A constraint-based model represents knowledge about a domain by a set of constraints, which must be satisfied by solutions in that domain. These models may be used for reasoning, decision making and optimisation. Unfortunately, modelling itself is a hard and error-prone task that requires expertise. The automation of this process is often referred to as constraint acquisition and has been pursued for over 20 years. Methods typically learn constraints by testing candidates against a dataset of solutions and non-solutions, and often use some form of machine learning to decide which should be learned. However, few methods are robust under errors in the data, some cannot handle large sets of candidates, and most are computationally expensive even for small problems. We describe a statistical approach based on sequential analysis that is robust, fast and scalable to large biases. Its correctness depends on an assumption that does not always hold but which is, we show using Bayesian analysis , reasonable in practice.

Cloud computing has seen widespread adoption because it increases the productivity and efficiency of industries and allows for effective scalability of their business [1]. Guaranteeing performance levels is at the core of cloud services and requires huge computational resources, especially with the latest advances in technologies such as Artificial Intelligence and the Internet of Things [2]. Typically, customers subscribe to agreements where cloud providers ensure specific levels of reliability, availability and responsiveness to systems and applications and describe penalties if the service levels are not met. At the same time, massive computational resources are a cost for providers and have a significant environmental impact, which will increase in the future. It is estimated that the energy consumption of data centres (which host cloud services) will grow from 292 TWh in 2016 to 353 TWh in 2030 [3], and greenhouse gas emissions will increase over 14% in 2040, compared to a 1-1.6% increase in the 2007–2016 [4].

Providers of cloud computing systems need to manage resources carefully to meet the desired Quality of Service and reduce waste due to overallocation. An accurate prediction of future demand is crucial to allocate resources to service requests without excessive delays. Current state-of-the-art methods such as Long Short-Term Memory-based models make only point forecasts of demand without considering the uncertainty in their predictions. Forecasting a distribution would provide a more comprehensive picture and inform resource scheduler decisions. We investigate Bayesian Neural Networks and deep learning models to predict workload distribution and evaluate them on the time series forecasting of CPU and memory workload of 8 clusters on the Google Cloud data centre. Experiments show that the proposed models provide accurate demand prediction and better estimations of resource usage bounds, reducing overprediction and total predicted resources, while avoiding underprediction. These approaches have good runtime performance making them applicable for practitioners.

Constraint programming has been successfully used to model and solve problems in many domains, but its application can require significant expertise. This is sometimes called a modelling bottleneck, and the aim of constraint acquisition (CA) is to remove the bottleneck by automating constraint modelling. Current CA methods use forms of supervised learning: they learn constraints from a dataset of known solutions and (usually) non-solutions. Unfortunately this incurs a data collection bottleneck, as preparing such a dataset requires human effort. Removing this bottleneck might lead to the full automation of CA, for example allowing the use of data scraped from the Web without human intervention. In this paper we propose an unsupervised CA method inspired by data mining techniques, and show that it can learn several CA benchmarks. We also show that it has additional useful properties: it is robust under data errors, can learn from non-solutions only, and can learn over-constrained models.

Modeling a combinatorial problem is a hard and error-prone task requiring expertise.Constraint acquisition methods can automate this process by learning constraints from examples of solutions and (usually) non-solutions.We describe a new statistical approach based on sequential analysis that is orders of magnitude faster than existing methods, and gives accurate results on popular benchmarks.It is also robust in the sense that it can learn constraints correctly even when the data contain many errors.

One of the key unresolved challenges in Adjustable Robust Optimisation is how to deal with large discrete uncertainty sets. In this paper we present a technique for handling such sets based on symmetry breaking ideas from Constraint Programming. In earlier work we applied the technique to a pre-disaster planning problem modelled as a two-stage Stochastic Program, and we were able to solve exactly instances that were previously considered intractable and only had approximate solutions. In this paper we show that the technique can also be applied to an adjustable robust formulation that scales up to larger instances than the stochastic formulation. We also describe a new fast symmetry breaking heuristic that gives improved results.

We introduce statistical constraints, a declarative modelling tool that links statistics and constraint programming. We discuss two statistical constraints and some associated filtering algorithms. Finally, we illustrate applications to standard problems encountered in statistics and to a novel inspection scheduling problem in which the aim is to find inspection plans with desirable statistical properties.

In this paper we consider the problem of on-line stochastic ride-sharing and taxi-sharing with time windows. We study a scenario in which people needing a taxi, or a ride, assign their source and destination points plus other restrictions (such as earlier time to departure and maximum time to reach a destination), at the same time, there are taxis or drivers interested in providing a ride (also with departure and destination points, vehicle capacity and time restrictions). We model the time window restrictions as a soft constraint (a reasonable delay might be acceptable in a realistic scenario), and consider the problem as an on-line continual planning problem, in which additional ride requests may arrive while plans for previous ride-matching are being executed. Finally, such new requests may arrive at each time step with some probability. The aim is to maximize the shared trips while minimising the expected travel delay for each trip. In this paper we propose an on-line stochastic optimization planning approach in which instead of myopically optimising for the offered trips and requested trips that are known, incorporate information that partially describes the stochastic future into the model in order to improve the quality of the solution. We prove the effectiveness of the method in a real world scenario using a number of instances extracted from a travel survey in north-eastern Illinois (USA) conducted by the Chicago Metropolitan Agency for Planning.

Partial deduction systems must be guided by an unfolding strategy, telling them which atoms to unfold and when to stop unfolding. Online strategies exploit knowledge accumulated during the unfolding itself, for example in a goal stack, while offline strategies are fixed before unfolding begins. Online strategies are more powerful, but a major overhead for large programs is the analysis time spent on each atom, which increases as the knowledge grows. We describe an online strategy whose analysis time for each atom is independent of the amount of knowledge about that atom. This reduces transformation times for programs with large search spaces by an order of magnitude, while retaining the power of online analysis. Correctness, termination and nontriviality are shown.