This work focuses on macromolecule (poly-e-caprolactone, PCL) self-assembly in acetone/water mixtures by a novel multiscale approach which combines molecular dynamics (MD), a Smoluchowski population balance model (PBM) and computational fluid dynamics (CFD), to model the self-assembly process from the atomistic to the macro-scale
A Pseudo-Boolean (PB) constraint is a linear arithmetic constraint over Boolean variables. PB constraints are and widely used in declarative languages for expressing NP-hard search problems. While there are solvers for sets of PB constraints, there are also reasons to be interested in transforming these to propositional CNF formulas, and a number of methods for doing this have been reported. We introduce a new, two-step, method for transforming PB constraints to propositional CNF formulas. The first step re-writes each PB constraint as a conjunction of PB-Mod constraints, and the second transforms each PB-Mod constraint to CNF. The resulting CNF formulas are compact, and make effective use of unit propagation, in that unit propagation can derive facts from these CNF formulas which it cannot derive from the CNF formulas produced by other commonlyused transformation. We present a preliminary experimental evaluation of the method, using instances of the number partitioning problem as a benchmark set, which indicates that our method out-performs other transformations to CNF when the coefficients of the PB constraints are not small.
Learning representations from data is one of the fundamental problems of artificial intelligence and machine learning. Many different approaches exist for learning representations, but what constitutes a good representation is not yet well understood. In this work, we view the problem of representation learning as one of learning features (e.g., hidden units of neural networks) such that performance of the underlying base system continually improves. We study an important case where learning is done fully online (i.e., on an example-by-example basis) from an unending stream of data, and the computational cost of the learning element should not grow with time or cannot be much more than that of the performance element. Few methods can be used effectively in this case. We show that a search approach to representation learning can naturally fit with this setting. In this approach good representations are searched by generating different features and then testing them for utility. We develop new representation-search methods and show that the generate-and-test approach can be utilized in a simple and effective way for continually improving representations. Our methods are fully online and add only a small fraction to the overall computation. We believe online representation search constitutes an important step toward effective and inexpensive solutions to representation learning problems.
In this paper, a new approach for clauses learning is proposed. By traversing the implication graph sepa- rately from x and ¬x, we derive a new class of bi-asserting clauses that can lead to a more compact implication graph. These new kinds of bi-asserting clauses are much shorter and tend to induce more implications than the classical bi-asserting clauses. Experimental results show that exploiting this new class of bi-asserting clauses improves the performance of state-of-the-art SAT solvers particularly on crafted instances.
Pattern databases (PDBs) have been widely used as heuristics for many types of search spaces, but they have always been computed so as to fit in the main memory of the machine using the PDB. This paper studies the how external-memory PDBs can be used. It presents results of both using hard disk drives and solid-state drives directly to access the data, and of just loading a portion of the PDB into RAM. For the time being, all of these approaches are inferior to building the largest PDB that fits into RAM.
A mutex pair in a state space is a pair of assignments of values to state variables that does not occur in any reachable state. Detecting mutex pairs is a problem that has been addressed frequently in the planning literature. In this paper, we present the Coarse Abstraction (CA) method, a new efficient method for detecting mutex pairs in state spaces represented with multi-valued variables. CA detects mutex pairs based on exhaustive search in a collection of very small abstract state spaces. While in general CA may miss some mutex pairs, we provide a formal guarantee that CA finds all mutex pairs under a simple and quite natural condition. Using this formal guarantee, we prove that these properties hold for a range of common benchmark domains. We also show that CA can find all mutex pairs even if the formal guarantee is not satisfied. Finally, we show that CA’s effectiveness depends on how the domain is represented, and that it can fail to find mutex pairs in some domains and representations.
Many real-world applications require the successful combination of spatial and temporal reasoning. In this paper, we study the general framework of the Traveling Salesman Problem with Simple Temporal Constraints. Representationally, this framework subsumes the Traveling Salesman Problem, Simple Temporal Problems, as well as many of the frameworks described in the literature. We analyze the theoretical properties of the combined problem providing strong inapproximability results for the general problem, and positive results for some special cases.
In this paper, we present fast polynomial-time algorithms for solving classes of submodular constraints over Boolean domains. We pose the identified classes of problems within the general framework of Weighted Constraint Satisfaction Problems (WCSPs), reformulated as minimum weighted vertex cover problems. We examine the Constraint Composite Graphs (CCGs) associated with these WCSPs and provide simple arguments for establishing their tractability. We construct simple - almost trivial - bipartite graph representations for submodular cost functions, and reformulate these WCSPs as max-flow problems on bipartite graphs. By doing this, we achieve better time complexities than state-of-the-art algorithms. We also use CCGs to exploit planarity in variable interaction graphs, and provide algorithms with significantly improved time complexities for classes of submodular constraints. Moreover, our framework for exploiting planarity is not limited to submodular constraints. Our work confirms the usefulness of studying CCGs associated with combinatorial problems modeled as WCSPs.
AI Planning is inherently hard and hence it is desirable to derive as much information as we can from the structure of the planning problem and let this information be exploited by a planner. Many recent planners use the finite-domain state-variable representation of the problem instead of the traditional propositional representation. However, most planning problems are still specified in the propositional representation due to the widespread modeling language PDDL and it is hard to generate a compact and computationally efficient state variable representation from the propositional model. In this paper we propose a novel method for automaticallygenerating an efficient state-variable representation from the propositional representation. This method groups sets of propositions into state variables based onthe mutex relations introduced in the planning graph. As we shall show experimentally, our method outperforms the current state-of-the-art method both in the smaller number of generated state variables and in the increased performance of planners.
In this paper, we present an efficient algorithm for verifying path-consistency on a binary constraint network. The complexities of our algorithm beat the previous conjectures on the lower bounds for verifying path-consistency. We therefore defeat the proofs for several published results that incorrectly rely on these conjectures. Our algorithm is motivated by the idea of reformulating path-consistency verification as fast matrix multiplication. Further, for a computational model that counts arithmetic operations (rather than bit operations), a clever use of the properties of prime numbers allows us to design an even faster variant of the algorithm. Based on our algorithm, we hope to inspire a new class of techniques for verifying and even establishing varying levels of local-consistency on given constraint networks.
Analysing the structures of solution plans generated by AI Planning engines is helpful in improving the generative planning process, as well as shedding light in the study of its theoretical foundations.We investigate a specific property of solution plans, that we called linearity, which refers to a situation where each action achieves an atom (or atoms) for a directly following action, or achieves goal atom(s). Similarly, linearity can be defined for parallel plans where each action in a set of actions executed at some time step, achieves either goal atom(s) or atom(s) for some action executed in the directly following time step. In this paper, we present a general and problem-independent theoretical framework focusing on the analysis of planning operator schema, namely relations of achiever, clobberer and independence, in order to determine whether solvable planning problems using a given operator schema have as solutions optimal (parallel) plans which are linear. The findings presented in this paper deepen current theoretical knowledge, provide helpful information to engineers of new planning domain models, and suggest new ways of improving the performance of state-of-theart (optimal) planning engines.
In Automated Planning, learning and exploiting additional knowledge within a domain model, in order to improve plan generation speed-up and increase the scope of problems solved, has attracted much research. Reformulation techniques such as those based on macro-operators or entanglements are very promising because they are to some extent domain model and planning engine independent. This paper aims to exploit recent work on inner entanglements, relations between pairs of planning operators and predicates encapsulating exclusivity of predicate ‘achievements‘ or ‘requirements’, for generating macro-operators. We discuss conditions which are necessary for generating such macro-operators and conditions that allow removing primitive operators without compromising solvability of a given (class of) problem(s). The effectiveness of our approach will be experimentally shown on a set of well-known benchmark domains using several highperforming planning engines.
We propose an algorithm to reformulate aggregate queries using views in a data integration LAV setting. Our algorithm considers a special case of reformulations where aggregates in the query are expressed as views over aggregates in the view definitions. Although the problem of determining whether two queries are equivalent is undecidable, our algorithm returns an equivalent rewriting if one exists.
We suggest to employ propositional satisfiability techniques in solving a problem of cooperative multi-robot path-finding optimally. Several propositional encodings of path-finding problems have been suggested recently. In this paper we evaluate how efficient these encodings are in solving certain cases of cooperative path-findings problems optimally. Particularly, a case where robots have multiple optional locations as their targets is considered in this paper.
A Pseudo-Boolean (PB) constraint is a linear arithmetic constraint over Boolean variables. PB constraints are and widely used in declarative languages for expressing NP-hard search problems. While there are solvers for sets of PB constraints, there are also reasons to be interested in transforming these to propositional CNF formulas, and a number of methods for doing this have been reported. We introduce a new, two-step, method for transforming PB constraints to propositional CNF formulas. The first step re-writes each PB constraint as a conjunction of PB-Mod constraints, and the second transforms each PB-Mod constraint to CNF. The resulting CNF formulas are compact, and make effective use of unit propagation, in that unit propagation can derive facts from these CNF formulas which it cannot derive from the CNF formulas produced by other commonlyused transformation. We present a preliminary experimental evaluation of the method, using instances of the number partitioning problem as a benchmark set, which indicates that our method out-performs other transformations to CNF when the coefficients of the PB constraints are not small.
Learning representations from data is one of the fundamental problems of artificial intelligence and machine learning. Many different approaches exist for learning representations, but what constitutes a good representation is not yet well understood. In this work, we view the problem of representation learning as one of learning features (e.g., hidden units of neural networks) such that performance of the underlying base system continually improves. We study an important case where learning is done fully online (i.e., on an example-by-example basis) from an unending stream of data. In the presence of an unending stream of data, the computational cost of the learning element should not grow with time and cannot be much more than that of the performance element. Few methods can be used effectively in this case. We show that a search approach to representation learning can naturally fit with this setting. In this approach good representations are searched by generating different features and then testing them for utility. We develop new representation-search methods and show that the generate-and-test approach can be utilized in a simple and effective way for learning representations. Our methods are fully online and add only a small fraction to the overall computation. They constitute an important step toward effective and inexpensive solutions to representation learning problems.
of the keynote speech presented at the Tenth Symposium of Abstraction, Reformulation, and Approximation (SARA 2013).
In his 1997 paper on solving Rubik's Cube optimally using IDA* and pattern database heuristics (PDBs), Rich Korf conjectured that there was an inverse relationship between the size of a PDB and the amount of time required for IDA* to solve a problem instance on average. In the current paper, I examine the implications of this relationship, in particular how it limits the ability of abstraction-based heuristic methods, such as PDBs, to scale to larger problems. My overall conclusion is that abstraction will play an important, but auxiliary role in heuristic search systems of the future, in contrast to the primary role it played in Korf's Rubik's Cube work and in much work since.
