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.

We provide an overview of the organization and results of the deterministic part of the 4th International Planning Competition, i.e., of the part concerned with evaluating systems doing deterministic planning. IPC-4 attracted even more competing systems than its already large predecessors, and the competition event was revised in several important respects. After giving an introduction to the IPC, we briefly explain the main differences between the deterministic part of IPC-4 and its predecessors. We then introduce formally the language used, called PDDL2.2 that extends PDDL2.1 by derived predicates and timed initial literals. We list the competing systems and overview the results of the competition. The entire set of data is far too large to be presented in full. We provide a detailed summary; the complete data is available in an online appendix. We explain how we awarded the competition prizes.

Real-time search methods are suited for tasks in which the agent is interacting with an initially unknown environment in real time. In such simultaneous planning and learning problems, the agent has to select its actions in a limited amount of time, while sensing only a local part of the environment centered at the agents current location. Real-time heuristic search agents select actions using a limited lookahead search and evaluating the frontier states with a heuristic function. Over repeated experiences, they refine heuristic values of states to avoid infinite loops and to converge to better solutions. The wide spread of such settings in autonomous software and hardware agents has led to an explosion of real-time search algorithms over the last two decades. Not only is a potential user confronted with a hodgepodge of algorithms, but he also faces the choice of control parameters they use. In this paper we address both problems. The first contribution is an introduction of a simple three-parameter framework (named LRTS) which extracts the core ideas behind many existing algorithms. We then prove that LRTA*, epsilon-LRTA*, SLA*, and gamma-Trap algorithms are special cases of our framework. Thus, they are unified and extended with additional features. Second, we prove completeness and convergence of any algorithm covered by the LRTS framework. Third, we prove several upper-bounds relating the control parameters and solution quality. Finally, we analyze the influence of the three control parameters empirically in the realistic scalable domains of real-time navigation on initially unknown maps from a commercial role-playing game as well as routing in ad hoc sensor networks.

A decision process in which rewards depend on history rather than merely on the current state is called a decision process with non-Markovian rewards (NMRDP). In decision-theoretic planning, where many desirable behaviours are more naturally expressed as properties of execution sequences rather than as properties of states, NMRDPs form a more natural model than the commonly adopted fully Markovian decision process (MDP) model. While the more tractable solution methods developed for MDPs do not directly apply in the presence of non-Markovian rewards, a number of solution methods for NMRDPs have been proposed in the literature. These all exploit a compact specification of the non-Markovian reward function in temporal logic, to automatically translate the NMRDP into an equivalent MDP which is solved using efficient MDP solution methods. This paper presents NMRDPP (Non-Markovian Reward Decision Process Planner), a software platform for the development and experimentation of methods for decision-theoretic planning with non-Markovian rewards. The current version of NMRDPP implements, under a single interface, a family of methods based on existing as well as new approaches which we describe in detail. These include dynamic programming, heuristic search, and structured methods. Using NMRDPP, we compare the methods and identify certain problem features that affect their performance. NMRDPPs treatment of non-Markovian rewards is inspired by the treatment of domain-specific search control knowledge in the TLPlan planner, which it incorporates as a special case. In the First International Probabilistic Planning Competition, NMRDPP was able to compete and perform well in both the domain-independent and hand-coded tracks, using search control knowledge in the latter.

Tabu search is one of the most effective heuristics for locating high-quality solutions to a diverse array of NP-hard combinatorial optimization problems. Despite the widespread success of tabu search, researchers have a poor understanding of many key theoretical aspects of this algorithm, including models of the high-level run-time dynamics and identification of those search space features that influence problem difficulty. We consider these questions in the context of the job-shop scheduling problem (JSP), a domain where tabu search algorithms have been shown to be remarkably effective. Previously, we demonstrated that the mean distance between random local optima and the nearest optimal solution is highly correlated with problem difficulty for a well-known tabu search algorithm for the JSP introduced by Taillard. In this paper, we discuss various shortcomings of this measure and develop a new model of problem difficulty that corrects these deficiencies. We show that Taillards algorithm can be modeled with high fidelity as a simple variant of a straightforward random walk. The random walk model accounts for nearly all of the variability in the cost required to locate both optimal and sub-optimal solutions to random JSPs, and provides an explanation for differences in the difficulty of random versus structured JSPs. Finally, we discuss and empirically substantiate two novel predictions regarding tabu search algorithm behavior. First, the method for constructing the initial solution is highly unlikely to impact the performance of tabu search. Second, tabu tenure should be selected to be as small as possible while simultaneously avoiding search stagnation; values larger than necessary lead to significant degradations in performance.

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature.

This paper studies the problem of learning diagnostic policies from training examples. A diagnostic policy is a complete description of the decision-making actions of a diagnostician (i.e., tests followed by a diagnostic decision) for all possible combinations of test results. An optimal diagnostic policy is one that minimizes the expected total cost, which is the sum of measurement costs and misdiagnosis costs. In most diagnostic settings, there is a tradeoff between these two kinds of costs. This paper formalizes diagnostic decision making as a Markov Decision Process (MDP). The paper introduces a new family of systematic search algorithms based on the AO* algorithm to solve this MDP. To make AO* efficient, the paper describes an admissible heuristic that enables AO* to prune large parts of the search space. The paper also introduces several greedy algorithms including some improvements over previously-published methods. The paper then addresses the question of learning diagnostic policies from examples. When the probabilities of diseases and test results are computed from training data, there is a great danger of overfitting. To reduce overfitting, regularizers are integrated into the search algorithms. Finally, the paper compares the proposed methods on five benchmark diagnostic data sets. The studies show that in most cases the systematic search methods produce better diagnostic policies than the greedy methods. In addition, the studies show that for training sets of realistic size, the systematic search algorithms are practical on todays desktop computers.

This work focuses on improving state-of-the-art in stochastic local search (SLS) for solving Boolean satisfiability (SAT) instances arising from real-world industrial SAT application domains. The recently introduced SLS method CRSat has been shown to noticeably improve on previously suggested SLS techniques in solving such real-world instances by combining justification-based local search with limited Boolean constraint propagation on the non-clausal formula representation form of Boolean circuits. In this work, we study possibilities of further improving the performance of CRSat by exploiting circuit-level structural knowledge for developing new search heuristics for CRSat. To this end, we introduce and experimentally evaluate a variety of search heuristics, many of which are motivated by circuit-level heuristics originally developed in completely different contexts, e.g., for electronic design automation applications. To the best of our knowledge, most of the heuristics are novel in the context of SLS for SAT and, more generally, SLS for constraint satisfaction problems.

This is the second of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper presents the theoretical basis for the ideas underlying ZAP, arguing that existing ideas in this area exploit a single, recurring structure in that multiple database axioms can be obtained by operating on a single axiom using a subgroup of the group of permutations on the literals in the problem. We argue that the group structure precisely captures the general structure at which earlier approaches hinted, and give numerous examples of its use. We go on to extend the Davis-Putnam-Logemann-Loveland inference procedure to this broader setting, and show that earlier computational improvements are either subsumed or left intact by the new method. The third paper in this series discusses ZAPs implementation and presents experimental performance results.

Variable elimination is a general technique for constraint processing. It is often discarded because of its high space complexity. However, it can be extremely useful when combined with other techniques. In this paper we study the applicability of variable elimination to the challenging problem of finding still-lifes. We illustrate several alternatives: variable elimination as a stand-alone algorithm, interleaved with search, and as a source of good quality lower bounds. We show that these techniques are the best known option both theoretically and empirically. In our experiments we have been able to solve the n=20 instance, which is far beyond reach with alternative approaches.