The Complexity Of The NP-Class

This paper presents a novel and straight formulation, and gives a complete insight towards the understanding of the complexity of the problems of the so called NP-Class. In particular, this paper focuses in the Searching of the Optimal Geometrical Structures and the Travelling Salesman Problems. The main results are the polynomial reduction procedure and the solution to the Noted Conjecture of the NP-Class

Decision Forest: A Nonparametric Approach to Modeling Irrational Choice

Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In this paper, we propose a new nonparametric choice model that relaxes this assumption and can model a wider range of customer behavior, such as decoy effects between products. In this model, each customer type is associated with a binary decision tree, which represents a decision process for making a purchase based on checking for the existence of specific products in the assortment. Together with a probability distribution over customer types, we show that the resulting model -- a decision forest -- is able to represent any customer choice model, including models that are inconsistent with weak rationality. We theoretically characterize the depth of the forest needed to fit a data set of historical assortments and prove that with high probability, a forest whose depth scales logarithmically in the number of assortments is sufficient to fit most data sets. We also propose two practical algorithms -- one based on column generation and one based on random sampling -- for estimating such models from data. Using synthetic data and real transaction data exhibiting non-rational behavior, we show that the model outperforms both rational and non-rational benchmark models in out-of-sample predictive ability.Comment: The paper is forthcoming in Management Science (accepted on July 25, 2021

SMT-Based Bounded Model Checking of Fixed-Point Digital Controllers

Digital controllers have several advantages with respect to their flexibility and design's simplicity. However, they are subject to problems that are not faced by analog controllers. In particular, these problems are related to the finite word-length implementation that might lead to overflows, limit cycles, and time constraints in fixed-point processors. This paper proposes a new method to detect design's errors in digital controllers using a state-of-the art bounded model checker based on satisfiability modulo theories. The experiments with digital controllers for a ball and beam plant demonstrate that the proposed method can be very effective in finding errors in digital controllers than other existing approaches based on traditional simulations tools

Rare event simulation for highly dependable systems with fast repairs

Stochastic model checking has been used recently to assess, among others, dependability measures for a variety of systems. However, the employed numerical methods, as, e.g., supported by model checking tools such as PRISM and MRMC, suffer from the state-space explosion problem. The main alternative is statistical model checking, which uses standard simulation, but this performs poorly when small probabilities need to be estimated. Therefore, we propose a method based on importance sampling to speed up the simulation process in cases where the failure probabilities are small due to the high speed of the system's repair units. This setting arises naturally in Markovian models of highly dependable systems. We show that our method compares favourably to standard simulation, to existing importance sampling techniques and to the numerical techniques of PRISM

Grey-box Modelling of a Household Refrigeration Unit Using Time Series Data in Application to Demand Side Management

This paper describes the application of stochastic grey-box modeling to identify electrical power consumption-to-temperature models of a domestic freezer using experimental measurements. The models are formulated using stochastic differential equations (SDEs), estimated by maximum likelihood estimation (MLE), validated through the model residuals analysis and cross-validated to detect model over-fitting. A nonlinear model based on the reversed Carnot cycle is also presented and included in the modeling performance analysis. As an application of the models, we apply model predictive control (MPC) to shift the electricity consumption of a freezer in demand response experiments, thereby addressing the model selection problem also from the application point of view and showing in an experimental context the ability of MPC to exploit the freezer as a demand side resource (DSR).Comment: Submitted to Sustainable Energy Grids and Networks (SEGAN). Accepted for publicatio