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

In this paper, we introduce DLS-MC, a new stochastic local search algorithm for the maximum clique problem. DLS-MC alternates between phases of iterative improvement, during which suitable vertices are added to the current clique, and plateau search, during which vertices of the current clique are swapped with vertices not contained in the current clique. The selection of vertices is solely based on vertex penalties that are dynamically adjusted during the search, and a perturbation mechanism is used to overcome search stagnation. The behaviour of DLS-MC is controlled by a single parameter, penalty delay, which controls the frequency at which vertex penalties are reduced. We show empirically that DLS-MC achieves substantial performance improvements over state-of-the-art algorithms for the maximum clique problem over a large range of the commonly used DIMACS benchmark instances. 1.

Abstract. Many current local search algorithms for SAT fall into one of two classes. Random walk algorithms such as Walksat/SKC, Novelty+ and HWSAT are very successful but can be trapped for long periods in deep local minima. Clause weighting algorithms such as DLM, GLS, ESG and SAPS are good at escaping local minima but require expensive smoothing phases in which all weights are updated. We show that Walksat performance can be greatly enhanced by weighting variables instead of clauses, giving the best known results on some benchmarks. The new algorithm uses an efficient weight smoothing technique with no smoothing phase. 1

Abstract. The effects of combining search and modelling techniques can be complex and unpredictable, so guidelines are very important for the design and development of effective and robust solvers and models. A recently observed phenomenon is the negative effect of symmetry breaking constraints on local search performance. The reasons for this are poorly understood, and we attempt to shed light on the phenomenon by testing three conjectures: that the constraints create deep new local optima; that they can reduce the relative size of the basins of attraction of global optima; and that complex local search heuristics reduce their negative effects. 1

In this paper, we study the behaviour of the Scaling and Probabilistic Smoothing (SAPS) dynamic local search algorithm on the unweighted MAX-SAT problem. MAX-SAT is a conceptually simple combinatorial problem of substantial theoretical and practical interest; many application-relevant problems, including scheduling problems or most probable explanation finding in Bayes nets, can be encoded and solved as MAX-SAT. This paper is a natural extension of our previous work, where we introduced SAPS, and demonstrated that it is amongst the state-of-the-art local search algorithms for solvable SAT problem instances.

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

Local search procedures for solving satisfiability problems have attracted considerable attention since the development of GSAT in 1992. However, recent work indicates that for many real-world problems, complete search methods have the advantage, because modern heuristics are able to effectively exploit problem structure. Indeed, to develop a local search technique that can effectively deal with variable dependencies has been an open challenge since1997. In this paper we show that local search techniques can effectively exploit information about problem structure producing significant improvements in performance on structured problem instances. Building on the earlier work of Ostrowski et al. we describe how information about variable dependencies can be built into a local search, so that only independent variables are considered for flipping. The cost effect of a flip is then dynamically calculated using a dependency lattice that models dependent variables using gates (specifically and, or and equivalence gates). The experimental study on hard structured benchmark problems demonstrates that our new approach significantly outperforms the previously reported best local search techniques. 1

Systematic search and local search paradigms for combinatorial problems are generally believed to have complementary strengths. Nevertheless, attempts to combine the power of the two paradigms have had limited success, due in part to the expensive information communication overhead involved. We propose a hybrid strategy based on shared memory, ideally suited for multi-core processor architectures. This method enables continuous information exchange between two solvers without slowing down either of the two. Such a hybrid search strategy is surprisingly effective, leading to substantially better quality solutions to many challenging Maximum Satisfiability (MaxSAT) instances than what the current best exact or heuristic methods yield, and it often achieves this within seconds. This hybrid approach is naturally best suited to MaxSAT instances for which proving unsatisfiability is already hard; otherwise the method falls back to pure local search. 1

Abstract. The optimization of algorithm performance by automatically identifying good parameter settings is an important problem that has recently attracted much attention in the discrete optimization community. One promising approach constructs predictive performance models and uses them to focus attention on promising regions of a design space. Such methods have become quite sophisticated and have achieved significant successes on other problems, particularly in experimental design applications. However, they have typically been designed to achieve good performance only under a budget expressed as a number of function evaluations (e.g., target algorithm runs). In this work, we show how to extend the Sequential Parameter Optimization framework [SPO; see 5] to operate effectively under time bounds. Our methods take into account both the varying amount of time required for different algorithm runs and the complexity of model building and evaluation; they are particularly useful for minimizing target algorithm runtime. Specifically, we introduce a novel intensification mechanism, and show how to reduce the overhead incurred by constructing and using models. Overall, we show that our method represents a new state of the art in model-based optimization of algorithms with continuous parameters on single problem instances. 1

Abstract. Local search is widely applied to satisfiable SAT problems, and on some classes outperforms backtrack search. An intriguing challenge posed by Selman, Kautz and McAllester in 1997 is to use it instead to prove unsatisfiability. We investigate two distinct approaches. Firstly we apply standard local search to a reformulation of the problem, such that a solution to the reformulation corresponds to a refutation of the original problem. Secondly we design a greedy randomised resolution algorithm that will eventually discover proofs of any size while using bounded memory. We show experimentally that both approaches can refute some problems more quickly than backtrack search. 1