ignoring the delete effects of the actions. In several planning domains, however, this relaxation produces rather weak estimates to guide search effectively. We present a relaxation using (integer) linear programming that respects delete effects but ignores action ordering, which in a number of problems provides better distance estimates. Moreover, our approach can be used as an admissible heuristic for optimal planning.

Inconsistent heuristics

Abstract: In the field of heuristic search it is well-known that improving the quality of an admissible heuristic can significantly decrease the search effort required to find an optimal solution. Existing literature often assumes that admissible heuristics are consistent, implying that consistency is a desirable attribute. To the contrary, this paper shows that an inconsistent heuristic can be preferable to a consistent heuristic. Theoretical and empirical results show that, in many cases, inconsistency can be used to achieve large performance improvements.

A hybrid linear programming and relaxed plan heuristic for partial satisfaction planning problems

Abstract: The availability of informed (but inadmissible) planning heuristics has enabled the development of highly scalable planning systems. Due to this success, a body of work has grown around modifying these heuristics to handle extensions to classical planning. Most recently, there has been an interest in addressing partial satisfaction planning problems, but existing heuristics fail to address the complex interactions that occur in these problems between action and goal selection. In this paper we provide a unique admissible heuristic based on linear programming that we use to solve a relaxed version of the partial satisfaction planning problem. We incorporate this heuristic in conjunction with a lookahead strategy in a branch and bound algorithm to solve a class of over-subscribed planning problems.

Online Learning of Search Heuristics

Abstract: In this paper we learn heuristic functions that efficiently find the shortest path between two nodes in a graph. We rely on the fact that often, several elementary admissible heuristics might be provided, either by human designers or from formal domain abstractions. These simple heuristics are traditionally composed into a new admissible heuristic by selecting the highest scoring elementary heuristic in each distance evaluation. We suggest that learning a weighted sum over the elementary heuristics can often generate a heuristic with higher dominance than the heuristic defined by the highest score selection. The weights within our composite heuristic are trained in an online manner using nodes to which the true distance has already been revealed during previous search stages. Several experiments demonstrate that the proposed method typically finds the optimal path while significantly reducing the search complexity. Our theoretical analysis describes conditions under which finding the shortest path can be guaranteed.

Solving Planning Under Uncertainty: Quantitative and Qualitative Approach

Abstract: Classical decision-theoretic planning methods assume that the probabilistic model of the domain is always accurate. We present two algorithms rLAO* and qLAO* in this paper. rLAO* and qLAO* can solve uncertainty Markov decision problems and qualitative Markov decision problems respectively. We prove that given an admissible heuristic function, both rLAO* and qLAO* can find an optimal solution. Experimental results also show that rLAO* and qLAO* inherit the merits of excellent performance of LAO* for solving uncertainty problems.

Near-optimal search in continuous domains

Abstract: We investigate search problems in continuous state and action spaces with no uncertainty Actions have costs and can only be taken at discrete time steps (unlike the case with continuous control) Given an admissible heuristic function and a starting state, the objective is to find a minimum-cost plan that reaches a goal state As the continuous domain does not allow the tight optimality results that are possible in the discrete case (for example by A*), we instead propose and analyze an approximate forward-search algorithm that has the following provable properties Given a desired accuracy E, and a bound d on the length of the plan, the algorithm computes a lower bound L on the cost of any plan It either (a) returns a plan of cost L that is at most E more than the optimal plan, or (b) if, according to the heuristic estimate, there may exist a plan of cost L of length > d, returns a partial plan that traces the first d steps of such plan To our knowledge, this is the first algorithm that provides optimality guarantees in continuous domains with discrete control and without uncertainty

Overestimation for Multiple Sequence Alignment

Abstract: Multiple sequence alignment is an important problem in computational biology. A-star is an algorithm that can be used to find exact alignments. We present a simple modification of the A-star algorithm that improves much multiple sequence alignment, both in time and memory, at the cost of a small accuracy loss. It consists in overestimating the admissible heuristic. A typical speedup for random sequences of length two hundred fifty is 47 associated to a memory gain of 13 with an error rate of 0.09%. Concerning real sequences, the speedup can be greater than 20,000 and the memory gain greater than 150, the error rate being in the range from 0.08% to 0.67% for the sequences we have tested. Overestimation can align sequences that are not possible to align with the exact algorithm

BDFS: A Real-Time Search Algorithm for Central Office (CO) Optimization

Abstract: Central office (CO) maintenance is becoming a major overhead for backbone service providers. Trunk to switch assignment (TSA) problem is seen as a crucial problem in maintenance of a central office. In this paper we formulate the TSA problem as a set partitioning problem and present an efficient heuristic search algorithm BDFS (block depth first search) for minimizing switching overhead in central offices. To guide this algorithm, we have developed a new lower bound function, based on relaxation of the problem of merging external trunks into switches. We used the lower bound admissible heuristic (H-III) along with the proposed technique to solve this problem. While comparing the performance of BDFS, we have found that BDFS outperforms IDA* on various performance metrics. We have also suggested a real-time version of BDFS algorithm that gives high quality sub-optimal or optimal solution with a user specified time. Real-time BDFS gives optimal solution within 50-60% of the total execution time for most of the problem instances. The real-time BDFS can be used to optimize the existing configurations with minimal changes and can also help service providers in taking quick decisions before making a detailed study regarding planning requirements