This paper describes ILP-PLAN, a framework for solving AI planning problems represented as integer linear programs. ILP-PLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can be effectively solved using both traditional branchand -bound IP solvers and efficient new integer local search algorithms. ILP-PLAN can find better quality solutions for a set of hard benchmark logistics planning problems than had been found by any earlier system. 1 Introduction In recent years the AI community witnessed the unexpected success of satisfiability testing as a method for solving state-space planning problems (Weld 1999). Kautz and Selman (1996) demonstrated that in certain computationally challenging domains, the approach of axiomatizing problems in propositional logic and solving them with general randomized SAT algorithms (SATPLAN) was competitive with or superior to the ...

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.

This paper introduces a new hybrid method for efficiently integrating Pseudo-Boolean (PB) constraints into generic SAT solvers in order to solve PB satisfiability and optimization problems. To achieve this, we adopt the cutting-plane technique to draw inferences among PB constraints and combine it with generic implication graph analysis for conflictinduced learning. Novel features of our approach include a light-weight and efficient hybrid learning and backjumping strategy for analyzing PB constraints and CNF clauses in order to simultaneously learn both a CNF clause and a PB constraint with minimum overhead and use both to determine the backtrack level. Several techniques for handling the original and learned PB constraints are introduced. Overall, our method benefits significantly from the pruning power of the learned PB constraints, while keeping the overhead of adding them into the problem low. In this paper, we also address two other methods for solving PB problems, namely Integer Linear Programming (ILP) and pre-processing to CNF SAT, and present a thorough comparison between them and our hybrid method. Experimental comparison of our method against other hybrid approaches is also demonstrated. Additionally, we provide details of the MiniSAT-based implementation of our solver Pueblo to enable the reader to construct a similar one.

Many constraint satisfaction and optimisation problems can be expressed using linear constraints on pseudo-Boolean (0/1) variables. Problems expressed in this form are usually solved by integer programming techniques, but good results have also been obtained using generalisations of SAT algorithms based on both backtracking and local search. A recent class of algorithm uses randomised backtracking to combine constraint propagation with local search-like scalability, at the cost of completeness. This paper describes such an algorithm for linear pseudo-Boolean constraint problems. In experiments it compares well with state-of-the-art algorithms on hardware verification and balanced incomplete block design generation, and finds improved solutions for three instances of the Social Golfer Problem.

We study local-search satisfiability solvers for propositional logic extended with cardinality atoms, that is, expressions that provide explicit ways to model constraints on cardinalities of sets. Adding cardinality atoms to the language of propositional logic facilitates modeling search problems and often results in very concise encodings. We propose two "native" local-search solvers for theories in the extended language.

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In recent years, there has been an explosion of research in AI into propositional satis ability (or Sat). There are many factors behind the increased interest in this area. One factor is the improvement in search procedures for Sat. New local search procedures like Gsat are able to solve Sat problems with thousands of variables. At the same time, implementations of complete search algorithms like Davis-Putnam have been able to solve open mathematical problems. Another factor is the identi cation of hard Sat problems at a phase transition in solubility. A third factor is the demonstration that we can often solve real world problems by encoding them into Sat. There has also seen an improved theoretical understanding of Sat, particularly in the analysis of such phase transition behaviour. This paper reviews the state of the art for research into satis ability, and discuss applications in which algorithms for satis ability have proved successful.

Abstract. In 1997 we presented ten challenges for research on satisfiability testing [1]. In this paper we review recent progress towards each of these challenges, including our own work on the power of clause learning and randomized restart policies. 1

This paper describes ILP-PLAN, a framework for solving AI planning problems represented as integer linear programs. ILP-PLAN extends the planning as satisfiability framework to handle plans with resources, action costs, and complex objective functions. We show that challenging planning problems can be effectively solved using both traditional branch-and-bound integer programming solvers and efficient new integer local search algorithms. ILP-PLAN can find better quality solutions for a set of hard benchmark logistics planning problems than had been found by any earlier system. 1

Integer and combinatorial optimization problems constitute a major challenge for algorithmics. They arise when a large number of discrete organizational decisions have to be made, subject to constraints and optimization criteria. This thesis