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82
Boosting combinatorial search through randomization
, 1998
"... Unpredictability in the running time of complete search procedures can often be explained by the phenomenon of “heavytailed cost distributions”, meaning that at any time during the experiment there is a nonnegligible probability of hitting a problem that requires exponentially more time to solve t ..."
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Cited by 359 (34 self)
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Unpredictability in the running time of complete search procedures can often be explained by the phenomenon of “heavytailed cost distributions”, meaning that at any time during the experiment there is a nonnegligible probability of hitting a problem that requires exponentially more time to solve than any that has been encountered before (Gomes et al. 1998a). We present a general method for introducing controlled randomization into complete search algorithms. The “boosted ” search methods provably eliminate heavytails to the right of the median. Furthermore, they can take advantage of heavytails to the left of the median (that is, a nonnegligible chance of very short runs) to dramatically shorten the solution time. We demonstrate speedups of several orders of magnitude for stateoftheart complete search procedures running on hard, realworld problems.
HeavyTailed Phenomena in Satisfiability and Constraint Satisfaction Problems
 J. of Autom. Reasoning
, 2000
"... Abstract. We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by ver ..."
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Cited by 162 (27 self)
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Abstract. We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by very long tails or “heavy tails”. We will show that these distributions are best characterized by a general class of distributions that can have infinite moments (i.e., an infinite mean, variance, etc.). Such nonstandard distributions have recently been observed in areas as diverse as economics, statistical physics, and geophysics. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We also show how random restarts can effectively eliminate heavytailed behavior. Furthermore, for harder problem instances, we observe long tails on the lefthand side of the distribution, which is indicative of a nonnegligible fraction of relatively short, successful runs. A rapid restart strategy eliminates heavytailed behavior and takes advantage of short runs, significantly reducing expected solution time. We demonstrate speedups of up to two orders of magnitude on SAT and CSP encodings of hard problems in planning, scheduling, and circuit synthesis. Key words: satisfiability, constraint satisfaction, heavy tails, backtracking 1.
ParamILS: An automatic algorithm configuration framework
, 2009
"... The identification of performanceoptimizing parameter settings is an important part of the development and application of algorithms. We describe an automatic framework for this algorithm configuration problem. More formally, we provide methods for optimizing a target algorithm’s performance on a g ..."
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Cited by 145 (39 self)
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The identification of performanceoptimizing parameter settings is an important part of the development and application of algorithms. We describe an automatic framework for this algorithm configuration problem. More formally, we provide methods for optimizing a target algorithm’s performance on a given class of problem instances by varying a set of ordinal and/or categorical parameters. We review a family of localsearchbased algorithm configuration procedures and present novel techniques for accelerating them by adaptively limiting the time spent for evaluating individual configurations. We describe the results of a comprehensive experimental evaluation of our methods, based on the configuration of prominent complete and incomplete algorithms for SAT. We also present what is, to our knowledge, the first published work on automatically configuring the CPLEX mixed integer programming solver. All the algorithms we considered had default parameter settings that were manually identified with considerable effort. Nevertheless, using our automated algorithm configuration procedures, we achieved substantial and consistent performance improvements.
Search in a Small World
, 1998
"... In a graph with a "small world" topology, nodes are highly clustered yet the path length between them is small. Such a topology can make search problems very difficulty since local decisions quickly propagate globally. We show that graphs associated with many different search problem ..."
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Cited by 118 (13 self)
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In a graph with a "small world" topology, nodes are highly clustered yet the path length between them is small. Such a topology can make search problems very difficulty since local decisions quickly propagate globally. We show that graphs associated with many different search problems have a small world topology, and that the cost of solving search problems with such a topology can have a heavytailed distribution.
Sequential ModelBased Optimization for General Algorithm Configuration (extended version)
"... Abstract. Stateoftheart algorithms for hard computational problems often expose many parameters that can be modified to improve empirical performance. However, manually exploring the resulting combinatorial space of parameter settings is tedious and tends to lead to unsatisfactory outcomes. Recen ..."
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Cited by 98 (28 self)
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Abstract. Stateoftheart algorithms for hard computational problems often expose many parameters that can be modified to improve empirical performance. However, manually exploring the resulting combinatorial space of parameter settings is tedious and tends to lead to unsatisfactory outcomes. Recently, automated approaches for solving this algorithm configuration problem have led to substantial improvements in the state of the art for solving various problems. One promising approach constructs explicit regression models to describe the dependence of target algorithm performance on parameter settings; however, this approach has so far been limited to the optimization of few numerical algorithm parameters on single instances. In this paper, we extend this paradigm for the first time to general algorithm configuration problems, allowing many categorical parameters and optimization for sets of instances. We experimentally validate our new algorithm configuration procedure by optimizing a local search and a tree search solver for the propositional satisfiability problem (SAT), as well as the commercial mixed integer programming (MIP) solver CPLEX. In these experiments, our procedure yielded stateoftheart performance, and in many cases outperformed the previous best configuration approach. 1
Generating satisfiable problem instances
 In AAAI/IAAI
, 2000
"... A major difficulty in evaluating incomplete local search style algorithms for constraint satisfaction problems is the need for a source of hard problem instances that are guaranteed to be satisfiable. A standard approach to evaluate incomplete search methods has been to use a general problem generat ..."
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Cited by 89 (11 self)
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A major difficulty in evaluating incomplete local search style algorithms for constraint satisfaction problems is the need for a source of hard problem instances that are guaranteed to be satisfiable. A standard approach to evaluate incomplete search methods has been to use a general problem generator and a complete search method to filter out the unsatisfiable instances. Unfortunately, this approach cannot be used to create problem instances that are beyond the reach of complete search methods. So far, it has proven to be surprisingly difficult to develop a direct generator for satisfiable instances only. In this paper, we propose a generator that only outputs satisfiable problem instances. We also show how one can finely control the hardness of the satisfiable instances by establishing a connection between problem hardness and a new kind of phase transition phenomenon in the space of problem instances. Finally, we use our problem distribution to show the easyhardeasy pattern in search complexity for local search procedures, analogous to the previously reported pattern for complete search methods.
Random constraint satisfaction: Flaws and structure
 Constraints
, 2001
"... 4, and Toby Walsh 5 ..."
Learning the Empirical Hardness of Optimization Problems: The case of combinatorial auctions
 In CP
, 2002
"... We propose a new approach to understanding the algorithmspecific empirical hardness of optimization problems. In this work we focus on the empirical hardness of the winner determination probleman optimization problem arising in combinatorial auctionswhen solved by ILOG's CPLEX software. ..."
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Cited by 76 (23 self)
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We propose a new approach to understanding the algorithmspecific empirical hardness of optimization problems. In this work we focus on the empirical hardness of the winner determination probleman optimization problem arising in combinatorial auctionswhen solved by ILOG's CPLEX software. We consider nine widelyused problem distributions and sample randomly from a continuum of parameter settings for each distribution. First, we contrast the overall empirical hardness of the different distributions. Second, we identify a large number of distributionnonspecific features of data instances and use statistical regression techniques to learn, evaluate and interpret a function from these features to the predicted hardness of an instance.
Local search algorithms for SAT: An empirical evaluation
 JOURNAL OF AUTOMATED REASONING
, 2000
"... Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and Operations Research. For SAT, some of the most successful and powerful algorithms are based on stochastic local search and in the past 10 years a large num ..."
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Cited by 72 (18 self)
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Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and Operations Research. For SAT, some of the most successful and powerful algorithms are based on stochastic local search and in the past 10 years a large number of such algorithms have been proposed and investigated. In this article, we focus on two particularly wellknown families of local search algorithms for SAT, the GSAT and WalkSAT architectures. We present a detailed comparative analysis of these algorithms' performance using a benchmark set which contains instances from randomised distributions as well as SATencoded problems from various domains. We also investigate the robustness of the observed performance characteristics as algorithmdependent and problemdependent parameters are changed. Our empirical analysis gives a very detailed picture of the algorithms' performance for various domains of SAT problems; it also reveals a fundamental weakness in some of the bestperforming algorithms and shows how this can be overcome.
A Bayesian Approach to Tackling Hard Computational Problems
 IN UAI
, 2001
"... We describe research and results centering on the construction and use of Bayesian models that can predict the run time of problem solvers. Our efforts are motivated by observations of high variance in the time required to solve instances for several challenging problems. The methods ..."
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Cited by 72 (11 self)
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We describe research and results centering on the construction and use of Bayesian models that can predict the run time of problem solvers. Our efforts are motivated by observations of high variance in the time required to solve instances for several challenging problems. The methods