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

Propositional Satisfiability (SAT) and Constraint Programming (CP) have developed as two relatively independent threads of research, cross-fertilising occasionally. These two approaches to problem solving have a lot in common, as evidenced by similar ideas underlying the branch and prune algorithms that are most successful at solving both kinds of problems. They also exhibit differences in the way they are used to state and solve problems, since SAT’s approach is in general a black-box approach, while CP aims at being tunable and programmable. This survey overviews the two areas in a comparative way, emphasising the similarities and differences between the two and the points where we feel that one technology can benefit from ideas or experience acquired

Abstract. In recent years, dynamic local search (DLS) clause weighting algorithms have emerged as the local search state-of-the-art for solving propositional satisfiability problems. However, most DLS algorithms require the tuning of domain dependent parameters before their performance becomes competitive. If manual parameter tuning is impractical then various mechanisms have been developed that can automatically adjust a parameter value during the search. To date, the most effective adaptive clause weighting algorithm is RSAPS. However, RSAPS is unable to convincingly outperform the best non-weighting adaptive algorithm AdaptNovelty +, even though manually tuned clause weighting algorithms can routinely outperform the Novelty + heuristic on which AdaptNovelty + is based. In this study we introduce R+DDFW +, an enhanced version of the DDFW clause weighting algorithm developed in 2005, that not only adapts the total amount of weight according to the degree of stagnation in the search, but also incorporates the latest resolution-based preprocessing approach used by the winner of the 2005 SAT competition (R+AdaptNovelty +). In an empirical study we show R+DDFW + improves on DDFW and outperforms the other leading adaptive (R+Adapt-Novelty +, R+RSAPS) and non-adaptive (R+G 2 WSAT) local search solvers over a range of random and structured benchmark problems. 1

Algorithm selection is typically based on models of algorithm performance, learned during a separate offline training sequence, which can be prohibitively expensive. In recent work, we adopted an online approach, in which a performance model is iteratively updated and used to guide selection on a sequence of problem instances. The resulting exploration-exploitation trade-off was represented as a bandit problem with expert advice, using an existing solver for this game, but this required the setting of an arbitrary bound on algorithm runtimes, thus invalidating the optimal regret of the solver. In this paper, we propose a simpler framework for representing algorithm selection as a bandit problem, with partial information, and an unknown bound on losses. We adapt an existing solver to this game, proving a bound on its expected regret, which holds also for the resulting algorithm selection technique. We present preliminary experiments with a set of SAT solvers on a mixed SAT-UNSAT benchmark.

We present a new method for instance-specific algorithm configuration (ISAC). It is based on the integration of the algorithm configuration system GGA and the recently proposed stochastic offline programming paradigm. ISAC is provided a solver with categorical, ordinal, and/or continuous parameters, a training benchmark set of input instances for that solver, and an algorithm that computes a feature vector that characterizes any given instance. ISAC then provides high quality parameter settings for any new input instance. Experiments on a variety of different constrained optimization and constraint satisfaction solvers show that automatic algorithm configuration vastly outperforms manual tuning. Moreover, we show that instance-specific tuning frequently leads to significant speed-ups over instance-oblivious configurations.

Abstract This paper proposes a flexible software architecture for interactive multiobjective optimization, with a user interface for visualizing the results and facilitating the solution analysis and decision making process. The architecture is modular, it allows for problem-specific extensions, and it is applicable as a post-processing tool for all optimization schemes with a number of different potential solutions. When the architecture is tightly coupled to a specific problem-solving or optimization method, effective interactive schemes where the final decision maker is in the loop can be developed. An application to Reactive Search Optimization is presented. Visualization and optimization are connected through user interaction: the user is in the loop and the system rapidly reacts to user inputs, like specifying a focus of analysis, or preferences for exploring and intensifying the search in interesting areas. The novelty of the visualization approach consists of using recent online graph drawing techniques, with sampling and mental map preserving schemes, in the framework of stochastic local search optimization. Anecdotal results to demonstrate the effectiveness of the approach are shown for some relevant optimization tasks. 1

Abstract. In this work, we present the concept of Continuous Search, the objective of which is to allow any user to eventually get top performance from their constraint solver. Unlike previous approaches (see [9] for a recent survey), Continuous Search does not require the disposal of a large set of representative instances to properly train and learn parameters. It only assumes that once the solver runs in a real situation (often called production mode), instances will come over time, and allow for proper offline continuous training. The objective is therefore not to instantly provide good parameters for top performance, but to take advantage of the real situation to train in the background and improve the performances of the system in an incremental manner. 1

Algorithm portfolio selection as a bandit problem

Algorithm selection can be performed using a model of runtime distribution, learned during a preliminary training phase. There is a trade-off between the performance of model-based algorithm selection, and the cost of learning the model. In this paper, we treat this trade-off in the context of bandit problems. We propose a fully dynamic and online algorithm selection technique, with no separate training phase: all candidate algorithms are run in parallel, while a model incrementally learns their runtime distributions. A redundant set of time allocators uses the partially trained model to propose machine time shares for the algorithms. A bandit problem solver mixes the model-based shares with a uniform share, gradually increasing the impact of the best time allocators as the model improves. We present experiments with a set of SAT solvers on a mixed SAT-UNSAT benchmark; and with a set of solvers for the Auction Winner Determination problem.