Abstract. Machine learning can be used to build models that predict the runtime of search algorithms for hard combinatorial problems. Such empirical hardness models have previously been studied for complete, deterministic search algorithms. In this work, we demonstrate that such models can also make surprisingly accurate predictions of the run-time distributions of incomplete and randomized search methods, such as stochastic local search algorithms. We also show for the first time how information about an algorithm’s parameter settings can be incorporated into a model, and how such models can be used to automatically adjust the algorithm’s parameters on a per-instance basis in order to optimize its performance. Empirical results for Novelty + and SAPS on structured and unstructured SAT instances show very good predictive performance and significant speedups of our automatically determined parameter settings when compared to the default and best fixed distribution-specific parameter settings. 1

The determination of appropriate values for free algorithm parameters is a challenging and tedious task in the design of effective algorithms for hard problems. Such parameters include categorical choices (e.g., neighborhood structure in local search or variable/value ordering heuristics in tree search), as well as numerical parameters (e.g., noise or restart timing). In practice, tuning of these parameters is largely carried out manually by applying rules of thumb and crude heuristics, while more principled approaches are only rarely used. In this paper, we present a local search approach for algorithm configuration and prove its convergence to the globally optimal parameter configuration. Our approach is very versatile: it can, e.g., be used for minimising run-time in decision problems or for maximising solution quality in optimisation problems. It further applies to arbitrary algorithms, including heuristic tree search and local search algorithms, with no limitation on the number of parameters. Experiments in four algorithm configuration scenarios demonstrate that our automatically determined parameter settings always outperform the algorithm defaults, sometimes by several orders of magnitude. Our approach also shows better performance and greater flexibility than the recent CALIBRA system. Our ParamILS code, along with instructions on how to use it for tuning your own algorithms, is available on-line at

The identification of performance-optimizing 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 local-search-based 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. 1.

Parameterized heuristics abound in computer aided design and verification, and manual tuning of the respective parameters is difficult and time-consuming. Very recent results from the artificial intelligence (AI) community suggest that this tuning process can be automated, and that doing so can lead to significant performance improvements; furthermore, automated parameter optimization can provide valuable guidance during the development of heuristic algorithms. In this paper, we study how such an AI approach can improve a state-of-theart SAT solver for large, real-world bounded model-checking and software verification instances. The resulting, automaticallyderived parameter settings yielded runtimes on average 4.5 times faster on bounded model checking instances and 500 times faster on software verification problems than extensive handtuning of the decision procedure. Furthermore, the availability of automatic tuning influenced the design of the solver, and the automatically-derived parameter settings provided a deeper insight into the properties of problem instances.

Abstract. A problem that is inherent to the development and efficient use of solvers is that of tuning parameters. The CP community has a long history of addressing this task automatically. We propose a robust, inherently parallel genetic algorithm for the problem of configuring solvers automatically. In order to cope with the high costs of evaluating the fitness of individuals, we introduce a gender separation whereby we apply different selection pressure on both genders. Experimental results on a selection of SAT solvers show significant performance and robustness gains over the current state-of-the-art in automatic algorithm configuration. 1

Tuning an algorithm’s parameters for robust and high performance is a tedious and time-consuming task that often requires knowledge about both the domain and the algorithm of interest. Furthermore, the optimal parameter configuration to use may differ considerably across problem instances. In this report, we define and tackle the algorithm configuration problem, which is to automatically choose the optimal parameter configuration for a given algorithm on a per-instance base. We employ an indirect approach that predicts algorithm runtime for the problem instance at hand and each (continuous) parameter configuration, and then simply chooses the configuration that minimizes the prediction. This approach is based on similar work by Leyton-Brown et al. [LBNS02, NLBD + 04] who tackle the algorithm selection problem [Ric76] (given a problem instance, choose the best algorithm to solve it). While all previous studies for runtime prediction focussed on tree search algorithm, we demonstrate that it is possible to fairly accurately predict the runtime of SAPS [HTH02], one of the best-performing stochastic local search algorithms for SAT. We also show that our approach automatically picks parameter configurations that speed up SAPS by an average factor of more than two when compared to its default parameter configuration. Finally, we introduce sequential Bayesian learning to the problem of runtime prediction, enabling an incremental learning approach and yielding very informative estimates of predictive uncertainty. 1

Abstract. State-of-the-art solvers for mixed integer programming (MIP) problems are highly parameterized, and finding parameter settings that achieve high performance for specific types of MIP instances is challenging. We study the application of an automated algorithm configuration procedure to different MIP solvers, instance types and optimization objectives. We show that this fullyautomated process yields substantial improvements to the performance of three MIP solvers: CPLEX,GUROBI,andLPSOLVE. Although our method can be used “out of the box ” without any domain knowledge specific to MIP, we show that it outperforms the CPLEX special-purpose automated tuning tool. 1

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High-performance algorithms play an important role in many areas of computer science and are core components of many software systems used in real-world applications. Traditionally, the creation of these algorithms requires considerable expertise and experience, often in combination with a substantial amount of trial and error. Here, we outline a new approach to the process of designing high-performance algorithms that is based on the use of automated procedures for exploring potentially very large spaces of candidate designs. We contrast this computer-aided design approach with the traditional approach and discuss why it can be expected to yield better performing, yet simpler algorithms. Finally, we sketch out the high-level design of a software environment that supports our new design approach. Existing work on algorithm portfolios, algorithm selection, algorithm configuration and parameter tuning, but also on general methods for discrete and continuous optimisation methods fits naturally into our design approach and can be integrated into the proposed software environment. 1

This research uses a Design of Experiments (DOE) approach to build a predictive model of the performance of a combinatorial optimization heuristic over a range of heuristic tuning parameter settings and problem instance characteristics. The heuristic is Ant Colony System (ACS) for the Travelling Salesperson Problem. 10 heurstic tuning parameters and 2 problem characteristics are considered. Response Surface Models (RSM) of the solution quality and solution time predicted ACS performance on both new instances from a publicly available problem generator and new real-world instances from the TSPLIB benchmark library. A numerical optimisation of the RSMs is used to find the tuning parameter settings that yield optimal performance in terms of solution quality and solution time. This paper is the first use of desirability functions, a well-established technique in DOE, to simultaneously optimise these conflicting goals. Finally, overlay plots are used to examine the robustness of the performance of the optimised heuristic across a range of problem instance characteristics. These plots give predictions on the range of problem instances for which a given solution quality can be expected within a given solution time.