Automatically exploiting high-level problem structure in local-search

Constraint Programming is the study of modelling and solving complex combinatorial problems. Systematic-search and local-search are both well-researched approaches to solving constraint problems. Systematic-search exhaustively explores the entire search space and can be used to guarantee optimality, prove infeasibility or enumerate all possible solutions. Conversely, local-search is a heuristic-based approach to solving constraint problems. Often used in industrial applications, local-search is used to discover high-quality solutions quickly, usually sacrificing the ability to cover the entire search space. For this reason, it is preferred in applications where the scale of the problems being solved are beyond what can be feasibly searched using systematic methods. This work investigates methods of using information derived from high-level specifications of problems to augment the performance and scalability of local-search systems. Typically, abstract high-level constraint specifications or models are refined into lowlevel representations suitable for input to a constraint solver, erasing any knowledge of the specifications' high-level structures. We propose that whilst these lower-level models are equivalent in their description of the problems being solved, the original high-level specification, if retained, can be used to augment both the performance and scalability of local-search systems. In doing this, two approaches have been implemented and benchmarked. In the first approach, Structured Neighbourhood Search (SNS), a systematic solver is adapted to support declarative large neighbourhood search, using the high-level types such as sets, sequences and partitions in the original problem specification to automatically construct higher-quality, structured neighbourhoods. Our experiments demonstrate the performance of SNS when applied to structured problems. In the second approach, a novel constraint-based local-search solver is designed to operate on the high-level structures without refining these structures into lower-level representations. The new solver Athanor can directly instantiate and operate on the types in the Essence abstract specification language, supporting arbitrarily nested types such as sets of partitions, multi-sets of sequences and so on. Athanor retains the performance of SNS but boasts a unique benefit; on some classes of problems, the high-level solver is shown to be able to efficiently operate on instances that are too large for low-level solvers to even begin search

Athanor: High-Level Local Search Over Abstract Constraint Specifications in Essence

This paper presents Athanor, a novel local search solver that operates on abstract constraint specifications of combinatorial problems in the Essence language. It is unique in that it operates directly on the high level, nested types in Essence, such as set of partitions or multiset of sequences, without refining such types into low level representations. This approach has two main advantages. First, the structure present in the high level types allows high quality neighbourhoods for local search to be automatically derived. Second, it allows Athanor to scale much better than solvers that operate on the equivalent, but much larger, low-level representations. The paper details how Athanor operates, covering incremental evaluation, dynamic unrolling of quantified expressions and neighbourhood construction. A series of case studies show the performance of Athanor, benchmarked against several local search solvers on a range of problem classes

Portfolio Approaches in Constraint Programming

Recent research has shown that the performance of a single, arbitrarily efficient algorithm can be significantly outperformed by using a portfolio of —possibly on-average slower— algorithms. Within the Constraint Programming (CP) context, a portfolio solver can be seen as a particular constraint solver that exploits the synergy between the constituent solvers of its portfolio for predicting which is (or which are) the best solver(s) to run for solving a new, unseen instance. In this thesis we examine the benefits of portfolio solvers in CP. Despite portfolio approaches have been extensively studied for Boolean Satisfiability (SAT) problems, in the more general CP field these techniques have been only marginally studied and used. We conducted this work through the investigation, the analysis and the construction of several portfolio approaches for solving both satisfaction and optimization problems. We focused in particular on sequential approaches, i.e., single-threaded portfolio solvers always running on the same core. We started from a first empirical evaluation on portfolio approaches for solving Constraint Satisfaction Problems (CSPs), and then we improved on it by introducing new data, solvers, features, algorithms, and tools. Afterwards, we addressed the more general Constraint Optimization Problems (COPs) by implementing and testing a number of models for dealing with COP portfolio solvers. Finally, we have come full circle by developing sunny-cp: a sequential CP portfolio solver that turned out to be competitive also in the MiniZinc Challenge, the reference competition for CP solvers

High-level efficient constraint dominance programming for pattern mining problems

Pattern mining is a sub-field of data mining that focuses on discovering patterns in data to extract knowledge. There are various techniques to identify different types of patterns in a dataset. Constraint-based mining is a well-known approach to this where additional constraints are introduced to retrieve only interesting patterns. However, in these systems, there are limitations on imposing complex constraints. Constraint programming is a declarative methodology where the problem is modelled using constraints. Generic solvers can operate on a model to find the solutions. Constraint programming has been shown to be a well-suited and generic framework for various pattern mining problems with a selection of constraints and their combinations. However, a system that handles arbitrary constraints in a generic way has been missing in this field. In this thesis, we propose a declarative framework where the pattern mining models can be represented in high-level constraint specifications with arbitrary additional constraints. These models can be efficiently solved using underlying optimisations. The first contribution of this thesis is to determine the key aspects of solving pattern mining problems by creating an ad-hoc solver system. We investigate this further and create Constraint Dominance Programming (CDP) to be able to capture certain behaviours of pattern mining problems in an abstract way. To that end, we integrate CDP into the high-level \essence pipeline. Early empirical evaluation presents that CDP is already competitive with current existing techniques. The second contribution of this thesis is to exploit an additional behaviour, the incomparability, in pattern mining problems. By including the incomparability condition to CDP, we create CDP+I, a more explicit and even more efficient framework to represent these problems. We also prototype an automated system to deduct the optimal incomparability information for a given modelled problem. The third contribution of this thesis is to focus on the underlying solving of CDP+I to bring further efficiency. By creating the Solver Interactive Interface (SII) on SAT and SMT back-ends, we highly optimise not only CDP+I but any iterative modelling and solving, such as optimisation problems. The final contribution of this thesis is to investigate creating an automated configuration selection system to determine the best performing solving methodologies of CDP+I and introduce a portfolio of configurations that can perform better than any single best solver. In summary, this thesis presents a highly efficient, high-level declarative framework to tackle pattern mining problems

Actes de la conférence BDA 2014 : Gestion de données - principes, technologies et applications

International audienceActes de la conférence BDA 2014 Conférence soutenue par l'Université Joseph Fourier, Grenoble INP, le CNRS et le laboratoire LIG. Site de la conférence : http://bda2014.imag.fr Actes en ligne : https://hal.inria.fr/BDA201