CONJURE: automatic generation of constraint models from problem specifications

Funding: Engineering and Physical Sciences Research Council (EP/V027182/1, EP/P015638/1), Royal Society (URF/R/180015).When solving a combinatorial problem, the formulation or model of the problem is critical tothe efficiency of the solver. Automating the modelling process has long been of interest because of the expertise and time required to produce an effective model of a given problem. We describe a method to automatically produce constraint models from a problem specification written in the abstract constraint specification language Essence. Our approach is to incrementally refine the specification into a concrete model by applying a chosen refinement rule at each step. Any nontrivial specification may be refined in multiple ways, creating a space of models to choose from. The handling of symmetries is a particularly important aspect of automated modelling. Many combinatorial optimisation problems contain symmetry, which can lead to redundant search. If a partial assignment is shown to be invalid, we are wasting time if we ever consider a symmetric equivalent of it. A particularly important class of symmetries are those introduced by the constraint modelling process: modelling symmetries. We show how modelling symmetries may be broken automatically as they enter a model during refinement, obviating the need for an expensive symmetry detection step following model formulation. Our approach is implemented in a system called Conjure. We compare the models producedby Conjure to constraint models from the literature that are known to be effective. Our empirical results confirm that Conjure can reproduce successfully the kernels of the constraint models of 42 benchmark problems found in the literature.Publisher PDFPeer reviewe

Learning for Optimization with Virtual Savant

Optimization problems arising in multiple fields of study demand efficient algorithms that can exploit modern parallel computing platforms. The remarkable development of machine learning offers an opportunity to incorporate learning into optimization algorithms to efficiently solve large and complex problems. This thesis explores Virtual Savant, a paradigm that combines machine learning and parallel computing to solve optimization problems. Virtual Savant is inspired in the Savant Syndrome, a mental condition where patients excel at a specific ability far above the average. In analogy to the Savant Syndrome, Virtual Savant extracts patterns from previously-solved instances to learn how to solve a given optimization problem in a massively-parallel fashion. In this thesis, Virtual Savant is applied to three optimization problems related to software engineering, task scheduling, and public transportation. The efficacy of Virtual Savant is evaluated in different computing platforms and the experimental results are compared against exact and approximate solutions for both synthetic and realistic instances of the studied problems. Results show that Virtual Savant can find accurate solutions, effectively scale in the problem dimension, and take advantage of the availability of multiple computing resources.Los problemas de optimización que surgen en múltiples campos de estudio demandan algoritmos eficientes que puedan explotar las plataformas modernas de computación paralela. El notable desarrollo del aprendizaje automático ofrece la oportunidad de incorporar el aprendizaje en algoritmos de optimización para resolver problemas complejos y de grandes dimensiones de manera eficiente. Esta tesis explora Savant Virtual, un paradigma que combina aprendizaje automático y computación paralela para resolver problemas de optimización. Savant Virtual está inspirado en el Sı́ndrome de Savant, una condición mental en la que los pacientes se destacan en una habilidad especı́fica muy por encima del promedio. En analogı́a con el sı́ndrome de Savant, Savant Virtual extrae patrones de instancias previamente resueltas para aprender a resolver un determinado problema de optimización de forma masivamente paralela. En esta tesis, Savant Virtual se aplica a tres problemas de optimización relacionados con la ingenierı́a de software, la planificación de tareas y el transporte público. La eficacia de Savant Virtual se evalúa en diferentes plataformas informáticas y los resultados se comparan con soluciones exactas y aproximadas para instancias tanto sintéticas como realistas de los problemas estudiados. Los resultados muestran que Savant Virtual puede encontrar soluciones precisas, escalar eficazmente en la dimensión del problema y aprovechar la disponibilidad de múltiples recursos de cómputo.Fundación Carolina Agencia Nacional de Investigación e Innovación (ANII, Uruguay) Universidad de Cádiz Universidad de la Repúblic

Knowledge Refinement via Rule Selection

In several different applications, including data transformation and entity resolution, rules are used to capture aspects of knowledge about the application at hand. Often, a large set of such rules is generated automatically or semi-automatically, and the challenge is to refine the encapsulated knowledge by selecting a subset of rules based on the expected operational behavior of the rules on available data. In this paper, we carry out a systematic complexity-theoretic investigation of the following rule selection problem: given a set of rules specified by Horn formulas, and a pair of an input database and an output database, find a subset of the rules that minimizes the total error, that is, the number of false positive and false negative errors arising from the selected rules. We first establish computational hardness results for the decision problems underlying this minimization problem, as well as upper and lower bounds for its approximability. We then investigate a bi-objective optimization version of the rule selection problem in which both the total error and the size of the selected rules are taken into account. We show that testing for membership in the Pareto front of this bi-objective optimization problem is DP-complete. Finally, we show that a similar DP-completeness result holds for a bi-level optimization version of the rule selection problem, where one minimizes first the total error and then the size

Faster Predict-and-Optimize with Davis-Yin Splitting

In many applications, a combinatorial problem must be repeatedly solved with similar, but distinct parameters. Yet, the parameters $w$ are not directly observed; only contextual data $d$ that correlates with $w$ is available. It is tempting to use a neural network to predict $w$ given $d$, but training such a model requires reconciling the discrete nature of combinatorial optimization with the gradient-based frameworks used to train neural networks. When the problem in question is an Integer Linear Program (ILP), one approach to overcoming this issue is to consider a continuous relaxation of the combinatorial problem. While existing methods utilizing this approach have shown to be highly effective on small problems (10-100 variables), they do not scale well to large problems. In this work, we draw on ideas from modern convex optimization to design a network and training scheme which scales effortlessly to problems with thousands of variables

Disjunctive Inequalities: Applications and Extensions

A general optimization problem can be expressed in the form min{cx: x ∈ S}, (1) where x ∈ R n is the vector of decision variables, c ∈ R n is a linear objective function and S ⊂ R n is the set of feasible solutions of (1). Because S is generall

Fast approximation schemes for multi-criteria combinatorial optimization

Cover title.Includes bibliographical references (p. 38-44).by Hershel M. Safer, James B. Orlin