Anastasia Paparrizou

New algorithms for max restricted path consistency

Max Restricted Path Consistency (maxRPC) is a local consistency for binary constraints that enforces a higher order of consistency than arc consistency. Despite the strong pruning that can be achieved, maxRPC is rarely used because existing maxRPC algorithms suffer from overheads and redundancies as they can repeatedly perform many constraint checks without triggering any value deletions. In this paper we propose and evaluate techniques that can boost the performance of maxRPC algorithms by eliminating many of these overheads and redundancies. These include the combined use of two data structures to avoid many redundant constraint checks, and the exploitation of residues to quickly verify the existence of supports. Based on these, we propose a number of closely related maxRPC algorithms. The first one, maxRPC3, has optimal O(end3) time complexity, displays good performance when used stand-alone, but is expensive to apply during search. The second one, maxRPC3rm, has O(en2d4) time complexity, but a restricted version with O(end4) complexity can be very efficient when used during search. The other algorithms are simple modifications of maxRPC3rm. All algorithms have O(ed) space complexity when used stand-alone. However, maxRPC3 has O(end) space complexity when used during search, while the others retain the O(ed) complexity. Experimental results demonstrate that the resulting methods constantly outperform previous algorithms for maxRPC, often by large margins, and constitute a viable alternative to arc consistency on some problem classes.

Evaluating Simple Fully Automated Heuristics for Adaptive Constraint Propagation

Despite the advancements in constraint propagation methods, most CP solvers still apply fixed predetermined propagators on each constraint of the problem. However, selecting the appropriate propagator for a constraint can be a difficult task that requires expertise. One way to overcome this is through the use of machine learning. A different approach uses heuristics to dynamically adapt the propagation method during search. The heuristics of this category proposed in [1] displayed promising results, but their evaluation and application suffered from two important drawbacks: They were only defined and tested on binary constraints and they required calibration of their input parameters. In this paper we follow this line of work by describing and evaluating simple, fully automated heuristics that are applicable on constraints of any arity. Experimental results from various problems show that the proposed heuristics can outperform a standard approach that applies a preselected propagator on each constraint resulting in an efficient and robust solver.

Improving the performance of maxRPC

Max Restricted Path Consistency (maxRPC) is a local consistency for binary constraints that can achieve considerably stronger pruning than arc consistency. However, existing maxRPC algorithms suffer from overheads and redundancies as they can repeatedly perform many constraint checks without triggering any value deletions. In this paper we propose techniques that can boost the performance of maxRPC algorithms. These include the combined use of two data structures to avoid many redundant constraint checks, and heuristics for the efficient ordering and execution of certain operations. Based on these, we propose two closely related maxRPC algorithms. The first one has optimal O(end3) time complexity, displays good performance when used stand-alone, but is expensive to apply during search. The second one has O(en2d4) time complexity, but a restricted version with O(end4) complexity can be very efficient when used during search. Both algorithms have O(ed) space complexity when used stand-alone. However, the first algorithm has O(end) space complexity when used during search, while the second retains the O(ed) complexity. Experimental results demonstrate that the resulting methods constantly outperform previous algorithms for maxRPC, often by large margins, and constitute a more than viable alternative to arc consistency.

Simulation of impacts of irrigated agriculture on income, employment and environment

This paper uses a multicriteria mathematical programming model to estimate the farmer’s utility function and simulate different scenarios and policies as well as to make alternative production plans. Application of this model was carried out in the irrigated region of the Xanthi Prefecture in Greece, as well as to three different farm clusters. The three farm clusters -small, medium and large sizes- were the result of a cluster analysis into a sample of farms of the region. In all these four cases, we considered three criteria for the estimation of the utility function; the maximization of total gross margin, the minimization of its variance and the minimization of labor. The estimated utility functions were used as objective functions of Linear or Quadratic (when the variance is considered) Programming models in order to find the optimum production plan of the total region and each farm size separately. These models were used to simulate the impacts on the production plan, income, employment and the environment due to a policy, which increases the price of irrigation water.

On Neighborhood Singleton Consistencies

CP solvers predominantly use arc consistency (AC) as the default propagation method. Many stronger consistencies, such as triangle consistencies (e.g. RPC and maxRPC) exist, but their use is limited despite results showing that they outperform AC on many problems. This is due to the intricacies involved in incorporating them into solvers. On the other hand, singleton consistencies such as SAC can be easily crafted into solvers but they are too expensive. We seek a balance between the efficiency of triangle consistencies and the ease of implementation of singleton ones. Using the recently proposed variant of SAC called Neighborhood SAC as basis, we propose a family of weaker singleton consistencies. We study them theoretically, comparing their pruning power to existing consistencies. We make a detailed experimental study using a very simple algorithm for their implementation. Results demonstrate that they outperform the existing propagation techniques, often by orders of magnitude, on a wide range of problems.

The inductive constraint programming loop

Constraint programming is used for a variety of real-world optimization problems, such as planning, scheduling, and resource allocation problems, all while we continuously gather vast amounts of data about these problems. Current constraint programming software doesn’t exploit such data to update schedules, resources, and plans. The authors propose a new framework that they call the inductive constraint programming loop. In this approach, data is gathered and analyzed systematically to dynamically revise and adapt constraints and optimization criteria. Inductive constraint programming aims to bridge the gap between the areas of data mining and machine learning on one hand and constraint programming on the other.

Strong local consistency algorithms for table constraints

Table constraints are important in constraint programming as they are present in many real problems from areas such as configuration and databases. As a result, numerous specialized algorithms that achieve generalized arc consistency (GAC) on table constraints have been proposed. Since these algorithms achieve GAC, they operate on one constraint at a time. In this paper we propose new filtering algorithms for positive table constraints that achieve stronger local consistency properties than GAC by exploiting intersections between constraints. The first algorithm, called maxRPWC+, is a domain filtering algorithm that is based on the local consistency maxRPWC and extends the GAC algorithm of Lecoutre and Szymanek (2006). The second algorithm extends the state-of-the-art STR-based algorithms to stronger relation filtering consistencies, i.e., consistencies that can remove tuples from constraints’ relations. Experimental results from benchmark problems demonstrate that the proposed algorithms are quite competitive with standard GAC algorithms like STR2 in some classes of problems with intersecting table constraints, being orders of magnitude faster in some cases.

Defining and Evaluating Heuristics for the Compilation of Constraint Networks

Several branching heuristics for compiling in a top-down fashion finite-domain constraint networks into multi-valued decision diagrams (MDD) or decomposable multi-valued decision graphs (MDDG) are empirically evaluated, using the cn2mddg compiler. This MDDG compiler has been enriched with various additional branching rules. These rules can be gathered into two families, the one consisting of heuristics for the satisfaction problem (which are suited to compiling networks into MDD representations) and the family of heuristics favoring decompositions (which are relevant when the MDDG language is targeted). Our empirical investigation on a large dataset shows the value of decomposability (targeting MDDG allows for compiling many more instances and leads to much smaller compiled representations). The well-known (Dom/Wdeg) heuristics appears as the best choice for compiling networks into MDD. When MDDG is the target, a new rule, based on a dynamic, yet parsimonious use of hypergraph partitioning for the decomposition purpose turns out to be the best option. As expected, the best heuristics for the satisfaction problem perform better than the best heuristics favoring decompositions when MDD is targeted, and the converse is the case when MDDG is targeted.

Collective Singleton-Based Consistency for Qualitative Constraint Networks

Partial singleton closure under weak composition, or partial singleton (weak) path-consistency for short, is essential for approximating satisfiability of qualitative constraints networks. Briefly put, partial singleton path-consistency ensures that each base relation of each of the constraints of a qualitative constraint network can define a singleton relation in the corresponding partial closure of that network under weak composition, or in its corresponding partially (weak) path-consistent subnetwork for short. In particular, partial singleton path-consistency has been shown to play a crucial role in tackling the minimal labeling problem of a qualitative constraint network, which is the problem of finding the strongest implied constraints of that network. In this paper, we propose a stronger local consistency that couples partial singleton path-consistency with the idea of collectively deleting certain unfeasible base relations by exploiting singleton checks. We then propose an efficient algorithm for enforcing this consistency that, given a qualitative constraint network, performs fewer constraint checks than the respective algorithm for enforcing partial singleton path-consistency in that network. We formally prove certain properties of our new local consistency, and motivate its usefulness through demonstrative examples and a preliminary experimental evaluation with qualitative constraint networks of Interval Algebra.

Complexity Results in Optimistic/Pessimistic Preference Reasoning

Preference reasoning is a central problem in decision support. There exist various ways to interpret a set of qualitative preferences. Conditional preference logics allow to deal with semantics such as optimistic, pessimistic, strong or not. In this paper, we study the complexity of the main problems in optimistic/pessimistic preference logic: undominated, consistency and dominance. We show that they are all NP-hard in general, with some becoming polynomial under specific semantics. Our second contribution is to show that the dominance problem, which has an online component in its definition, is compilable to polynomial time.