Automatically generating streamlined constraint models with ESSENCE and CONJURE

Streamlined constraint reasoning is the addition of uninferred constraints to a constraint model to reduce the search space, while retaining at least one solution. Previously, effective streamlined models have been constructed by hand, requiring an expert to examine closely solutions to small instances of a problem class and identify regularities. We present a system that automatically generates many conjectured regularities for a given Essence specification of a problem class by examining the domains of decision variables present in the problem specification. These conjectures are evaluated independently and in conjunction with one another on a set of instances from the specified class via an automated modelling tool-chain comprising of Conjure, Savile Row and Minion. Once the system has identified effective conjectures they are used to generate streamlined models that allow instances of much larger scale to be solved. Our results demonstrate good models can be identified for problems in combinatorial design, Ramsey theory, graph theory and group theory - often resulting in order of magnitude speed-ups.Postprin

Streamlined constraint reasoning : an automated approach from high level constraint specifications

Constraint Programming (CP) is a powerful technique for solving large-scale combinatorial (optimisation) problems. Solving a problem proceeds in two distinct phases: modelling and solving. Effective modelling has a huge impact on the performance of the solving process. Even with the advance of modern automated modelling tools, search spaces involved can be so vast that problems can still be difficult to solve. To further constrain the model a more aggressive step that can be taken is the addition of streamliner constraints, which are not guaranteed to be sound but are designed to focus effort on a highly restricted but promising portion of the search space. Previously, producing effective streamlined models was a manual, difficult and time-consuming task. This thesis presents a completely automated process to the generation, search and selection of streamliner portfolios to produce a substantial reduction in search effort across a diverse range of problems. First, we propose a method for the generation and evaluation of streamliner conjectures automatically from the type structure present in an Essence specification. Second, the possible streamliner combinations are structured into a lattice and a multi-objective search method for searching the lattice of combinations and building a portfolio of streamliner combinations is defined. Third, the problem of "Streamliner Selection" is introduced which deals with selecting from the portfolio an effective streamliner for an unseen instance. The work is evaluated by presenting two sets of experiments on a variety of problem classes. Lastly, we explore the effect of model selection in the context of streamlined specifications and discuss the process of streamlining for Constrained Optimization Problems."This work was supported by: EPSRC funding award EP/N509759/1" -- Fundin

Automatic generation and selection of streamlined constraint models via Monte Carlo search on a model lattice

Funding: EPSRC EP/P015638/1.Streamlined constraint reasoning is the addition of uninferred constraints to a constraint model to reduce the search space, while retaining at least one solution. Previously it has been established that it is possible to generate streamliners automatically from abstract constraint specifications in Essence and that effective combinations of streamliners can allow instances of much larger scale to be solved. A shortcoming of the previous approach was the crude exploration of the power set of all combinations using depth and breadth first search. We present a new approach based on Monte Carlo search over the lattice of streamlined models, which efficiently identifies effective streamliner combinations.Postprin

Hybrid SAT-Based Consistency Checking Algorithms for Simple Temporal Networks with Decisions

A Simple Temporal Network (STN) consists of time points modeling temporal events and constraints modeling the minimal and maximal temporal distance between them. A Simple Temporal Network with Decisions (STND) extends an STN by adding decision time points to model temporal plans with decisions. A decision time point is a special kind of time point that once executed allows for deciding a truth value for an associated Boolean proposition. Furthermore, STNDs label time points and constraints by conjunctions of literals saying for which scenarios (i.e., complete truth value assignments to the propositions) they are relevant. Thus, an STND models a family of STNs each obtained as a projection of the initial STND onto a scenario. An STND is consistent if there exists a consistent scenario (i.e., a scenario such that the corresponding STN projection is consistent). Recently, a hybrid SAT-based consistency checking algorithm (HSCC) was proposed to check the consistency of an STND. Unfortunately, that approach lacks experimental evaluation and does not allow for the synthesis of all consistent scenarios. In this paper, we propose an incremental HSCC algorithm for STNDs that (i) is faster than the previous one and (ii) allows for the synthesis of all consistent scenarios and related early execution schedules (offline temporal planning). Then, we carry out an experimental evaluation with KAPPA, a tool that we developed for STNDs. Finally, we prove that STNDs and disjunctive temporal networks (DTNs) are equivalent

A Streamlined Model of Conditional Simple Temporal Networks - Semantics and Equivalence Results

A Conditional Simple Temporal Network (CSTN) augments a Simple Temporal Network to include a new kind of time-points, called observation time-points. The execution of an observation time-point generates information in real time, specifically, the truth value of a propositional letter. In addition, time-points and temporal constraints may be labeled by conjunctions of (positive or negative) propositional letters. A CSTN is called dynamically consistent (DC) if there exists a dynamic strategy for executing its time-points such that no matter how the observations turn out during execution, the time-points whose labels are consistent with those observations have all been executed, and the constraints whose labels are consistent with those observations have all been satisfied. The strategy is dynamic in that its execution decisions may react to observations. The original formulation of CSTNs included propositional labels only on time-points, but the DC-checking algorithm was impractical because it was based on a conversion of the semantic constraints into an exponentially-sized Disjunctive Temporal Network. Later work added propositional labels to temporal constraints, and yielded a sound-and-complete propagation-based DC-checking algorithm, empirically demonstrated to be practical across a variety of CSTNs. This paper introduces a streamlined version of a CSTN in which propositional labels may appear on constraints, but not on time-points. This change simplifies the definition of the DC property, as well as the propagation rules for the DC-checking algorithm. It also simplifies the proofs of the soundness and completeness of those rules. This paper provides two translations from traditional CSTNs to streamlined CSTNs. Each translation preserves the DC property and, for any DC network, ensures that any dynamic execution strategy for that network can be extended to a strategy for its streamlined counterpart. Finally, this paper presents an empirical comparison of two versions of the DC-checking algorithm: the original version and a simplified version for streamlined CSTNs. The comparison is based on CSTN benchmarks from earlier work. For small-sized CSTNs, the original version shows the best performance, but the performance difference between the two versions decreases as the number of time-points in the CSTN increases. We conclude that the simplified algorithm is a practical alternative for checking the dynamic consistency of CSTNs

Bit-Vector Model Counting using Statistical Estimation

Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity constraints (XOR streamlining) and then checking satisfiability is an effective approximation technique, but it requires a prior hypothesis about the model count to produce useful results. We propose an approach inspired by statistical estimation to continually refine a probabilistic estimate of the model count for a formula, so that each XOR-streamlined query yields as much information as possible. We implement this approach, with an approximate probability model, as a wrapper around an off-the-shelf SMT solver or SAT solver. Experimental results show that the implementation is faster than the most similar previous approaches which used simpler refinement strategies. The technique also lets us model count formulas over floating-point constraints, which we demonstrate with an application to a vulnerability in differential privacy mechanisms