Meta-Level Techniques for Planning, Search, and Scheduling

Metareasoning is a core idea in AI at that captures the essence of being both human and intelligent. This idea is that much can be gained by thinking (reasoning) about one's own thinking. In the context of search and planning, metareasoning concerns with making explicit decisions about computation steps, by comparing their `cost' in computational resources, against the gain they can be expected to make towards advancing the search for solution (or plan) and thus making better decisions. To apply metareasoning, a meta-level problem needs to be defined and solved with respect to a specific framework or algorithm. In some cases, these meta-level problems can be very hard to solve. Yet, even a fast-to-compute approximation of meta-level problems can yield good results and improve the algorithms to which they are applied. This paper provides an overview of different settings in which we applied metareasoning to improve search, planning and scheduling

On the Differences and Similarities of fMM and GBFHS

fMM and GBFSH are two prominent bidirectional heuristic search algorithms. Over the past few years, there has been a great deal of theoretical and empirical work on both of these algorithms. As part of the research conducted on these algorithms, some interesting theoretical properties were proven for fMM and not for GBFSH and vice versa. In addition, both of them are used as benchmarks for evaluation bidirectional heuristic search algorithms. In this paper we show that fMM infused by a lower-bound propagation and GBFSH are equivalent. In essence, every instance of fMM can be mapped to an instance of GBFSH that expands the exact sequence of nodes and vice versa. This equivalence indicates that all theoretical properties proven for one algorithm hold for both algorithm, and that future analyses and benchmarks can consider only one of these algorithms

The Closed List Is an Obstacle Too

The baseline approach for optimal path finding in 4-connected grids is A* with Manhattan Distance. Nevertheless, a large number of enhancements were suggested over the years, usually requiring a preprocessing phase and/or additional memory to store smart lookup tables. In this paper we introduce an enhancement to A* (called BOXA*) on grids which does not need any preprocessing and only needs negligible additional memory. The main idea is to treat the closed-list as a dynamic obstacle. We maintain a list of rectangles which surround CLOSED nodes and calculate an admissible heuristic using the fact that an optimal path from a given node must go around these rectangles. We experimentally show the benefits of this approach on a variety of grid domains

Metareasoning for Interleaved Planning and Execution

Agents that plan and act in the real world must deal with the fact that time passes as they are planning. In the presence of tight deadlines, there may be insufficient time to complete the search for a plan before it is time to act. One can gain additional time to search by starting to act before a complete plan is found, incurring the risk of making incorrect action choices. This tradeoff between opportunity and risk, inherent in interleaving planning and execution, is a non-trivial metareasoning problem addressed in this paper

Algorithm Selection in Optimization and Application to Angry Birds

Consider the MaxScore algorithm selection problem: given some optimization problem instances, a set of algorithms that solve them, and a time limit, what is the optimal policy for selecting (algorithm, instance) runs so as to maximize the sum of solution qualities for all problem instances?We analyze the computational complexity of restrictions of MaxScore (NP-hard), and provide a dynamic programming approximation algorithm. This algorithm, as well as new greedy algorithms, are evaluated empirically on data from agent runs on Angry Birds problem instances. Results show a significant improvement over a hyper-agent greedy scheme from related work.Solomon Eyal ShimonyAvinoam Yehezke

Improving Bidirectional Heuristic Search by Bounds Propagation

Recent work in bidirectional heuristic search characterize pairs of nodes from which at least one node must be expanded in order to ensure optimality of solutions. We use these findings to propose a method for improving existing heuristics by propagating lower bounds between the forward and backward frontiers. We then define a number of desirable properties for bidirectional heuristic search algorithms, and show that applying the bound propagations adds these properties to many existing algorithms (e.g. to the MM family of algorithms). Finally, experimental results show that applying these propagations significantly reduce the running time of various algorithms

Predicting the Effectiveness of Bidirectional Heuristic Search

The question of when bidirectional heuristic search outperforms unidirectional heuristic search has been revisited numerous times in the field of Artificial Intelligence. This paper re-addresses the question of when bidirectional search outperforms unidirectional search using an updated theoretical understanding of the problem. We show that a core set of critical states in the state space are the primary factor determining whether a bidirectional search can outperform a unidirectional search and provide simple measures to determine whether a state space and heuristic contains these critical states. We similarly discuss and show the impact that asymmetry in the underlying problem graph has on the performance of bidirectional algorithms. Experimental results show the impact of these factors on whether a problem should be solved using unidirectional or bidirectional search

Iterative-deepening Bidirectional Heuristic Search with Restricted Memory

The field of bidirectional heuristic search has recently seen great advances. However, the subject of memory-restricted bidirectional search has not received recent attention. In this paper we introduce a general iterative deepening bidirectional heuristic search algorithm (IDBiHS) that searches simultaneously in both directions while controlling the meeting point of the search frontiers. First, we present the basic variant of IDBiHS, whose memory is linear in the search depth. We then add improvements that exploit consistency and front-to-front heuristics. Next, we move to the case where a fixed amount of memory is available to store nodes during the search and develop two variants of IDBiHS: (1) A*+IDBiHS, that starts with A* and moves to IDBiHS as soon as memory is exhausted. (2) A variant that stores partial forward frontiers until memory is exhausted and then tries to match each of them from the backward side. Finally, we experimentally compare the new algorithms to existing unidirectional and bidirectional ones. In many cases our new algorithms outperform previous ones in both node expansions and time

Iterative-Deepening Bidirectional Heuristic Search with Restricted Memory

This extended abstract presents a bidirectional heuristic search algorithm called IDBiHS that operates under restricted memory. Several variants of this algorithm are introduced for different types of memory restrictions, and are compared against existing algorithms with similar restrictions