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Incremental Lower Bounds for Additive Cost Planning Problems
"... We present a novel method for computing increasing lower bounds on the cost of solving planning problems, based on repeatedly solving and strengthening the delete relaxation of the problem. Strengthening is done by compiling select conjunctions into new atoms, similar to theP m ⋆ construction. Becau ..."
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We present a novel method for computing increasing lower bounds on the cost of solving planning problems, based on repeatedly solving and strengthening the delete relaxation of the problem. Strengthening is done by compiling select conjunctions into new atoms, similar to theP m ⋆ construction. Because it does not rely on search in the state space, this method does not suffer some of the weaknesses of admissible search algorithms and therefore is able to prove higher lower bounds for many problems that are too hard for optimal planners to solve, thus narrowing the gap between lower bound and cost of the best known plan, providing better assurances of plan quality.
CostBased Heuristic Search is Sensitive to the Ratio of Operator Costs
"... In many domains, different actions have different costs. In this paper, we show that various kinds of bestfirst search algorithms are sensitive to the ratio between the lowest and highest operator costs. First, we take common benchmark domains and show that when we increase the ratio of operator co ..."
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Cited by 5 (1 self)
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In many domains, different actions have different costs. In this paper, we show that various kinds of bestfirst search algorithms are sensitive to the ratio between the lowest and highest operator costs. First, we take common benchmark domains and show that when we increase the ratio of operator costs, the number of node expansions required to find a solution increases. Second, we provide a theoretical analysis showing one reason this phenomenon occurs. We also discuss additional domain features that can cause this increased difficulty. Third, we show that searching using distancetogo estimates can significantly ameliorate this problem. Our analysis takes an important step toward understanding algorithm performance in the presence of differing costs. This research direction will likely only grow in importance as heuristic search is deployed to solve realworld problems.
Towards Rational Deployment of Multiple Heuristics in A*
"... The obvious way to use several admissible heuristics in A ∗ is to take their maximum. In this paper we aim to reduce the time spent on computing heuristics. We discuss Lazy A ∗ , a variant of A ∗ where heuristics are evaluated lazily: only when they are essential to a decision to be made in the A ∗ ..."
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Cited by 4 (2 self)
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The obvious way to use several admissible heuristics in A ∗ is to take their maximum. In this paper we aim to reduce the time spent on computing heuristics. We discuss Lazy A ∗ , a variant of A ∗ where heuristics are evaluated lazily: only when they are essential to a decision to be made in the A ∗ search process. We present a new rational metareasoning based scheme, rational lazy A ∗, which decides whether to compute the more expensive heuristics at all, based on a myopic value of information estimate. Both methods are examined theoretically. Empirical evaluation on several domains supports the theoretical results, and shows that lazy A ∗ and rational lazy A ∗ are stateoftheart heuristic combination methods. 1
Are We There Yet? – Estimating Search Progress
"... Heuristic search is a general problem solving technique. While most evaluations of heuristic search focus on the speed of search, there are relatively few techniques for predicting when search will end. This paper provides a study of progress estimating techniques for optimal, suboptimal, and bounde ..."
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Heuristic search is a general problem solving technique. While most evaluations of heuristic search focus on the speed of search, there are relatively few techniques for predicting when search will end. This paper provides a study of progress estimating techniques for optimal, suboptimal, and bounded suboptimal heuristic search algorithms. We examine two previously proposed techniques, search velocity and search vacillation, as well as two new approaches, pathbased estimation and distributionbased estimation. We find that both new approaches are better at estimating the remaining amount of search effort than previous work in all three varieties of search, occasionally erring by less than 5%.
S.: Detecting mutex pairs in state spaces by sampling
 In: 26th Australasian Joint Conference on Artificial Intelligence
, 2013
"... Abstract. In the context of state space planning, a mutex pair is a pair of variablevalue assignments that does not occur in any reachable state. Detecting mutex pairs is a problem that has been addressed frequently in the planning literature. In this paper, we present the Missing Mass Method (MMM) ..."
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Abstract. In the context of state space planning, a mutex pair is a pair of variablevalue assignments that does not occur in any reachable state. Detecting mutex pairs is a problem that has been addressed frequently in the planning literature. In this paper, we present the Missing Mass Method (MMM)—a new efficient and domainindependent method for mutex pair detection, based on sampling reachable states. We exploit a recent result from statistical theory, proven by Berend and Kontorovich in [1], that bounds the probability mass of missing events in a sample of a given size. We tested MMM empirically on various sizes of four standard benchmark domains from the planning and heuristic search literature. In many cases, MMM works perfectly, i.e., finds all and only the mutex pairs. In the other cases, it is nearperfect: it correctly labels all mutex pairs and more than 99.99 % of all nonmutex pairs. 1
Everything You Always Wanted to Know About Planning (But Were Afraid to Ask)
, 2011
"... Abstract. Domainindependent planning is one of the longstanding subareas of Artificial Intelligence (AI), aiming at approaching human problemsolving flexibility. The area has long had an affinity towards playful illustrative examples, imprinting it on the mind of many a student as an area concer ..."
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Abstract. Domainindependent planning is one of the longstanding subareas of Artificial Intelligence (AI), aiming at approaching human problemsolving flexibility. The area has long had an affinity towards playful illustrative examples, imprinting it on the mind of many a student as an area concerned with the rearrangement of blocks, and with the order in which to put on socks and shoes (not to mention the disposal of bombs in toilets). Working on the assumption that this “student ” is you – the readers in earlier stages of their careers – I herein aim to answer three questions that you surely desired to ask back then already: What is it good for? Does it work? Is it interesting to do research in? Answering the latter two questions in the affirmative (of course!), I outline some of the major developments of the last decade, revolutionizing the ability of planning to scale up, and the understanding of the enabling technology. Answering the first question, I point out that modern planning proves to be quite useful for solving practical problems including, perhaps, yours.
Using Alternative Suboptimality Bounds in Heuristic Search
 In Proceedings of the TwentyThird International Conference on Automated Planning and Scheduling, ICAPS 2013
, 2013
"... Most bounded suboptimal algorithms in the search literature have been developed so as to be admissible. This means that the solutions found by these algorithms are guaranteed to be no more than a factor of (1 + ) greater than optimal. However, this is not the only possible form of suboptimality bou ..."
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Most bounded suboptimal algorithms in the search literature have been developed so as to be admissible. This means that the solutions found by these algorithms are guaranteed to be no more than a factor of (1 + ) greater than optimal. However, this is not the only possible form of suboptimality bounding. For example, another possible suboptimality guarantee is that of additive bounding, which requires that the cost of the solution found is no more than the cost of the optimal solution plus a constant γ. In this work, we consider the problem of developing algorithms so as to satisfy a given, and arbitrary, suboptimality requirement. To do so, we develop a theoretical framework which can be used to construct algorithms for a large class of possible suboptimality paradigms. We then use the framework to develop additively bounded algorithms, and show that in practice these new algorithms effectively tradeoff additive solution suboptimality for runtime. 1
Better Time Constrained Search via Randomization and Postprocessing
"... Most of the satisficing planners which are based on heuristic search iteratively improve their solution quality through an anytime approach. Typically, the lowestcost solution found so far is used to constrain the search. This avoids areas of the state space which cannot directly lead to lower cost ..."
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Most of the satisficing planners which are based on heuristic search iteratively improve their solution quality through an anytime approach. Typically, the lowestcost solution found so far is used to constrain the search. This avoids areas of the state space which cannot directly lead to lower cost solutions. However, in this paper we show that when used in conjunction with a postprocessing plan improvement system such as ARAS, this bounding approach can harm a planner’s performance since the bound may prevent the search from ever finding additional plans for the postprocessor to improve. The new anytime search framework of Diverse AnyTime Search addresses this issue through the use of restarts, randomization, and by not bounding as strictly as is done by previous approaches. Below, we will show that by using these techniques, the framework is able to generate a more diverse set of “raw " input plans for the postprocessor to work on. We then show that when adding both Diverse AnyTime Search and the ARAS postprocessor to LAMA2011, the winner of the most recent IPC planning competition, the performance according to the IPC scoring metric improves from 511 points to over 570 points when tested on the 550 problems from IPC 2008 and IPC 2011. Performance gains are also seen when these techniques are added to Anytime Explicit Estimation Algorithm (AEES), as the performance improves from 440 points to over 513 points on the same problem set.
Suboptimal Variants of the ConflictBased Search Algorithm for the MultiAgent Pathfinding Problem
"... The task in the multiagent path finding problem (MAPF) is to find paths for multiple agents, each with a different start and goal position, such that agents do not collide. A successful optimal MAPF solver is the conflictbased search (CBS) algorithm. CBS is a two level algorithm where special con ..."
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The task in the multiagent path finding problem (MAPF) is to find paths for multiple agents, each with a different start and goal position, such that agents do not collide. A successful optimal MAPF solver is the conflictbased search (CBS) algorithm. CBS is a two level algorithm where special conditions ensure it returns the optimal solution. Solving MAPF optimally is proven to be NPhard, hence CBS and all other optimal solvers do not scale up. We propose several ways to relax the optimality conditions of CBS trading solution quality for runtime as well as boundedsuboptimal variants, where the returned solution is guaranteed to be within a constant factor from optimal solution cost. Experimental results show the benefits of our new approach; a massive reduction in running time is presented while sacrificing a minor loss in solution quality. Our new algorithms outperform other existing algorithms in most of the cases.
Proceedings of the TwentySecond International Joint Conference on Artificial Intelligence Bounded Suboptimal Search: A Direct Approach Using Inadmissible Estimates
"... Bounded suboptimal search algorithms offer shorter solving times by sacrificing optimality and instead guaranteeing solution costs within a desired factor of optimal. Typically these algorithms use a single admissible heuristic both for guiding search and bounding solution cost. In this paper, we pr ..."
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Bounded suboptimal search algorithms offer shorter solving times by sacrificing optimality and instead guaranteeing solution costs within a desired factor of optimal. Typically these algorithms use a single admissible heuristic both for guiding search and bounding solution cost. In this paper, we present a new approach to bounded suboptimal search, Explicit Estimation Search, that separates these roles, consulting potentially inadmissible information to determine search order and using admissible information to guarantee the cost bound. Unlike previous proposals, it successfully combines estimates of solution length and solution cost to predict which node will lead most quickly to a solution within the suboptimality bound. An empirical evaluation across six diverse benchmark domains shows that Explicit Estimation Search is competitive with the previous state of the art in domains with unitcost actions and substantially outperforms previously proposed techniques for domains in which solution cost and length can differ. 1