Combinatorial auctions (CAs) have emerged as an important model in economics and show promise as a useful tool for tackling resource allocation in AI. Unfortunately, winner determination for CAs is NP-hard and recent algorithms have difficulty with problems involving goods and bids beyond the hundreds. We apply a new stochastic local search algorithm, Casanova, to this problem, and demonstrate that it finds high quality (even optimal) solutions much faster than recently proposed methods (up to several orders of magnitude), particularly for large problems. We also propose a logical language for naturally expressing combinatorial bids in which a single logical bid corresponds to a large (often exponential) number of explicit bids. We show that Casanovaperforms much better than systematic methods on such problems. 1

Stochastic local search (SLS) algorithms for the propositional satisfiability problem (SAT) have been successfully applied to solve suitably encoded search problems from various domains. One drawback of these algorithms is that they are usually incomplete. We refine the notion of incompleteness for stochastic decision algorithms by introducing the notion of "probabilistic asymptotic completeness" (PAC) and prove for a number of well-known SLS algorithms whether or not they have this property. We also give evidence for the practical impact of the PAC property and show how to achieve the PAC property and significantly improved performance in practice for some of the most powerful SLS algorithms for SAT, using a simple and general technique called "random walk extension".

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 well-known 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 SAT-encoded problems from various domains. We also investigate the robustness of the observed performance characteristics as algorithm-dependent and problem-dependent 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 best-performing algorithms and shows how this can be overcome.

Stochastic local search (SLS) algorithms have been successfully applied to hard combinatorial problems from different domains. Due to their inherent randomness, the run-time behaviour of these algorithms is characterised by a random variable. The detailed knowledge of the run-time distribution provides important information about the behaviour of SLS algorithms. In this paper we investigate the empirical run-time distributions for Walksat, one of the most powerful SLS algorithms for the Propositional Satisfiability Problem (SAT). Using statistical analysis techniques, we show that on hard Random-3-SAT problems, Walksat's run-time behaviour can be characterised by exponential distributions. This characterisation can be generalised to various SLS algorithms for SAT and to encoded problems from other domains. This result also has a number of consequences which are of theoretical as well as practical interest. One of these is the fact that these algorithms can be easily parallelised such that optimal speed-up is achieved for hard problem instances.

We are interested in supporting multi-agent contracting, in which customer agents solicit the resources and capabilities of other, self-interested agents in order to accomplish their goals. Goals may

Stochastic local search (SLS) algorithms for propositional satisfiability testing (SAT) have become popular and powerful tools for solving suitably encoded hard combinatorial from different domains like, e.g., planning. Consequently, there is a considerable interest in finding SAT-encodings which facilitate the efficient application of SLS algorithms. In this work, we study how two encodings schemes for combinatorial problems, like the well-known Constraint Satisfaction or Hamilton Circuit Problem, affect SLS performance on the SAT-encoded instances. To explain the observed performance differences, we identify features of the induces search spaces which affect SLS performance. We furthermore present initial results of a comparitive analysis of the performance of the SAT-encoding and-solving approach versus that of native SLS algorithms directly applied to the unencoded problem instances. 1

The performance of stochastic optimisers can be assessed experimentally on given problems by performing multiple optimisation runs, and analysing the results. Since an optimiser may be viewed as an estimator for the (Pareto) minimum of a (vector) function, stochastic optimiser performance is discussed in the light of the criteria applicable to more usual statistical estimators. Multiobjective optimisers are shown to deviate considerably from standard point estimators, and to require special statistical methodology. The attainment function is formulated, and related results from random closed-set theory are presented, which cast the attainment function as a mean-like measure for the outcomes of multiobjective optimisers. Finally, a covariance-measure is defined, which should bring additional insight into the stochastic behaviour of multiobjective optimisers. Computational issues and directions for further work are discussed at the end of the paper.

Abstract. In this paper, we show how Guided Local Search (GLS) can be applied to the SAT problem and show how the resulting algorithm can be naturally extended to solve the weighted MAX-SAT problem. GLS is a general, penalty-based metaheuristic, which sits on top of local search algorithms to help guide them out of local minima. GLS has been shown to be successful in solving a number of practical real life problems, such as the travelling salesman problem, BT's workforce scheduling problem, the radio link frequency assignment problem and the vehicle routing problem. We present empirical results of applying GLS to instances of the SAT problem from the DIMACS archive and also a small set of weighted MAX-SAT problem instances and compare them against the results of other local search algorithms for the SAT problem. Keywords: SAT problem, Local Search, Meta-heuristics, Optimisation 1.

Conventional ways of using local search are difficult to generalize. Increased efficiency is the only goal, generality often being disregarded. This is manifested in the highly monolithic encodings of complex problems and the application of highly specific satisfaction methods. Other approaches take the general constraint programming framework as a starting point and try to introduce local search methods for constraint satisfaction. These methods frequently fail because they have only a very limited view of the unknown search-space structure. The present paper attempts to overcome the drawbacks of these two approaches by using global constraints. The use of global constraints for local search allows us to revise a current state on a more global level with domain-specific knowledge, while preserving features like reusability and maintenance. The proposed strategy is demonstrated on a dynamic job-shop scheduling problem.

Abstract. In this article we present an application of the Ant Colony Optimization (ACO) metaheuristic to the single machine total weighted tardiness problem. First, we briefly discuss the constructive phase of ACO in which a colony of artificial ants generates a set of feasible solutions. Then, we introduce some simple but very effective local search. Last, we combine the constructive phase with local search obtaining a novel ACO algorithm that uses a heterogeneous colony of ants and is highly effective in finding the best-known solutions on all instances of a widely used set of benchmark problems. 1