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31
Branch and Bound Algorithm Selection by Performance Prediction
- In AAAI
, 1998
"... We propose a method called Selection by Performance Prediction (SPP) which allows one, when faced with a particular problem instance, to select a Branch and Bound algorithm from among several promising ones. This method is based on Knuth's sampling method which estimates the efficiency of ..."
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Cited by 37 (1 self)
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We propose a method called Selection by Performance Prediction (SPP) which allows one, when faced with a particular problem instance, to select a Branch and Bound algorithm from among several promising ones. This method is based on Knuth's sampling method which estimates the efficiency of a backtrack program on a particular instance by iteratively generating random paths in the search tree. We present a simple adaptation of this estimator in the field of combinatorial optimization problems, more precisely for an extension of the maximal constraint satisfaction framework. Experiments both on random and strongly structured instances show that, in most cases, the proposed method is able to select, from a candidate list, the best algorithm for solving a given instance. Introduction The Branch and Bound search is a well-known algorithmic schema, widely used for solving combinatorial optimization problems. A lot of specific algorithms can be derived from this general schema. ...
Estimating Search Tree Size
- In Proceedings of the 21st National Conference on Artificial Intelligence (AAAI ’06
, 2006
"... We propose two new online methods for estimating the size of a backtracking search tree. The first method is based on a weighted sample of the branches visited by chronologi-cal backtracking. The second is a recursive method based on assuming that the unexplored part of the search tree will be simil ..."
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Cited by 26 (2 self)
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We propose two new online methods for estimating the size of a backtracking search tree. The first method is based on a weighted sample of the branches visited by chronologi-cal backtracking. The second is a recursive method based on assuming that the unexplored part of the search tree will be similar to the part we have so far explored. We compare these methods against an old method due to Knuth based on random probing. We show that these methods can reliably estimate the size of search trees explored by both optimiza-tion and decision procedures. We also demonstrate that these methods for estimating search tree size can be used to select the algorithm likely to perform best on a particular problem instance.
Statistical mechanics of combinatorial search
- In Proc. of the Workshop on Physics and Computation (PhysComp94
, 1994
"... The statistical mechanics of combinatorial search problems is described using the example of the well-known NP-complete graph coloring problem. We focus on a recently identified phase transition from under- to overconstrained problems, near which are concentrated many hard to solve search problems. ..."
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Cited by 21 (5 self)
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The statistical mechanics of combinatorial search problems is described using the example of the well-known NP-complete graph coloring problem. We focus on a recently identified phase transition from under- to overconstrained problems, near which are concentrated many hard to solve search problems. Thus, a readily computed measure of problem structure predicts the difficulty of solving the problem, on average. However, this prediction is associated with a large variance and depends on the somewhat arbitrary choice of the problem ensemble. Thus these results are of limited direct use for individual instances. To help address this limitation, additional parameters, describing problem structure as well as heuristic effectiveness, are introduced. This also highlights the distinction between the statistical mechanics of combinatorial search problems, with their exponentially large search spaces, and physical systems, whose interactions are often governed by a simple euclidean metric. Chapter 1
Early estimates of the size of branch-and-bound trees
- INFORMS Journal on Computing
, 2006
"... This paper intends to show that the time needed to solve mixed integer programming problems by branch and bound can be roughly predicted early in the solution process. We construct a procedure that can be implemented as part of an MIP solver. It is based on analyzing the partial tree resulting from ..."
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Cited by 15 (0 self)
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This paper intends to show that the time needed to solve mixed integer programming problems by branch and bound can be roughly predicted early in the solution process. We construct a procedure that can be implemented as part of an MIP solver. It is based on analyzing the partial tree resulting from running the algorithm for a short period of time, and predicting the shape of the whole tree. The procedure is tested on instances from the literature. This work was inspired by the practical applicability of such a result. 1.
How to Avoid Building DataBlades That Know the Value of Everything and the Cost of Nothing
- Proc. of SSDBM
, 1999
"... The object-relational database management system (ORDBMS) offers many potential benefits for scientific, multimedia and financial applications. However, work remains in the integration of domain-specific class libraries into ORDBMS query processing. A major problem is that the standard mechanisms fo ..."
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Cited by 13 (0 self)
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The object-relational database management system (ORDBMS) offers many potential benefits for scientific, multimedia and financial applications. However, work remains in the integration of domain-specific class libraries into ORDBMS query processing. A major problem is that the standard mechanisms for query selectivity estimation, taken from relational database systems, rely on properties specific to the standard data types; creation of new mechanisms remains extremely difficult because the software interfaces provided by vendors are relatively low-level. In this paper, we discuss extensions of the generalized search tree, or GiST, to support a higher-level but less type-specific approach. Specifically, we discuss the computation of selectivity estimates with confidence intervals using a variety of index-based approaches and present results from an experimental comparison of these methods with several estimators from the literature. 1.
Satometer: How Much Have We Searched?
- In Design Automation Conf., 737–742. IEEE
, 2002
"... We introduce Satometer, a tool that can be used to estimate the percentage of the search space actually explored by a backtrack SAT solver. Satometer calculates a normalized rainterm count for those portions of the search space identified by conflicts. The computation is carried out using a zero-sup ..."
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Cited by 12 (0 self)
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We introduce Satometer, a tool that can be used to estimate the percentage of the search space actually explored by a backtrack SAT solver. Satometer calculates a normalized rainterm count for those portions of the search space identified by conflicts. The computation is carried out using a zero-suppressed BDD data structure and can have adjustable accuracy. The data provided by Satometer can help diagnose the performance of SAT solvers and can shed light on the nature of a SAT instance.
Combinatorics of Go
, 2007
"... We also study the Game Tree complexity of Go, proving an upper bound on the number of possible games of (mn)L(m,n) and a lower bound of 22 n2/2-O(n) on n * n and 22n-1 on 1 * n boards, in addition to exact counts for mn < = 4 and estimates up to mn = 9. We end with investigating whether one game ..."
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Cited by 7 (0 self)
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We also study the Game Tree complexity of Go, proving an upper bound on the number of possible games of (mn)L(m,n) and a lower bound of 22 n2/2-O(n) on n * n and 22n-1 on 1 * n boards, in addition to exact counts for mn < = 4 and estimates up to mn = 9. We end with investigating whether one game can encompass all legal positions.
A Sampling-Based Heuristic for Tree Search Applied to Grammar Induction
- In Proceedings of AAAI-98
, 1998
"... In the field of Operation Research and Artificial Intelligence, several stochastic search algorithms have been designed based on the theory of global random search (Zhigljavsky 1991). Basically, those techniques iteratively sample the search space with respect to a probability distribution which is ..."
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Cited by 7 (0 self)
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In the field of Operation Research and Artificial Intelligence, several stochastic search algorithms have been designed based on the theory of global random search (Zhigljavsky 1991). Basically, those techniques iteratively sample the search space with respect to a probability distribution which is updated according to the result of previous samples and some predefined strategy. Genetic Algorithms (GAs) (Goldberg 1989) or Greedy Randomized Adaptive Search Procedures (GRASP) (Feo & Resende 1995) are two particular instances of this paradigm. In this paper, we present SAGE, a search algorithm based on the same fundamental mechanisms as those techniques. However, it addresses a class of problems for which it is difficult to design transformation operators to perform local search because of intrinsic constraints in the definition of the problem itself. For those problems, a procedural approach is the natural way to construct solutions, resulting in a state space represented as a tree or a ...
Predicting optimal solution cost with bidirectional stratified sampling
- In ICAPS
, 2012
"... Optimal planning and heuristic search systems solve state-space search problems by finding a least-cost path from start to goal. As a byproduct of having an optimal path they also determine the optimal solution cost. In this paper we focus on the problem of determining the optimal solution cost for ..."
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Cited by 5 (5 self)
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Optimal planning and heuristic search systems solve state-space search problems by finding a least-cost path from start to goal. As a byproduct of having an optimal path they also determine the optimal solution cost. In this paper we focus on the problem of determining the optimal solution cost for a state-space search problem directly, i.e., without actually finding a solution path of that cost. We present an efficient algorithm, BiSS, based on ideas of bidirectional search and stratified sampling that produces accurate estimates of the optimal solution cost. Our method is guaranteed to return the optimal solution cost in the limit as the sample size goes to infinity. We show empirically that our method makes accurate predictions in several domains. In addition, we show that our method scales to state spaces much larger than can be solved optimally. In particular, we estimate the average solution cost for the 6x6, 7x7, and 8x8 Sliding-Tile Puzzle and provide indirect evidence that these estimates are accurate.
