Steven Prestwich

Andrea Rossi, Andrea Visentin, Diego Carraro et al.

Predicting future resource demand in Cloud Computing is essential for optimizing the trade-off between serving customers' requests efficiently and minimizing the provisioning cost. Modelling prediction uncertainty is also desirable to better inform the resource decision-making process, but research in this field is under-investigated. In this paper, we propose univariate and bivariate Bayesian deep learning models that provide predictions of future workload demand and its uncertainty. We run extensive experiments on Google and Alibaba clusters, where we first train our models with datasets from different cloud providers and compare them with LSTM-based baselines. Results show that modelling the uncertainty of predictions has a positive impact on performance, especially on service level metrics, because uncertainty quantification can be tailored to desired target service levels that are critical in cloud applications. Moreover, we investigate whether our models benefit transfer learning capabilities across different domains, i.e. dataset distributions. Experiments on the same workload datasets reveal that acceptable transfer learning performance can be achieved within the same provider (because distributions are more similar). Also, domain knowledge does not transfer when the source and target domains are very different (e.g. from different providers), but this performance degradation can be mitigated by increasing the training set size of the source domain.

Ciaran O'Connor, Joseph Collins, Steven Prestwich et al.

Short-term electricity markets are becoming more relevant due to less-predictable renewable energy sources, attracting considerable attention from the industry. The balancing market is the closest to real-time and the most volatile among them. Its price forecasting literature is limited, inconsistent and outdated, with few deep learning attempts and no public dataset. This work applies to the Irish balancing market a variety of price prediction techniques proven successful in the widely studied day-ahead market. We compare statistical, machine learning, and deep learning models using a framework that investigates the impact of different training sizes. The framework defines hyperparameters and calibration settings; the dataset and models are made public to ensure reproducibility and to be used as benchmarks for future works. An extensive numerical study shows that well-performing models in the day-ahead market do not perform well in the balancing one, highlighting that these markets are fundamentally different constructs. The best model is LEAR, a statistical approach based on LASSO, which outperforms more complex and computationally demanding approaches.

Ciaran O'Connor, Mohamed Bahloul, Roberto Rossi et al.

The integration of renewable energy into electricity markets poses significant challenges to price stability and increases the complexity of market operations. Accurate and reliable electricity price forecasting is crucial for effective market participation, where price dynamics can be significantly more challenging to predict. Probabilistic forecasting, through prediction intervals, efficiently quantifies the inherent uncertainties in electricity prices, supporting better decision-making for market participants. This study explores the enhancement of probabilistic price prediction using Conformal Prediction (CP) techniques, specifically Ensemble Batch Prediction Intervals and Sequential Predictive Conformal Inference. These methods provide precise and reliable prediction intervals, outperforming traditional models in validity metrics. We propose an ensemble approach that combines the efficiency of quantile regression models with the robust coverage properties of time series adapted CP techniques. This ensemble delivers both narrow prediction intervals and high coverage, leading to more reliable and accurate forecasts. We further evaluate the practical implications of CP techniques through a simulated trading algorithm applied to a battery storage system. The ensemble approach demonstrates improved financial returns in energy trading in both the Day-Ahead and Balancing Markets, highlighting its practical benefits for market participants.

Dimos Tsouros, Senne Berden, Steven Prestwich et al.

Constraint Acquisition (CA) aims to widen the use of constraint programming by assisting users in the modeling process. However, most CA methods suffer from a significant drawback: they learn a single set of individual constraints for a specific problem instance, but cannot generalize these constraints to the parameterized constraint specifications of the problem. In this paper, we address this limitation by proposing GenCon, a novel approach to learn parameterized constraint models capable of modeling varying instances of the same problem. To achieve this generalization, we make use of statistical learning techniques at the level of individual constraints. Specifically, we propose to train a classifier to predict, for any possible constraint and parameterization, whether the constraint belongs to the problem. We then show how, for some classes of classifiers, we can extract decision rules to construct interpretable constraint specifications. This enables the generation of ground constraints for any parameter instantiation. Additionally, we present a generate-and-test approach that can be used with any classifier, to generate the ground constraints on the fly. Our empirical results demonstrate that our approach achieves high accuracy and is robust to noise in the input instances.

Ciaran O'Connor, Mohamed Bahloul, Steven Prestwich et al.

Electricity price forecasting has become a critical tool for decision-making in energy markets, particularly as the increasing penetration of renewable energy introduces greater volatility and uncertainty. Historically, research in this field has been dominated by point forecasting methods, which provide single-value predictions but fail to quantify uncertainty. However, as power markets evolve due to renewable integration, smart grids, and regulatory changes, the need for probabilistic forecasting has become more pronounced, offering a more comprehensive approach to risk assessment and market participation. This paper presents a review of probabilistic forecasting methods, tracing their evolution from Bayesian and distribution based approaches, through quantile regression techniques, to recent developments in conformal prediction. Particular emphasis is placed on advancements in probabilistic forecasting, including validity-focused methods which address key limitations in uncertainty estimation. Additionally, this review extends beyond the Day-Ahead Market to include the Intra-Day and Balancing Markets, where forecasting challenges are intensified by higher temporal granularity and real-time operational constraints. We examine state of the art methodologies, key evaluation metrics, and ongoing challenges, such as forecast validity, model selection, and the absence of standardised benchmarks, providing researchers and practitioners with a comprehensive and timely resource for navigating the complexities of modern electricity markets.

Ciaran O'Connor, Joseph Collins, Steven Prestwich et al.

Efficiently integrating renewable resources into electricity markets is vital for addressing the challenges of matching real-time supply and demand while reducing the significant energy wastage resulting from curtailments. To address this challenge effectively, the incorporation of storage devices can enhance the reliability and efficiency of the grid, improving market liquidity and reducing price volatility. In short-term electricity markets, participants navigate numerous options, each presenting unique challenges and opportunities, underscoring the critical role of the trading strategy in maximizing profits. This study delves into the optimization of day-ahead and balancing market trading, leveraging quantile-based forecasts. Employing three trading approaches with practical constraints, our research enhances forecast assessment, increases trading frequency, and employs flexible timestamp orders. Our findings underscore the profit potential of simultaneous participation in both day-ahead and balancing markets, especially with larger battery storage systems; despite increased costs and narrower profit margins associated with higher-volume trading, the implementation of high-frequency strategies plays a significant role in maximizing profits and addressing market challenges. Finally, we modelled four commercial battery storage systems and evaluated their economic viability through a scenario analysis, with larger batteries showing a shorter return on investment.

Mervyn O'Luing, Steven Prestwich, S. Armagan Tarim

In this study we propose a hybrid estimation of distribution algorithm (HEDA) to solve the joint stratification and sample allocation problem. This is a complex problem in which each the quality of each stratification from the set of all possible stratifications is measured its optimal sample allocation. EDAs are stochastic black-box optimization algorithms which can be used to estimate, build and sample probability models in the search for an optimal stratification. In this paper we enhance the exploitation properties of the EDA by adding a simulated annealing algorithm to make it a hybrid EDA. Results of empirical comparisons for atomic and continuous strata show that the HEDA attains the bests results found so far when compared to benchmark tests on the same data using a grouping genetic algorithm, simulated annealing algorithm or hill-climbing algorithm. However, the execution times and total execution are, in general, higher for the HEDA.

Mervyn O'Luing, Steven Prestwich, S. Armagan Tarim

In this paper we combine the k-means and/or k-means type algorithms with a hill climbing algorithm in stages to solve the joint stratification and sample allocation problem. This is a combinatorial optimisation problem in which we search for the optimal stratification from the set of all possible stratifications of basic strata. Each stratification being a solution the quality of which is measured by its cost. This problem is intractable for larger sets. Furthermore evaluating the cost of each solution is expensive. A number of heuristic algorithms have already been developed to solve this problem with the aim of finding acceptable solutions in reasonable computation times. However, the heuristics for these algorithms need to be trained in order to optimise performance in each instance. We compare the above multi-stage combination of algorithms with three recent algorithms and report the solution costs, evaluation times and training times. The multi-stage combinations generally compare well with the recent algorithms both in the case of atomic and continuous strata and provide the survey designer with a greater choice of algorithms to choose from.

Mervyn O'Luing, Steven Prestwich, S. Armagan Tarim

This study combines simulated annealing with delta evaluation to solve the joint stratification and sample allocation problem. In this problem, atomic strata are partitioned into mutually exclusive and collectively exhaustive strata. Each partition of atomic strata is a possible solution to the stratification problem, the quality of which is measured by its cost. The Bell number of possible solutions is enormous, for even a moderate number of atomic strata, and an additional layer of complexity is added with the evaluation time of each solution. Many larger scale combinatorial optimisation problems cannot be solved to optimality, because the search for an optimum solution requires a prohibitive amount of computation time. A number of local search heuristic algorithms have been designed for this problem but these can become trapped in local minima preventing any further improvements. We add, to the existing suite of local search algorithms, a simulated annealing algorithm that allows for an escape from local minima and uses delta evaluation to exploit the similarity between consecutive solutions, and thereby reduces the evaluation time. We compared the simulated annealing algorithm with two recent algorithms. In both cases, the simulated annealing algorithm attained a solution of comparable quality in considerably less computation time.

John Mitro, Derek Bridge, Steven Prestwich

We propose denoising dictionary learning (DDL), a simple yet effective technique as a protection measure against adversarial perturbations. We examined denoising dictionary learning on MNIST and CIFAR10 perturbed under two different perturbation techniques, fast gradient sign (FGSM) and jacobian saliency maps (JSMA). We evaluated it against five different deep neural networks (DNN) representing the building blocks of most recent architectures indicating a successive progression of model complexity of each other. We show that each model tends to capture different representations based on their architecture. For each model we recorded its accuracy both on the perturbed test data previously misclassified with high confidence and on the denoised one after the reconstruction using dictionary learning. The reconstruction quality of each data point is assessed by means of PSNR (Peak Signal to Noise Ratio) and Structure Similarity Index (SSI). We show that after applying (DDL) the reconstruction of the original data point from a noisy

Roberto Rossi, Özgür Akgün, Steven Prestwich et al.

In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant counting and matrix constraints and associated decompositions, some of which novel, that are instrumental in the design of statistical constraints. Second, we introduce a selection of novel statistical constraints and associated decompositions, which constitute a self-contained toolbox that can be used to tackle a wide range of problems typically encountered by statisticians. Finally, we deploy these statistical constraints to a wide range of application areas drawn from classical statistics and we contrast our framework against established practices.

Steven Prestwich, Roberto Rossi, Armagan Tarim

Stochastic Constraint Programming (SCP) is an extension of Constraint Programming (CP) used for modelling and solving problems involving constraints and uncertainty. SCP inherits excellent modelling abilities and filtering algorithms from CP, but so far it has not been applied to large problems. Reinforcement Learning (RL) extends Dynamic Programming to large stochastic problems, but is problem-specific and has no generic solvers. We propose a hybrid combining the scalability of RL with the modelling and constraint filtering methods of CP. We implement a prototype in a CP system and demonstrate its usefulness on SCP problems.

Roberto Rossi, Özgür Akgün, Steven Prestwich et al.

We introduce the BIN_COUNTS constraint, which deals with the problem of counting the number of decision variables in a set which are assigned values that lie in given bins. We illustrate a decomposition and a filtering algorithm that achieves generalised arc consistency. We contrast the filtering power of these two approaches and we discuss a number of applications. We show that BIN_COUNTS can be employed to develop a decomposition for the $χ^2$ test constraint, a new statistical constraint that we introduce in this work. We also show how this new constraint can be employed in the context of the Balanced Academic Curriculum Problem and of the Balanced Nursing Workload Problem. For both these problems we carry out numerical studies involving our reformulations. Finally, we present a further application of the $χ^2$ test constraint in the context of confidence interval analysis.

Roberto Rossi, Steven Prestwich, S. Armagan Tarim

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.

Roberto Rossi, Steven Prestwich, S. Armagan Tarim et al.

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach can produce an upper and a lower bound for the associated cost. We apply our novel approach to three demand distribution in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist - e.g. based on maximum likelihood estimators - or Bayesian strategies.

Steven Prestwich

A recently identified problem is that of finding an optimal investment plan for a transportation network, given that a disaster such as an earthquake may destroy links in the network. The aim is to strengthen key links to preserve the expected network connectivity. A network based on the Istanbul highway system has thirty links and therefore a billion scenarios, but it has been estimated that sampling a million scenarios gives reasonable accuracy. In this paper we use symmetry reasoning to reduce the number of scenarios to a much smaller number, making sampling unnecessary. This result can be used to facilitate metaheuristic and exact approaches to the problem.