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Finding optimal solutions to Atomix
 KI 2001: ADVANCES IN ARTIFICIAL INTELLIGENCE, VOLUME 2174 OF LNCS/LNAI
, 2001
"... We present solutions of benchmark instances to the solitaire computer game Atomix found with different heuristic search methods. The problem is PSPACEcomplete. An implementation of the heuristic algorithm A * is presented that needs no priority queue, thereby having very low memory overhead. The li ..."
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We present solutions of benchmark instances to the solitaire computer game Atomix found with different heuristic search methods. The problem is PSPACEcomplete. An implementation of the heuristic algorithm A * is presented that needs no priority queue, thereby having very low memory overhead. The limited memory algorithm IDA * is handicapped by the fact that, due to move transpositions, duplicates appear very frequently in the problem space; several schemes of using memory to mitigate this weakness are explored, among those, “partial” schemes which trade memory savings for a small probability of not finding an optimal solution. Even though the underlying search graph is directed, backward search is shown to be viable, since the branching factor can be proven to be the same as for forward search.
Admissible Heuristics for Automated Planning
 Ph.D. Dissertation, Linköpings Universitet
"... The problem of domainindependent automated planning has been a topic of research in Artificial Intelligence since the very beginnings of the field. Due to the desire not to rely on vast quantities of problem specific knowledge, the most widely adopted approach to automated planning is search. The t ..."
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The problem of domainindependent automated planning has been a topic of research in Artificial Intelligence since the very beginnings of the field. Due to the desire not to rely on vast quantities of problem specific knowledge, the most widely adopted approach to automated planning is search. The topic of this thesis is the development of methods for achieving effective search control for domainindependent optimal planning through the construction of admissible heuristics. The particular planning problem considered is the so called “classical ” AI planning problem, which makes several restricting assumptions. Optimality with respect to two measures of plan cost are considered: in planning with additive cost, the cost of a plan is the sum of the costs of the actions that make up the plan, which are assumed independent, while in planning with time, the cost of a plan is the total execution time – makespan – of the plan. The makespan optimization objective can not, in general, be formulated as a sum of independent action costs and therefore necessitates a problem model slightly different from the classical one. A further small extension to the classical
Singlefrontier bidirectional search
 In AAAI
, 2010
"... Abstract On the surface, bidirectional search (BDS) is an attractive idea with the potential for significant asymptotic reductions in search effort. However, the results in practice often fall far short of expectations. We introduce a new bidirectional search algorithm, SingleFrontier Bidirectiona ..."
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Abstract On the surface, bidirectional search (BDS) is an attractive idea with the potential for significant asymptotic reductions in search effort. However, the results in practice often fall far short of expectations. We introduce a new bidirectional search algorithm, SingleFrontier Bidirectional Search (SFBDS). Unlike traditional BDS which keeps two frontiers, SFBDS uses a single frontier. Each node in the tree can be seen as an independent task of finding the shortest path between the current start and current goal. At a particular node we can decide to search from start to goal or from goal to start, choosing the direction with the highest potential for minimizing the total work done. Theoretical results give insights as to when this approach will work and experimental data validates the algorithm for a broad range of domains.
Stateset search
 In Symposium on Combinatorial Search (SoCS
, 2011
"... Stateset search is state space search when the states being manipulated by the search algorithm are sets of states from some underlying state space. Stateset search arises commonly in planning and abstraction systems, but this paper provides the first formal, general analysis of stateset search. ..."
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Stateset search is state space search when the states being manipulated by the search algorithm are sets of states from some underlying state space. Stateset search arises commonly in planning and abstraction systems, but this paper provides the first formal, general analysis of stateset search. We show that the stateset distance computed by planning systems is different than that computed by abstraction systems and introduce a distance in between the two, dww, the maximum admissible distance. We introduce the concept of state in the same abstract space, describe the first implementation of a multiabstraction system that computes dww, and give initial experimental evidence that it can be superior to domain abstraction.
Stronger Abstraction Heuristics Through Perimeter Search
"... Perimeter search is a bidirectional search algorithm consisting of two phases. In the first phase, a limited regression search computes the perimeter, a region which must necessarily be passed in every solution. In the second phase, a heuristic forward search finds an optimal plan from the initial s ..."
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Perimeter search is a bidirectional search algorithm consisting of two phases. In the first phase, a limited regression search computes the perimeter, a region which must necessarily be passed in every solution. In the second phase, a heuristic forward search finds an optimal plan from the initial state to the perimeter. The drawback of perimeter search is the need to compute heuristic estimates towards every state on the perimeter in the forward phase. We show that this limitation can be effectively overcome when using pattern database (PDB) heuristics in the forward phase. The combination of perimeter search and PDB heuristics has been considered previously by Felner and Ofek for solving combinatorial puzzles. They claimed that, based on theoretical considerations and experimental evidence, the use of perimeter search in this context offers ”limited or no benefits”. Our theoretical and experimental results show that this assessment should be revisited.
Towards a Standardized Comparison of Search Algorithms
, 1998
"... Although many search algorithms have been developed and still are under development, it is difficult to compare them on a fair basis. Theoretical comparisons are desirable, but it is difficult to make the right assumptions in modeling realworld problems. Since useful theoretical comparisons are als ..."
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Although many search algorithms have been developed and still are under development, it is difficult to compare them on a fair basis. Theoretical comparisons are desirable, but it is difficult to make the right assumptions in modeling realworld problems. Since useful theoretical comparisons are also difficult to achieve, it usually takes some time until a newly developed search algorithm is appropriately compared to its competitors. At least in addition to theoretical comparisons, therefore, welldesigned experiments should be performed. Unfortunately, however, we still observe severe problems in the current "nonstandard" of how empirical comparisons of heuristic search algorithms are reported in the literature. We illustrate the most important issues based on our own experience with developing search algorithms and comparing them empirically in real domains. For analyzing experimental results, it is necessary to apply statistical methods. This is not sufficient, however, since the r...
A case study of revisiting bestfirst vs. depthfirst search
 in: Proceedings of the Sixteenth European Conference on Artificial Intelligence (ECAI04
, 2004
"... Abstract. Bestfirst search usually has exponential space requirements on difficult problems. Depthfirst search can solve difficult problems with linear space requirements, but it cannot utilize large additional memory available on today's machines. Therefore, we revisit the issue of when bes ..."
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Abstract. Bestfirst search usually has exponential space requirements on difficult problems. Depthfirst search can solve difficult problems with linear space requirements, but it cannot utilize large additional memory available on today's machines. Therefore, we revisit the issue of when bestfirst or depthfirst search is preferable to use. Through algorithmic improvements, it was possible for the first time to find optimal solutions of certain difficult problems (the complete benchmark set of Fifteen Puzzle problems) using traditional bestfirst search (with the Manhattan distance heuristic only). Our experimental results show that this search can solve them overall faster than any of the previously published approaches (using this heuristic). Note that this search approach was believed to be incapable of solving randomly generated instances of the Fifteen Puzzle within practical resource limits because of its exponential space requirements. So, our case study suggests that changes in hardware and algorithmic improvements together can revise the previous assessment of bestfirst search. Notation s, t Start node and goal node, respectively. Γ(n) Successors of node n in the problem graph. Γ(n) Parents of node n in the problem graph. ci(m, n) Cost of the direct arc from m to n if i = 1, or from n to m if i = 2. ki(m, n) Cost of an optimal path from m to n if i = 1, or from n to m if i = 2. Cost of an optimal path from s to n if i = 1, Cost of an optimal path from n to t if i = 1, or from n to Cost of an optimal path from s to t. Lmin Cost of the best (least costly) complete path found so far from s to t. TREE1 The forward search tree. TREE2 The backward search tree. OPENi The set of open nodes in TREEi. OPENi Number of nodes in OPENi. CLOSEDi The set of closed nodes in TREEi.
Switching from bidirectional to unidirectional search
 In Proc. Sixteenth International Joint Conference on Artificial Intelligence (IJCAI99
, 1999
"... Recently, we showed that for traditional bidirectional search with "fronttoend " evaluations, it is not the meeting of search fronts but the cost of proving the optimality of a solution that is problematic. Using our improved understanding of the problem, we developed a new approach to ..."
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Recently, we showed that for traditional bidirectional search with "fronttoend " evaluations, it is not the meeting of search fronts but the cost of proving the optimality of a solution that is problematic. Using our improved understanding of the problem, we developed a new approach to improving this kind of search: switching to unidirectional search after the search frontiers meet for the first time (with the first solution found). This new approach shows improvements over previous bidirectional search approaches and (partly) also over the corresponding unidirectional search approaches in different domains. Together with a specialpurpose improvement for the TSP, this approach showed better results than the standard search algorithms using the same knowledge. 1
Guidelines for the Experimental Comparison of Search Algorithms
 IJCAI99 Workshop on Empirical AI
, 1999
"... Although many search algorithms have been developed and still are under development, it is difficult to compare them on a fair basis. Since useful theoretical comparisons are difficult to achieve, it usually takes some time until a newly developed search algorithm is appropriately compared to its ..."
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Although many search algorithms have been developed and still are under development, it is difficult to compare them on a fair basis. Since useful theoretical comparisons are difficult to achieve, it usually takes some time until a newly developed search algorithm is appropriately compared to its competitors. At least in addition to theoretical comparisons, therefore, welldesigned experiments should be performed. Unfortunately, however, we still observe severe problems in the current way of how empirical comparisons of heuristic search algorithms are reported in the literature. Based on our own experience with developing search algorithms and comparing them through experiments in real domains, we recommend specific guidelines for experimental comparisons. 1 Introduction Many heuristic search algorithms have been developed and still are under development. Yet it is difficult to compare search algorithms on a fair basis. At least in addition to theoretical comparisons, welld...
Optimal Graph Search with Iterated Graph Cuts
"... Informed search algorithms such as A * use heuristics to focus exploration on states with low total path cost. To the extent that heuristics underestimate forward costs, a wider cost radius of suboptimal states will be explored. For many weighted graphs, however, a small distance in terms of cost ma ..."
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Informed search algorithms such as A * use heuristics to focus exploration on states with low total path cost. To the extent that heuristics underestimate forward costs, a wider cost radius of suboptimal states will be explored. For many weighted graphs, however, a small distance in terms of cost may encompass a large fraction of the unweighted graph. We present a new informed search algorithm, Iterative Monotonically Bounded A* (IMBA*), which first proves that no optimal paths exist in a bounded cut of the graph before considering larger cuts. We prove that IMBA * has the same optimality and completeness guarantees as A * and, in a nonuniform pathfinding application, we empirically demonstrate substantial speed improvements over classic